sign in sign up
<<
Home , Harris Mayer, John Nuckolls, Julius Ashkin, Marshall Rosenbluth, Sylvanus Thayer Award, Yuri Babayev

Centennial Symposium Modern and the Scientific Legacy of Edward Teller

7154 tp.indd 1 3/25/10 1:50:19 PM This page intentionally left blank Edward Teller Centennial Symposium Modern Physics and the Scientific Legacy of Edward Teller

Livermore, CA, USA 28 May 2008

Editors Stephen B. Libby Lawrence Livermore National Laboratory, USA Karl A. van Bibber Lawrence Livermore National Laboratory, USA Naval Postgraduate School, USA

World Scientific

N E W J E R S E Y • LONDON • SINGAPORE • BEIJING • SHANGHAI • H O N G K O N G • TAIPEI • CHENNAI Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE

British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library.

PROCEEDINGS OF EDWARD TELLER CENTENNIAL SYMPOSIUM Copyright © 2010 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.

ISBN-13 978-981-283-799-8 ISBN-10 981-283-799-X

Printed in Singapore.

Julia - Edward Teller Centennial.pmd 1 11/19/2009, 11:27 AM v

EDWARD TELLER’S POEM ON THEORY AND EXPERIMENT ON WHITE HOUSE STATIONERY∗

∗Date unknown. Discovered by Paul Teller in the back of his father’s desk. Sung by George Schultz, to the tune of a Cole Porter melody, (poem attributed to Teller) at a banquet in 1973.

This page intentionally left blank vii

PREFACE

With the death of Edward Teller in 2003, the world lost one of the last giants of twentieth century physics. Of all the larger-than-life theoretical physicists who developed and applied the ‘new physics’ in the revolutionary years 1925–40, he was survived only by and John Wheeler; now they too are gone. For Teller’s many friends, colleagues and students, it was impossible not to commemorate his centenary, particularly for those of us who have had the privilege of being part of his proudest legacy, the Lawrence Livermore National Laboratory. We decided that a fitting tribute to his memory would be a celebration of his science. Science was his lifelong passion and importantly, we wanted to focus on Teller’s remarkable achievements in basic and applied science, which, in the past, have often been overshadowed by Teller’s broader impact on national defense. From the outset, we were aware that arranging the one-day symposium would pose a challenge. Teller’s significant contributions to science and education were numerous and very wide-ranging, and we wanted speakers who were not only world-leaders in the topics he had pioneered or enriched, but also knew how to capture and present the ideas in a way that reflected Teller’s own approach to science: beginning from basics and always grounded in physical phenomena. In this regard, we feel that we succeeded with the ten lectures that were presented at the symposium. Held on May 28th, 2008 in the Bankhead Theatre in Livermore, California, the symposium was attended by over 200 guests from around the world. Focusing on snapshots of Teller’s key achievements in science, their still growing impact, as well as Teller’s legacy in scientific education, the speakers illuminated his contributions in a wide variety of areas ranging from

viii quantum chemistry, basic nuclear and , condensed matter, and physics. Beginning with charming reminiscences of Teller at the labs by George Miller, Bruce Tarter, Siegfried Hecker, current and former directors of the Livermore and Los Alamos labs, the program continued with an overview (by one of us, SBL) of Teller’s intellectual origins and his science. Partly anticipating some of the subsequent speakers, examples discussed here included Teller’s physical explanation of Landau diagmagnetism, the Jahn-Teller effect, Gamow-Teller interactions in beta decay, conical intersections (and how they later led to ‘Berry’s phase’), the Lyddane-Sachs-Teller relation in dielectrics and, by analogy Goldhaber-Teller nuclear resonances, and the Northrop-Teller adiabatic invariant in charged particle motion in dipole magnetic fields. Then, Robert Littlejohn, of UC Berkeley, discussed Teller’s 1930’s work on the conical intersections of the energy surfaces of three or more interacting atoms and their ramifications for chemical kinetics, beautiful generalizations to Stern-Gerlach systems, and Littlejohn’s and his collaborators’ work on the consequences of mode crossings for ionospheric waves. Wick Haxton, of the University of Washington, next took up the legacy of two of Teller’s major contributions to nuclear and particle physics: Gamow-Teller transitions and Goldhaber-Teller resonances. Gamow-Teller transitions, are, of course, a key ingredient in the theory of beta decay and overall electro-weak unification. Haxton’s talk focused on how neutrino physics has shed particular clarity on the role of G-T transitions in the standard model of elementary particles and beyond. In addition, keeping to his theme of neutrino physics, he described how, in his own work, a standard model vector- axial vector current generalization of Goldhaber-Teller resonances led to the understanding of the astrophysical production of fluorine. The afternoon sessions began with talks on Teller’s influence on the development of plasma physics — in both ‘high energy density’ physics and magnetic fusion. Steven Rose, of Imperial College, London, described Teller’s post war intellectual influence over development of the theory and application of dense plasmas including equations of state, radiation opacities, -plasma physics and inertial fusion, finally bringing it into contact with his own recent

ix work on novel ‘fast ignition’ configurations. Illustrating Teller’s physics teaching style from the same period, he gave interesting examples from the written notes for a quantum mechanics course Teller and Konopinski gave at Los Alamos in 1946. Nathaniel Fisch, of , followed, describing Teller’s tremendous impact on fusion, beginning with the demonstration of the Teller-Ulam invention, as well as his insights with Northrop concerning the stability of charged particle motion in magnetic dipole fields (the latter being important to Fisch’s own work). Fisch also discussed how many of Teller’s students and colleagues from the 1940s and 1950s (such as , Harold Furth, and Richard Post) played important roles in driving developments in magnetic fusion. Turning back to the microscopic properties of matter and statistical physics, Malvin Kalos of Livermore, described the powerful impact of the on modern computational physics. In particular, Kalos discussed applications of the ‘MR2T2’, or Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller method, often cited as one of the ten most important numerical methods of all time. Janos Kirz (of Lawrence Berkeley National Laboratory and Stony Brook University) talk beautifully wove together family remini- scences of living the Teller house in Berkeley several years in the late 1950’s after Kirz’s escape from Hungary, with a discussion of Teller’s ideas about future energy systems. Kirz pointed out that many of Teller’s ideas (for example, concerning reactors) are becoming more relevant today and deserve another look. Finally, John Holzrichter, President of the Hertz Foundation, described Teller’s remarkable impact on education, from his own students, to university life (both in Europe and the US), then driving applied physics education, and in the Hertz Foundation (which has funded over 1050 graduate fellows since its inception). In addition to the written contributions of these speakers, we have also appended DVD’s with videos of the presentations. These videos as well as the speakers’ slides may also be seen at: https://tellercentennial.llnl.gov. In this volume, we have also added the transcript of a never-before published April 2000 recording of Teller speaking on the history of science, his own role in the

x twentieth century physics and its applications, as well as his thoughts on the challenges facing the twenty-first. An event like this required the hard work of many dedicated colleagues. We would particularly like to thank Tiffany Ashworth, Lauren de Vore, George Kitrinos, Evelyn Laurant, Jim Mcinnis, Barbara Nichols, Joanne Smith, Kirsten Sprott, Denise Steele, Jeannette Tootle, and Kathy Young for their terrific efforts making the symposium a reality. Two local wineries, Retzlaff Estate Wines, and Fenestra Winery graciously contributed wines for the event. Finally, we would like to thank the Lawrence Livermore National Laboratory, The , The Hoover Institution of , and The Fannie and John Hertz Foundation for their generous support. Without them, this symposium would not have been possible.

Stephen B. Libby Physics Department Lawrence Livermore National Laboratory Livermore, California

Karl A. van Bibber Vice President and Dean of Research Naval Postgraduate School Monterey, California

November 10, 2009 8:44 WSPC - Proceedings Trim Size: 9in x 6in 03˙Teller

xi

8:00 a.m. Registration & Continental Breakfast Symposium Sponsors

Session 1 Chair: Karl van Bibber, LLNL Lawrence Livermore National Laboratory is a premier research and 8:30 a.m. Welcome development laboratory dedicated to the application of science and George Miller, LLNL technology to enhance national security, meet energy and 8:45 a.m. Scientific Reflections environment needs, and advance economic competitiveness. Bruce Tarter, LLNL Siegfried Hecker, Stanford University & LANL The mission of the University of California is to serve society as a 9:30 a.m. Edward Teller's Scientific Legacy center of higher learning, providing long-term societal benefits through Stephen Libby, LLNL transmitting advanced knowledge, discovering new knowledge, and functioning as an active working repository of organized knowledge. 10:15 a.m. Break The Hertz Foundation mission is to provide unique financial and Session 2 Chair: Hans Mark, University of Texas at Austin fellowship support to the nation's most remarkable Ph.D. students in 10:30 a.m. Conical Intersection, Light Cones, and Mode Conversion the physical, biological and engineering sciences. Hertz Fellows Robert Littlejohn, UC Berkeley become innovators and leaders serving in ways that benefit us all. 11:15 a.m. Edward Teller and Nuclei: Along the Trail to Neutrinos Wick Haxton, University of Washington The Hoover Institution, Stanford University, is a public policy research center devoted to advanced study of politics, economics, and political 12:00 p.m. Lunch economy—both domestic and foreign—as well as international affairs. The institution puts its accumulated knowledge to work as a Session 3 Chair: Cherry A. Murray, LLNL prominent contributor to the world marketplace of ideas defining a 1:15 p.m. Surprises in High-Energy-Density Physics free society. Steven Rose, Imperial College 2:00 p.m. Plasma Physics and Controlled Nuclear Fusion Nathaniel Fisch, Princeton University 2:45 p.m. Monte Carlo Methods in the Physical Sciences Malvin Kalos, LLNL Wines for this event were most graciously provided 3:30 p.m. Break by Fenestra Winery (www.fenestrawinery.com) and Retzlaff Estate Wines (www.retzlaffwinery.com). Session 4 Chair: Lowell Wood, Hoover Institution 3:45 p.m. Energy Catering presented by Checkers Catering & Special Events Janos Kirz, LBNL & Stony Brook University (www.checkerscatering.com). 4:30 p.m. Edward Teller and Higher Education John Holzrichter, Hertz Foundation

5:30 p.m. Reception

6:30 p.m. Adjourn This page intentionally left blank November 10, 2009 8:56 WSPC - Proceedings Trim Size: 9in x 6in contents

xiii

CONTENTS

Edward Teller Poem on Theory and Experiment v

Preface vii

Program xi

Brief Reflections on Edward Teller’s Scientific Life at Livermore 1 C. Bruce Tarter

Edward Teller Returns to Los Alamos 4 Siegfried S. Hecker

Edward Teller Biographical Memoir 13 Stephen B. Libby and Andrew M. Sessler

Conical Intersections, Light Cones, and Mode Conversion 62 Robert G. Littlejohn

Edward Teller and Nuclei: Along the Trail to the Neutrino 80 Wick Haxton

Surprises in High Energy Density Physics 96 Steven J. Rose

Plasma Physics and Controlled Nuclear Fusion 112 Nathaniel J. Fisch

Monte Carlo Methods in the Physical Sciences 128 Malvin H. Kalos

Teller on Energy 140 Janos Kirz November 10, 2009 8:56 WSPC - Proceedings Trim Size: 9in x 6in contents

xiv

Edward Teller and Higher Education 144 John F. Holzrichter

Message to the Next Generation 157 Edward Teller 1

BRIEF REFLECTIONS ON EDWARD TELLER’S SCIENTIFIC LIFE AT LIVERMORE

C. BRUCE TARTER Lawrence Livermore National Laboratory Livermore, California 94551

As George Miller indicated in his welcoming remarks the theme of today’s symposium is the scientific and educational legacy of Edward Teller. I will say a few words about his activities in those areas during the 50 plus years he spent at the Livermore Laboratory, Sig Hecker will touch on his re-engagement with the Los Alamos Laboratory during the last couple of decades of his life, and then we will show you a video with excerpts from the Memorial Service we held on November 3, 2003 after he passed away in September of that year. On the video you will get to hear comments by many of the people who knew Edward throughout much of his life, Hans Bethe, John Wheeler, Harold Agnew and many others. At Livermore much of Teller’s energy was devoted to national security and world affairs, but he always managed to retain his deep interest in science. Many of his individual contributions were made before he helped found the Laboratory in 1952, and Steve Libby will describe those in a later talk. I will concentrate on his impact on basic research, applied science, and education during the Livermore years. When Teller joined in starting the Livermore Laboratory he found himself in a very unusual situation. Among the initial staff of 100 he had no natural colleagues. Nobody from Los Alamos had come to Livermore, and none of the transplanted European scientists with whom he had so many fruitful collaborations joined him. Nearly everybody at Livermore in the initial years was one of Lawrence’s team at the Radiation Laboratory

2 in Berkeley, or at the very least part of the University of California at Berkeley. And, Lawrence was an experimentalist, as were most of the initial staff, and everyone except for Teller and Lawrence were essentially at the post-doc level. Edward Teller was truly a stranger in a strange land. Teller’s solution to this conundrum was straightforward and of great benefit to the embryonic young Lab. If his former colleagues wouldn’t join him full time at least they could visit. So, there began a steady stream of his closest colleagues, especially the Hungarians. , , George Gamow, Montgomery Johnson, his new RAND Corporation friends such as Albert Latter and many others made frequent visits to Livermore. Although most came to work on weapons, science was always on the table and many of the new Livermore staff participated in the free wheeling discussions that always characterized any Teller session. Not only did they gain insight from many of the best scientists in the world they also learned that there were no real barriers between physics and applied physics (or weapons physics). Throughout his 50 years at Livermore Teller would continue to use his prestige and personal associations to provide a powerful scientific conduit for the Laboratory. His own research at Livermore would focus on areas he had worked on in the past. He had graduate students, post-docs and active collaborations in Monte Carlo studies, in , in shock wave phenomena, and chemical physics. He would occasionally do work in astrophysics, and as part of the Plowshare program he became active in geosciences. His last scientific hurrah gave him great pleasure – when high temperature superconductivity was discovered he immersed himself in the field, talked to many of the major participants around the world, and made several contributions. In short, his life in basic science was that of a very senior, very broad theoretical physicist who thought about science most of his waking hours. His pursuit of applied science was equally intense and diverse. He was interested in nuclear reactors from the late 40’s on and was always looking for novel ways to improve their performance and safety. He led an early senior review group for what is now known as magnetic fusion and developed a lifelong nervousness about any

3

‘‘plasma based’’ system because of the instabilities encountered in all attempts to magnetically contain plasma. His special legacy, however, was his emphasis on high performance computing as a way to do science. From the earliest days it was well understood that nonlinear problems (like hydrodynamics) could only be done numerically, but Teller understood that the computer was essential to scientific progress, not an afterthought once the theory and intuition had been brought to bear. He made sure that Livermore always had the most powerful computer that was available or could be built, and he was relentless in his emphasis on computational physics (it is no accident that the Journal of Computational Physics was started and run from Livermore). The staff of the Laboratory joined in with great enthusiasm, and many seminal numerical papers were written by Livermore scientists in astrophysics, atmospheric science, , and related fields (as well as fundamental developments in weapons physics). Finally in education he has an extraordinary legacy. His reputation as a lecturer at Berkeley was legendary, and despite his politics his classes were always standing room only. He founded the Department of Applied Science (DAS) at the University of California at Davis, with the goal of creating a way for graduate students to do something between basic science and engineering-sometimes called engineering physics. The original faculty assembled at DAS — whose dominant Livermore branch became known as Teller Tech – was first rank, and many applied science students who had very successful careers received their PhDs at DAS. Perhaps his most lasting contribution is the Hertz Fellowship program. Established in the early 60’s as a complement to the prestigious NSF fellowships, Hertz Fellows were chosen equally selectively for their potential in applied science and a roster of Fellows is testimony to the power of the idea (and of the highly personalized process Teller set up to choose the Fellows). In summary Edward Teller made important and long lasting contributions in pure science, applied science, and education that stand alone as testaments to a professional life of the highest order. When one realizes that he was doing all this while engaging in a full spectrum of national security and world affairs activities, it brings forth the only plausible explanation: these Hungarians really were Martians.

4

EDWARD TELLER RETURNS TO LOS ALAMOS

SIEGFRIED S. HECKER Stanford University and Los Alamos National Laboratory

I was asked to share some reflections of Edward Teller’s return to Los Alamos during my directorship. I met Teller late in his life. My comments focus on that time and they will be mostly in the form of stories of my interactions and those of my colleagues with Teller. Although the focus of this symposium is on Teller’s contributions to science, at Los Alamos it was never possible to separate Teller’s science from policy and controversy. Different people have different views on what constituted the end of the Cold War. Some say it began to thaw when President Gorbachev met President Reagan at Reykjavik in October 1988. Others say it was the fall of the Berlin Wall in November 1989. Most say it was the dissolution of the Soviet Union at the end of 1991. I felt a definite thawing of the real Cold War, that between Los Alamos and Livermore, when Edward Teller returned to Los Alamos in 1986. A week before I took over the directorship at Los Alamos in mid- January, 1986, I got a call from Edward. He said, “Siegfried, we have to talk.” He offered to visit the laboratory. I was generally familiar with Teller’s difficult relationship with Los Alamos, but I had not met Edward in person. I also knew that he had not visited Los Alamos regularly in more than 30 years. So, I checked around and found that there was little enthusiasm for bringing Edward back. Those who remembered Teller’s testimony during the 1954 Oppenheimer security hearing, which culminated in Oppenheimer’s clearance being revoked, still did not forgive Teller for not supporting Oppenheimer. I was told it would be difficult to manage Teller’s visits along with those of Stanislaw Ulam, who lived in the area and 5 frequently came to the laboratory, and Hans Bethe, who visited every summer. Both had serious disputes with Edward going back to the development of the hydrogen bomb. In addition, many at Los Alamos believed that Teller not only went to work for the enemy, the Livermore laboratory; but that he created the enemy. And finally, there were some people, who were still upset with Teller playing the piano at 3 am 44 years ago in the flimsy Los Alamos apartments during the . Suffice it to say, not many people at Los Alamos wanted Teller back to visit. Nevertheless, when Edward called in 1986, I thought it was time to put the past behind us. Edward strongly believed that the future is more relevant than the past — and so did I. When Edward returned to Los Alamos, his immediate interests were strategic defense and nuclear power. He spent much time with Greg Canavan on various versions of defensive concepts. He gave talks to standing room-only crowds in our main auditorium — without notes — on the need and opportunities for nuclear power. But, soon his greatest passion was to understand high-temperature superconductivity (HTSC), which was discovered late in 1986. Edward later stated that “to explain superconductivity is much more difficult, much more exciting and much more appealing than thinking about military applications.” Edward was first and foremost a scientist. He spent a lot of time with Jim Smith and his colleagues at Los Alamos learning about superconductivity and trying to understand it. Edward attended international conferences on the topic. He was one of the most recognizable faces on the planet, yet he was just one of the attendees at a superconductivity meeting in Huntsville, Alabama in May 1989. One of my favorite photos (see Fig. 1) is one of Edward and Jim Smith at the conference. Teller’s name tag read “Hello — I am Edward Teller.” Edward told Jim Smith about his early involvement with electrons. After Edward moved from Munich to Leipzig in 1928, he listened to an argument between Werner Heisenberg and Lev Landau about whether a metal has a diamagnetic or paramagnetic response to an applied magnetic field. The two giants could not agree, so they turned to young Teller to work it out. Edward considered a piece of metal and how an electron would bounce around inside its edges in a 6

Fig. 1. Edward Teller with James L. Smith from the Los Alamos National Laboratory at a superconductivity meeting in Huntsville, Alabama in May 1989. field. It turned out that Landau was right — of course, we know that now because we learn about Landau diamagnetism in physics class. That work led to one of Edward’s first publications (see Fig. 2), “Der Diamagnetismus der freien Elektronen,” in Zeitschrift für Physik 67, 311 (1931). The acknowledgments in that paper are a strong testament to Edwards’s excellent scientific upbringing. In addition to Pauli, van Vleck, Peierls, and Heisenberg, whom he mentions in the paper, we know that Edward started his graduate studies with Sommerfeld at Munich, completed his PhD with Heisenberg at Leipzig, moved to Göttingen, spent a year with Neils Bohr in Copenhagen, and then moved to George Washington University at the invitation of George Gamow. This was all before he worked with Oppenheimer, Bethe, and colleagues during the Manhattan Project. Teller’s early interest in atomic and molecular physics prepared him well for his passion in superconductivity. His work on what became known as the Jahn–Teller effect has many applications

7

Fig. 2. One of Edward Teller’s first publications “Der Diamagnetismus der freien Elektronen,” in Zeitschrift für Physik 67, 311 (1931) settled an disagreement between Werner Heisenberg (left) and Lev Landau (right). in atomic and molecular physics. Jahn and Teller demonstrated that any molecule or complex ion in an electronically degenerate state will be unstable relative to a configuration of lower symmetry in which the degeneracy is absent. This simple molecular picture can be replaced by a lattice with appropriate symmetries, as it has been discussed in phenomena like superconductivity. I listened in on many of the superconductivity discussions with Edward at Los Alamos. We also held interesting discussions about the properties of , the most complex element in the periodic table. I told Edward that the monoclinic ground state of plutonium results from a Jahn–Teller-like distortion (or a similar solid state effect called the Peierls distortion). A slight distortion from a hexagonal close-packed arrangement lowers the energy sufficiently to favor the monoclinic structure. The results are dramatic. Instead of 8 plutonium being easy to cast and to mold, it is as brittle as glass. While Teller was busy thinking about the hydrogen bomb (or the Super as Teller called it) at Los Alamos, his colleagues, Cyril Stanley Smith and Ed Hammel (who is still alive today and is my neighbor in Los Alamos) discovered how to tame the complex metal — at least temporarily — by alloying it with a few atomic percent of gallium. Edward was fascinated by this story. He spent many hours discussing superconductivity with Jim Smith, Zachary Fisk and Los Alamos colleagues who discovered heavy-fermion superconductors a few years prior to the HTSC discovery. He tried to understand what makes the Perovskite structures superconducting at such high temperatures. In his usual fashion, he was able to see the overall shape of a very complex problem, always trying to reduce the problem to its simplest terms. He pursued that work both at Los Alamos and at Livermore. He also paid close attention to the experimental work. He was interested in the effect of a magnetic field by beginning at the limit of infinite field. Bruce Freeman and colleagues designed an experiment to generate very high explosively-driven magnetic fields. Figure 3 shows Edward with Bruce in the bunker at Firing Point 6 at Los Alamos during such an experiment. Teller published some papers on superconductivity — he stated “it is my conviction that we are just at the beginning of a new chapter of solid state physics, and that the behavior of the Perovskite layer may be just one of the surprises that could lead to new knowledge and new applications.” That is what Teller always believed. During these visits I was able to witness two interesting Teller traits that many of you have experienced during your association with Edward. We served on a number of committees together. Without fail, Edward would be sitting at the conference table leaning on his walking stick and appearing sound asleep. Yet, when it came to discussion time, Edward would ask most penetrating questions, including on the material during which he looked asleep. Edward also displayed his greatest charm and grace with women and children. I had occasion to have Edward and his wife, Mici, over for dinner in 1989. He thoroughly charmed my wife, Nina, and youngest daughter, Leslie. Leslie was about one year into piano lessons. So, I had asked Edward earlier in the day if he would be 9

Fig. 3. Edward Teller with Bruce Freeman in the bunker at Firing Point 6 at Los Alamos during an high explosively-driven magnetic field experiment designed to study superconductivity at high fields. willing to play on our Baby Grand piano. Edward obliged, but only after we got the music for specific works by Mozart and Beethoven. He was as remarkable at the piano as he was charming. He was a master of the compliment. As my colleague, Jim Smith, pointed out to 10

Fig. 4. Edward Teller with the “Tsar’s Bomba” in the museum of the Russian Federal Nuclear Center for Theoretical Physics (VNIITF) in the city of , the Urals region, Russia, 1994.

11 me, Edward belonged to the school of no compliment being too extreme to be acceptable, even if it is not credible. My last story is about Russia. During the Cold War, many American scientists visited the Soviet Union in an attempt to build scientific bonds. Teller had no interest in such visits. However, he was quite eager to go after the fall of the Soviet Union. So, he visited one of Russia’s secret nuclear cities. As you might expect, he chose what was called Chelyabinsk-70 (now the Russian Federal Nuclear Center for Theoretical Physics or VNIITF in the city of Snezhinsk, the Urals region) — the Russian Livermore. He was treated royally because the Russians respected his science and his work on the hydrogen bomb. Teller posed with Russian weapon scientists in front of a life-size model of the Tsar’s Bomba, the huge hydrogen bomb designed by and colleagues and detonated at half of its design yield of 100 Megatons over the island of Novaya Zemlya above the Arctic Circle on Oct. 30, 1961. This famous photo (Fig. 4) made worldwide news — you can imagine the symbolism of Teller in front of the Soviet hydrogen bomb, the biggest bomb ever designed and tested. But, this is only part of the story. This photo caused uproar at the Russian Los Alamos (Arzamas-16, the Russian Federal Nuclear Center for Experimental Physics or VNIIEF in the city of ). I had a long association with the Russian nuclear laboratories, especially with the Russian Los Alamos. I had become good friends with Academician Yuri A. Trutnev, who was one of the designers — along with Sakharov and Yuri Babaev — of the Tsar’s Bomba. During one of my visits to Sarov, Yuri confronted me with the Teller photo and a similar photo of me with the model of the bomb in Snezhinsk. He was outraged that his Russian colleagues at Snezhinsk posed in front of his bomb. Trutnev explained that he and his colleagues designed that bomb. “The designers in the Urals (in Snezhinsk) had nothing to do with the design,” he said. “All they contributed was to build the parachute.” He insisted that we have a photo taken of him and me in front of the bomb in the VNIIEF museum. I have used this one in all my subsequent presentations. During the photo session I also asked Trutnev if he could settle a dispute we had in the about that bomb. I had claimed that it was tested at 50 Megatons yield, while one of my American colleagues claimed 57 12

Megatons. When I asked Yuri to settle the dispute, he looked at me incredulously and said, “Sig, at that yield, it doesn’t matter.” He went on to explain that General Secretary Nikita Krushchev wanted that bomb designed and tested to send a political message to the United States. Trutnev said the bomb had no military utility. What I found most interesting about this exchange is that the two Russian labs had the same relationship with each other that Los Alamos had with Livermore. The competition is so fierce that it often erupts into strong personal disagreements. I couldn’t help but play on that relationship during my first visit to the Russian secret cities of Sarov and Snezhinsk. In fact, current Livermore director, George Miller, was there with then director, , at one of the banquets the Russians held to celebrate our arrival and anticipated scientific collaborations. When my turn came to propose a traditional vodka toast I told the Russians and Americans assembled in the Sarov dining hall that I found it interesting that we had so much in common, both at the laboratories and in our cities. We both understood how important competition was to keep us at the forefront of science and technology, and how an adversary often brings out the best through competition. I said now that the Russian and American labs appear to be heading away from an adversarial relationship toward cooperation, speaking for Los Alamos, I can only say “Thank God for Livermore.” Our Russian hosts hoisted the vodka glasses with a big laugh. They knew exactly what I meant. Let me conclude my remarks by changing that toast to say “thank Edward Teller for Livermore.” He helped create a laboratory that became one of the finest scientific institutions in the world — it helped provide for the security of the nation and the free world. And it made a Los Alamos a stronger place. I can only hope that our policy makers in Washington understand this.

Acknowledgments

I want to thank James L. Smith of the Los Alamos National Laboratory for sharing some of his experiences and stories of Edward Teller at Los Alamos. 13

EDWARD TELLER BIOGRAPHICAL MEMOIR

∗ STEPHEN B. LIBBY and ANDREW M. SESSLER† *Lawrence Livermore National Laboratory Livermore, California 94551 †Lawrence Berkeley National Laboratory University of California Berkeley, California 94720

1. Introduction

Edward Teller died on September 9, 2003 in Stanford, California at the age of 95. He was both one of the great theoretical physicists of the twentieth century and a leading figure in the development of nuclear weapons and broader defense advocacy. Teller’s work in physics, spanning many decades of the twentieth century, includes some of the most fundamental insights in the quantum behaviors of molecules and their spectra, nuclei, surfaces, solid state and spin systems, and plasmas. In the defense arena, Teller is best known for his key insight that made thermonuclear weapons possible. Teller took great pleasure in being counted as one of the five “Martians,” brilliant émigré scientists of Hungarian–Jewish origin, all renowned for their key roles in the development and application of science in the twentieth century. The other four were Theodore von Kármán, John von Neumann, Leo Szilárd, and Eugene Wigner.

∗ The work at LLNL was performed under the auspices of the U. S. Department of Energy both by the University of California, Lawrence Livermore National Laboratory under Contract No. W-7405-ENG-48, and Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344. † The work at LBNL was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, under Contract No. DE-AC02-05CH11231.

14

Teller was both a great scientific collaborator and physics teacher at all levels, known for his openness, generosity, personal warmth, and powerful physical intuition. Many of his graduate students went on to illustrious careers. Involved in nuclear matters from the beginning, Teller was an early figure in the Manhattan project. In fact, in 1939, shortly after the discovery of fission, he accompanied his old friend Leo Szilárd to ask Einstein to write to President Roosevelt recommending that the United States begin to investigate the potential for nuclear arms. Later, after the Second World War, in 1952, Ernest Lawrence and Teller co-founded the Lawrence Livermore Lab in order to accelerate the development of thermonuclear weapons. Because of his strong advocacy of defense programs, and particularly because of his role in nuclear arms, Teller was often seen as a controversial figure supporting unpopular positions on both the national and international stage. Yet, he was also not without his strong supporters and was surely influential. While any assessment of his science would easily arrive at the conclusion that his impact was great and still growing in surprising ways, a full assessment of his political role is more complex and may have to wait for a future removed from the passions of our age. Edward Teller was elected to the National Academy of Sciences for his many important contributions to physics. Thus, it seems appropriate to us, in this Memoir, to concentrate upon this aspect of Teller’s life. Therefore, the bulk of this memoir is in the section on Scientific Contributions. The other part of Teller’s life, the public aspect, has been described in many books and articles. We refer to some of them, and it would certainly be remiss not to touch upon this aspect of his life, but it seems not appropriate, or even necessary (given all the sources and critiques) to go into detail. In the later sections we very briefly — so as to give a complete picture of the man — describe the public aspects of Teller’s life. Finally, in the Concluding Section, we sum up the many sides of this remarkable, larger-than-life person.

2. Early Years (1908–1925) (Budapest)

Edward Teller was born in Budapest, Hungary on January 15, 1908, the second child — his two-year-old sister was Emmi — of Max Teller 15 and his wife Ilona Deutsch Teller. His father, Max, a distinguished lawyer, was associate editor of the law journal of Hungary. His mother, Ilona, was trained as a concert pianist and, although she never performed in public, she was a very accomplished pianist. The Jewish community of Budapest was rich in culture and accomplishment, and Teller’s parents were very much a part of this community. Teller’s love of music, his life-long playing of the piano, and his deep appreciation for German language and culture were received from his mother. His father had little influence upon Teller as a youth, but did play a role in his education and career choice. The years of Teller’s youth in Hungary were very difficult years, and it is quite understandable that simply adequate providing for the family required his father’s full attention. When Teller was only 10 years old, his father recognized his son’s talent in mathematics and arranged for him to receive special tutoring from a professor of mathematics. World War I produced severe hardship for the Tellers (and it was followed by a period of communism-only four months long, but most horrible for almost everyone) and then anti-Semitism (for the Jews were blamed for the terrible communist period). The Treaty of Trianon went into effect in the fall of 1919 and trapped Ilona and her two children in Lugos, Hungary — where they had gone for the summer and they had to stay on as the children caught chicken pox — for Lugos had become Lugoj, Romania. After eight months they were allowed to return to a greatly reduced Hungary. (The very extensive, and cultured, Austro-Hungarian Empire, having precipitated World War I, was disassembled). Thus, by the age of 12 Teller had experiences — hunger, run-away inflation, communism, anti-Semitism, and the collapse of his culture — that would shape his life. From age 7 to 14, Teller was greatly influenced by an au-pair girl, Magda Hesz, who knew English well, was of very sunny disposition, and only ten years older than he. Teller’s mother was devoted to her children, but she was a sad person and a worrier. (For example, she had Magda walk to school with Teller until he was age 15 and Magda left for the US.) Teller was also influenced by the mathematics 16 professor, mentioned above, and by a very fine piano teacher that he had during the brief time he was trapped in Lugoj. At age 9, Teller entered the Minta gymnasium; prior to that his mother had almost exclusively supervised his time. Teller’s experiences during his school years were similar to that of most youngsters: he was fearful at first, bullied a bit, then eventually accepted. During that time he met a friend’s younger sister, Augusta Hárkányi, called Mici. Later, in 1934, Mici became Teller’s wife. Their children, Paul and Wendy, were respectively born in 1943 and 1946. Also, probably due to his father’s efforts, he became friendly with three young Jews, Eugene Wigner, Johnny von Neumann and Leo Szilárd all of whom were to become great scientists. At age 17, in June of 1925, Teller graduated from gymnasium. His father wanted him to continue his studies in Germany, for the war had decimated Hungarian universities and anti-Semitism was everywhere and becoming even worse, effectively preventing Hungarian Jews from attending Universities. In contrast, the German Universities were still at the forefront of world scientific development and were also open to Jewish students. Teller wanted to study mathematics, his father wanted a practical course; they settled on chemistry. Teller’s mother insisted he was too young to leave home, but finally allowed him to go to Germany in January 1926. (This section based on “Memoirs” by Teller and Shoolery)

3. University Years (1926–1930) (Germany)

In early 1926, almost at age 18, Teller enrolled in Karlsruhe Technical Institute, which was chosen by his father with care and attention: with the I.G. Farben chemical company located in the same town, it was very good in chemistry. He was brought there, and settled into lodgings by his parents, but just a few months later moved into quarters with a grand piano. He found great pleasure in playing the piano, especially as he now was not taking lessons and under no compulsion to practice. He majored in chemistry, but studied a great deal of mathematics; in fact he was really undertaking a double major. He found that he did not enjoy chemistry laboratory work and that he much preferred mathematics and physics. He broached a possible 17 change of majors with his father, who then spoke with his teacher, a distant relative of his who was a professor of physics, as well as to the director of the Hungarian equivalent of General Electric (where Teller had worked during vacations). All were positive and Teller’s father allowed him to switch. At the end of the semester in April 1928, Teller left chemistry for good and went to the University of Munich to study under Arnold Sommerfeld. That summer he was able to see his-wife-to-be, Mici, a student at the University of Budapest, as she had a summer job in Germany teaching mathematics. However, one day that summer, Saturday, July 14, 1928 was a tragic day for Teller. Returning from a hike with his backpack on, he jumped off a moving streetcar, lost his balance, and his right foot was severed as the trolley rode over it. His parents and sister arrived quickly, he underwent surgery, and took many months to recover, first in Germany and then in Budapest. During that time he was visited by fellow students including Hans Bethe, two years his senior and then, when back in Budapest, a few hours each day by Mici. His family took good care of him, although he much preferred Mici’s cheer to his mother’s sadness. By the fall, Teller was fitted with prosthesis and fully recovered. Sommerfeld had gone abroad for the year, so Teller switched schools, still again, this time to Leipzig to work with Werner Heisenberg. Heisenberg was only six years older than Teller, but at that time already world-known as one of the greatest physicists of the century. Teller arrived, at age 20, a few weeks late but ready, now, to do physics in a big way. Under Heisenberg were a good number of students that were to become great physicists. These included Friedrich von Weizsäcker, Lev Landau (exactly Teller’s age, and already a superb physicist), Felix Bloch, Friedrich Hund, Rudolph Peierls, J.H. van Vleck, and Robert Mulliken. Teller fit well into the group and ended up making tea for the crowd, when they met once a week. Heisenberg, at that time a bachelor, spent much time with the students, doing physics, enjoying socializing and playing ping-pong. Teller was profoundly influenced by Heisenberg, and revered him all his life. It is interesting to note, as Teller did, given the controversy in subsequent years about Heisenberg’s activities under the Nazis, that nationality, religion, and political opinion played no role in Heisenberg’s interaction with his group in Leipzig. 18

Within a few weeks of arriving, Heisenberg put Teller to the task of sorting out a controversy about the ground state of the hydrogen molecular ion. Teller was able to quickly determine the right answer. Heisenberg then put Teller to the task of determining the higher energy levels and this work became his PhD thesis that he received in January 1930 just as he turned 22 and only 2 years after formally turning to physics. (This section based on “Memoirs” by Teller and Shoolery. See also “The Martians of Science,” by Hargittai).

4. Scientific Contributions

Edward Teller began his work in theoretical physics just after the formulation of quantum mechanics by Bohr, Heisenberg, Born, Schrödinger, Pauli, Jordan and Dirac. With the avenue open to the detailed understanding of atomistic phenomena, he and his contemporaries trained in Germany, who included Van Vleck, Oppenheimer, Bethe, Bloch, Landau, Herzberg, and many others, successfully applied the new framework to the analysis of diverse areas of physics and chemistry. Teller’s own work eventually included key early steps in quantum chemistry, molecular spectroscopy, quantum theory of magnetism, and nuclear physics. Later, he made key contributions to statistical mechanics, and the physics of solids, surfaces, and plasmas. In many cases, his contributions are widely known parts of the canon of twentieth century physics: examples include Gamow–Teller transitions, the Lyddane–Sachs–Teller relation, the Jahn–Teller effect and theorem, Goldhaber–Teller resonance, the “BET” equation of state, the Ashkin–Teller model, and the MR2T2algorithm. It is also interesting to remark that several of his papers that were initially somewhat less well known, such as the papers on diamagnetism, level crossings, many body valence bases, and the dissipation of sound have significant present ramifications. When Teller began his work in Leipzig in 1929 as Heisenberg’s student, he began the study of molecules again, but now from a theoretical physicist’s perspective. Born, Oppenheimer, Heitler, London, Pauling, Hund, and others were then laying down the foundations of quantum chemistry. Teller was soon to become a leading figure in the field. Appropriately, Teller’s thesis was about 19 the simplest molecule, the hydrogen molecular ion. Heisenberg drew Teller’s attention to the disagreement between the calculations of Carl Jensen Burrau and A. H. Wilson on the binding of the H2+ ion. In a detailed analysis applying both considerable analytic and numerical power, Teller resolved the argument in Burrau’s favor and went on to study the excited states. Teller always enjoyed telling a story from that time that illustrated his close relationship with Heisenberg. When he was working on his thesis, Teller lived in Heisenberg’s house and worked on his numerical calculations on a noisy mechanical calculator at all hours. Heisenberg would politely inquire on the status of the calculations and finally declared the thesis complete when he tired of the machine’s racket. Teller’s next foray into molecular physics was influenced by a puzzle he remembered from his earlier training in chemistry at Karlsruhe. It appeared that the spectroscopic shifts of the excited states of methyl halides were in contradiction with the basic separation of scales implied by the Born-Oppenheimer approximation. In collaboration with his friend László Tisza, whom he had known since their days competing in the Hungarian Eötvös competitions, he carried out the first example of a detailed analysis of the consequences of vibrational-rotational coupling in polyatomic molecules. The paradox was resolved, and Teller began a series of papers giving a comprehensive analysis of these couplings and their spectroscopic consequences in general molecules. Important collaborators in molecular physics from that time, first in Leipzig, then Göttingen, Copenhagen, and London, and finally in Washington include Gerhard Herzberg, James Franck, Lev Landau, Herta Sponer, G. Pöschl, George Placzek, E. Bartholme, Karl Weigert, Bruno Renner, R. C. Lord, F. O. Rice, G. Nordheim, A. Sklar, Robert Mulliken, B. M. Axilrod, Karl Herzfeld, George F. Donnan, Bryan Topley, R. F. Haupt, R. J. Seeger, Hermann A. Jahn, and Tisza. An important theme in Teller’s thinking that was to have significant, surprising later consequences in many branches of physics and chemistry began with the analysis of situations where the Born-Oppenheimer approximation breaks down. Under normal circumstances, if the electronic states are well separated in comparison to the matrix elements of the vibronic coupling due to the 20 nuclear motion, the corrections are perturbative. The Jahn–Teller effect arises in the opposite extreme: when the electronic terms are degenerate, for example, if there is orbital electron symmetry. Then, they found that the molecule inevitably deforms in a non-perturbative way causing the terms to be concomitantly split, resulting in a unique ground state. Normally, under this circumstance, the conditions for the Jahn–Teller deformations involve the zero eigenvalues of a matrix that is linear in the nuclear perturbations — whence the problem becomes one of group theoretic classification of the relevant polyatomic “wiring” as discussed in Jahn and Teller’s 1937 paper. Teller always credited Landau with stimulating his thinking in this direction and said that the famous result should be called the “Landau–Jahn–Teller effect.” Teller also set his student, Bruno Renner, to study the exceptional cases (such as the CO2 molecule) where the deviation from perfect degeneracy is quadratic in the nuclear motion and then the orbital electron symmetry can be maintained. The Jahn–Teller effect turned out to be widespread in polyatomic and condensed matter systems. A currently famous example is the deformation of the CuO6 octahedral complex in the K2NiF4 type unit cell of Müller and Bednorz’s undoped perovskite high Tc superconductor precursor La2CuO4. Another fascinating example of the breakdown of the Born- Oppenheimer separation of scales discussed by Teller is connected with a generalization of the well-known 1929 result of Eugene Wigner and John Von Neumann on quantum mechanical level repulsion in the case of a single real Hamiltonian tuning parameter. In molecular physics, the issue is whether one can enforce electronic level crossings by, for example changing the separation of two constituent atoms as would occur dynamically in a scattering experiment. In the diatomic case, there is one real length parameter, and the Wigner-von- Neumann theorem says that level crossings are avoided. Teller realized that, for example in three body interactions such as the simple case of H3, level intersections, now controlled by two real degrees of freedom, could occur. Many years later, in 1962, Teller’s old colleague Gerhard Herzberg and H. Christopher Longuet–Higgins analyzed the consequences of Teller’s result for the global behavior of the wave functions in systems with this type of level crossing and 21 discovered that it was multi-valued, thus producing the first molecular physics example of Berry’s topological phase. Teller first met Lev Landau in Leipzig and they worked together a few years later in Copenhagen. In addition to their fruitful discussions of the symmetry of complex molecules, they also developed a quantum mechanical description of sound dispersion and attenuation based on the idea of the dephasing of sound modes due to their coupling to internal degrees of freedom of the molecules in the medium. This led to immediate predictions of the damping rate dependence on molecular composition and temperature. Later, in 1941 during the early years of the Second World War, before either Teller or Hans Bethe had official connections with the Manhattan Project, they carried these ideas further in a detailed study of the deviations from thermal equilibrium in shocks under the auspices of the Army Aberdeen Research Laboratories. Their work proved critical to subsequent work on hypersonic ballistics in atmospheres. Bethe says in his commentary on their report, that they were motivated to contribute to the defense effort and approached von Karman, who suggested the problem. Shortly after that, when Teller was at , Arthur Kantrowitz carried out the first experiments to measure these deviations from equilibrium in shocks and Teller sponsored his thesis on the subject. Kantrowitz later went on to become a leading authority on hypersonic flight and was the inventor of hypersonic molecular beam sources. Teller continued to have a close relationship with Heisenberg after leaving Leipzig for Göttingen in 1930. On a return visit to Leipzig, Heisenberg posed to Teller the conundrum offered by Lev Landau’s 1930 quantum computation of the diamagnetic susceptibility of a free electron gas. The problem of diamagnetism was known to be outside the realm of classical physics because of an argument due to Bohr and van Leeuwen. There should be no classical diamagnetism at all since in a classical computation of the partition function, the influence of an external vector potential can be absorbed into the momentum sum. Heisenberg challenged Teller to give a more transparent physical argument explaining why Landau was correct. Teller did so in terms of the quantum population and current of what one would now call the skipping orbit or “edge state,” at the boundary of the sample. It is interesting to remark that Teller’s edge state 22 picture later reappeared usefully in the de Haas — van Alphen effect, and the quantum Hall effect. Also, in Göttingen, in 1932, Teller worked out, with the Russian physicist Georgi Rumer and Hermann Weyl the rules for suitable expansions of many spin wavefunction bases in terms of simpler spin eigenfunctions in a manner similar to Pauling’s contemporaneous idea of valence bonding. While this theorem is not as well known as some of Teller’s other papers, it is interesting to note that it was independently rediscovered at least twice: by Penrose, and then by Temperley and Lieb. More recently, this theorem has been useful in the analysis of spin chain states pertinent to Mott insulators. One other result from Teller’s time in Göttingen might be mentioned. With Herta Pöschl, he discovered a class of one- dimensional potentials that allowed for an analytic solution to anharmonic behavior. Subsequently, these reflection-less “Pöschl– Teller potentials have appeared in diverse areas of mathematical physics, most recently in the study of squeezed optical states. After the Nazis came to power in 1933, conditions for Jews in Germany rapidly deteriorated and Teller left the country taking two temporary positions in 1934–1935, first to Bohr’s Institute in Copenhagen, and then University College in London (the latter position made possible by the Rockefeller Foundation). The “Jahn– Teller” theorem, the culmination of the European phase of his career was worked out there. In 1935, George Gamow recruited Teller to a professorship at George Washington University, in Washington, D.C. There, his research focused on nuclear physics, early forays into astrophysics, the physics of dense plasmas, and solid state and statistical physics. At George Washington University, Teller’s fruitful collaboration with Gamow included their famous discovery of the “Gamow–Teller” transitions in beta-decay. This paper, written in 1936, reflects the rapidly developing, heroic period of nuclear physics in the 1930s. Two years earlier, had proposed his theory of beta decay, exploiting both Pauli’s neutrino hypothesis and an analogy with electromagnetic interactions. One of the consequences of Fermi’s theory was that non-zero nuclear spin changes ∆J were inevitably accompanied by final state multipole suppression factors of at least two orders of magnitude. Gamow and Teller soon realized that these 23

Fermi selection rules were at variance with some of the decay schemes of the “thorium active deposit,” and proposed a second set of decay matrix elements allowing for spin flips upon decay. In modern relativistic notation, they proposed to amend Fermi’s Hamiltonian with the added pieces:

µ 1 µ ρ ρ µ HC=( ΨΨΨΨ−Ψγ γ )( γ γ )C ( [γ γ − γ γ ] ΨΨ )( [ γµ γ −Ψ+ γρ γ µ ] ) h.c. ∑ A p5 n e µ 5 ν T4 p n e ρ ν Here, “axial” and “tensor” couplings were assumed to be of same order of magnitude as their scalar and vector analogs in Fermi’s original theory. “Gamow–Teller” transitions complemented Fermi’s original matrix elements, playing a very important role in the rapidly developing field of nuclear and particle beta decays, leading eventually to Lee and Yang’s discovery of parity violation, the proposal of the V-A theory of the fundamental weak interaction (which require the Gamow–Teller terms) and finally to the standard model. Interestingly, in a short 1937 follow on letter, Gamow and Teller point out, for the first time in the literature, the possible existence of weak neutral currents. It is also interesting to recall that their proposal, while playing a key role in fundamental physics, had an immediate, dramatic consequence in astrophysics. At that time, Hans Bethe was developing the theory of stellar nucleosynthesis, and realized that the Sun was too cool to be driven by his CNO cycle. Immediately after Gamow and Teller proposed their ‘spin-flip’ modification of the Fermi theory, Bethe, with Gamow, and Charles Critchfield (Teller’s student) realized that the Sun could be powered by the “pp chain” with the basic reaction being the weak interaction p + p → D + e+ + νe. This reaction is pure “Gamow–Teller” because of the Pauli principle and the deuteron’s angular momentum (one). Teller’s work in nuclear physics during the pre-war period at George Washington also included his 1937 papers with laying out the phase-shift analysis, including interference effects, for low energy scattering off hydrogen molecules. During this time, Teller also worked with Wigner, John Wheeler, L. 24

Hafstad, and his student Critchfield on forces and collective and rotational excitations in nuclei. With Gamow, Teller also carried out one of the earliest studies of the temperature dependence of thermonuclear reaction rates and applied their ideas to an investigation of energy production in red giant stars. During the late 1930’s Edward Teller also began to turn his attention to statistical and solid state physics. With his student Stephen Brunauer, and Paul H. Emmett, a chemist and catalysis expert at the Department of Agriculture, he gave a widely applied theory of physio-adsorption of gaseous species on substrates. The “BET” model isotherm extended Langmuir’s analysis of monolayer adhesion to the formation of puddles of adsorbate whose depth was controlled by balancing the simultaneous tendencies in equilibrium to evaporate and adhere. The “BET” model is typically applied to the determination of adsorbate areas in catalysis. In 1941, Teller with his co-workers Robert G. Sachs (later Director of Argonne National Laboratory), and Russell Lyddane gave a general rule for the ratio of asymptotic values of the dielectric constant of a polar crystal like NaCl in terms of the frequencies of transverse and longitudinal optical phonon modes:

ωT2/ωL2 = ε( ∞ )/ε(0) . This simple rule comes about from the realization that the poles and zeroes of the dielectric function are constrained by Gauss’s law. Of wide applicability, the divergence of ε(0) as ωT goes to zero has important implications for ferroelectricity. The Lyddane–Sachs–Teller relation also had an important consequence, by analogy, in nuclear physics. In 1948, several years after LST, Maurice Goldhaber, thinking about Baldwin and Klaiber’s experiments showing a ubiquitous rapidly varying photo-nuclear cross-section at high energy, realized that they might be explained by a collective resonance phenomenon similar to the “reststrahl” band in polar crystals. He sought out Teller, and together they predicted universal, giant photo-resonances in nuclei. In the early years of the war, during Teller’s time on the faculty at Columbia, he supervised Julius Ashkin’s thesis on a generalization of the 2-dimensional Ising model allowing for two different bond 25 strengths. They were motivated by the desire to discover variants of the basic Ising ferromagnet that retained Kramers–Wannier duality mapping between low and high temperature phases. In the context of the mathematical physics of phase transitions, their model came to take its place in the set of exactly soluble two-dimensional models. Philosophically, it is interesting to note, that when one of us, SBL, told Edward about the beautiful work done in the 1980’s analyzing two dimensional phase transitions (such as in the Ashkin–Teller model) with conformal symmetry, he was fascinated, but also eager to know if there was any practical application. This was a typical reflection of Teller’s conviction that the most interesting basic discoveries have practical applications. While at George Washington University, Teller began to think about what are now termed “high energy density” plasmas: that is, − plasmas of densities above that of air (10 3 gr/cm3) and pressures exceeding 100 kilobars. This subject, with its obvious ramifications for astrophysics, the Manhattan project, the hydrogen bomb, and more recently, “inertial” fusion was to interest him for the rest of his life. In 1939, with David Inglis, he proposed a theory of the lowering of the continuum in dense plasmas. Based on the intuitively appealing idea that the Rydberg states of excited ions in plasmas meld into the continuum as their Stark splittings due to neighboring ions approach the level spacing, the theory is still widely applied in treatments of the opacity and equation of state of plasmas. Later, as an outgrowth of the concern with equations of state of hot dense matter in the Manhattan project, he, with Richard Feynman and extended the Thomas–Fermi model of the atom to finite temperatures, producing a practical equation of state model for high energy density plasmas. Teller’s interest in the Thomas–Fermi method was not restricted to its implications for equations of state. In a short paper, written in 1962 honoring his old friend Eugene Wigner’s 60th birthday, he showed that molecular binding is impossible in the Thomas–Fermi and Thomas–Fermi–Dirac approximations. Later, Elliot Lieb and his collaborators exploited Teller’s reasoning in their study of the properties of matter under the Thomas–Fermi–Dirac and Thomas– Fermi–Weizäcker approximations. 26

In 1941, with Gregory Breit, Teller addressed the two-photon decay lifetimes of the metastable states of hydrogen and helium that occur in very dilute gases. Though an early, very influential analysis of two photon processes, the result was less important than originally thought, for in many practical plasmas there are small relativistic corrections to the states allowing single photon decay to compete with two-photon decay. Later, after the war, while they were working together on the hydrogen bomb, Teller and Frederick de Hoffman worked out the generalization of the Rankine–Hugoniot relations for shocked gases to the case of relativistic magnetohydrodynamics. Soon thereafter, Enrico Fermi exploited these ideas in his theory of cosmic ray generation. With Richtmyer, at that time, Teller also worked on cosmic ray generation mechanisms. Edward Teller’s most influential collaboration aimed at practical equation of state computations resulted in the “Metropolis” or “MR2T2” method for Monte Carlo calculations in statistical mechanics. This was done in 1953 with Nick Metropolis, Marshall Rosenbluth (who had been Teller’s student at Chicago), and Arianna Rosenbluth, and Mici Teller. Recently, in a paper written to celebrate the 50th anniversary of their now famous algorithm, Rosenbluth gave a beautiful description of the path toward its discovery and the initial applications. During the crucial period developing Teller’s concept for the hydrogen bomb, Teller created a theory group devoted to the necessary calculations. One of the tasks was to compute a wide variety of equations of state and, with Teller’s encouragement, they began to investigate computational methods to accurately approximate the needed statistical ensembles in order to compute the required expectation values. The Monte Carlo method, recently invented by Stan Ulam and applied to neutron-matter interactions, seemed natural, but in this case, many of the possible configuration space points were of very low a priori probability because they were weighted by the Boltzmann factor exp(-E/kT). Their idea, which Rosenbluth says Teller invented, was to develop appropriate configurations by starting with a representative one at the temperature in question and testing trial “moves” with the following rule: accept the move if the energy decreases, and if it increases, accept it with the probability exp(-∆E/kT), with ∆E the difference in 27 the energies of the two states. Seen from the viewpoint of computational compression, the MR2T2 algorithm is surely one of the most powerful in human history. As a point example, suppose one desired to compute expectation values of a quantity like magnetization in the 2D Ising model on a 100 × 100 lattice. The normal Boltzmann sum involves 21000 terms, beyond the reach of any computer. However, application of MR2T2 produces a decent answer in perhaps 106 steps (depending on temperature). Later, at Livermore, Teller continued to encourage the applications of large scale computing and in particular the computation of equations of state. There, 1966, working with Stephen Brush and Harry Sahlin, he carried out the first Monte Carlo analysis of the liquid-solid phase transition in the one- component plasma. In the late 1950’s both the development of the mirror-machine concept for magnetically confined fusion and the discovery of the Van Allen belts stimulated Teller and Theodore Northrop to address the question of the stability of the motion of point charges in a dipole magnetic field. Having discovered a new, approximate, “third” adiabatic invariant for the Earth’s imperfect dipole field, they conjectured that the problem might be in fact exactly soluble, like the Kepler problem, thereby giving an insight into the stability of the belts. Interestingly, about fifteen years later, Alex Dragt and John Finn showed that even the perfect dipole problem is not integrable, therefore leaving open the role of the Teller-Northrop invariant in such stability questions. During the period after the war and before he moved to California, Teller divided his time between the and Los Alamos. At Chicago he had many of his old, close friends as colleagues, including Enrico Fermi, James Franck, and Maria Mayer. There, with Fermi and Victor Weisskopf, Teller, by carefully studying how a strongly interacting particle had to stop and decay in matter, showed definitively that the then newly discovered muon could not be Yukawa’s hypothesized carrier of the nuclear force. Maria Mayer collaborated with Teller though the 1940’s. Their 1949 paper “The Origin of the Elements” was an early attempt to understand heavy element nucleosynthesis. Teller also frequently told an interesting story about how Maria Mayer began the field of 28 complex radiation opacities. Early in the Manhattan project, Teller began to wonder if the fission device could fail because of losing too much energy by radiation. This question relied on radiative opacities but, because heavy elements were involved, of a much more complex nature than the opacities that had been considered in the astrophysical community. Teller obtained Oppenheimer’s permission to ask Maria Mayer to consider the general question of such complex opacities. Her work, and subsequently that of her students Harris Mayer (no relation) and Boris Jacobson were the first significant steps in computing opacities with appreciable contributions from bound-bound absorption. At Chicago, he also had many of his best students, including Chen Ning Yang (whose thesis was a beautiful generalization Teller and Emil Konopinski’s paper on deuteron-deuteron reactions, and who later won the for the co-discovery of parity violation, with T. D. Lee), Marshall N. Rosenbluth (the leading plasma physicist of the modern era), and Marvin Goldberger (a major figure in particle physics and later President of Caltech and Director of the Institute for Advanced Study), Walter Selove (a particle physicist and Professor at the University of ), and Lincoln Wolfenstein (a particle physicist and Professor at Carnegie Mellon who later co- invented the ‘MSW’ mechanism for neutrino oscillation). Teller’s characteristic drive to apply the leading results of basic science is illustrated by the following anecdote from late in his life. To the end of his life, he often sought out colleagues to discuss the most exciting developments in all areas of science, from the most fundamental to the applied. Around 1998, when one of us (SBL), was telling him about quantum chromodynamics, it was initially difficult to convince him that this was indeed the correct underlying theory of the strong interactions. We tried many tacks. However, the moment I showed him the charmonium and bottomonium spectra, he got it right away, because we had been talking about asymptotic freedom and he saw the analogy of the bottomonium spectrum to positronium. After savoring this point for a few moments, he said: “You have finally convinced me! Now I have another question for you. I know from my own early work, that the moment quantum mechanics was elucidated, we could say many new things about molecules chemists didn’t know because we knew the underlying mechanics. What can 29 you now tell me about low energy nuclear physics that we didn’t know before?” (See also, “Edward Teller’s Scientific Life” by Libby and Weiss).

5. Los Alamos

Work, in the US, on a was initiated immediately after nuclear fission was discovered by Strassmann and Hahn and explained by Meitner and Frisch. Niels Bohr brought the news in January of 1939, to George Washington University, where George Gamow and Teller were running the fifth theoretical physics conference. As already mentioned, later that year, Teller drove Szilárd out on Long Island where Einstein signed his famous letter to President Roosevelt. The idea of fission precipitated experimental work to develop a working reactor and obtain the needed materials through gaseous diffusion, electromagnetic separation and reactor generation of plutonium. There was, however very little theoretical work, and actual thinking about possible bomb designs prior to the summer study which Oppenheimer called in Berkeley in the summer of 1942. The small group (only 9) included some of the best theoretical physicists in the country, including Teller. Interestingly enough, the group focused not upon the A-bomb, but rather on a (later to be called the H-Bomb). Later in 1942, the Manhattan Project under was formed and Oppenheimer was selected as leader of the effort. He selected the remote site of Los Alamos. Of course many books have been written about that work, perhaps the most comprehensive popular book being the one by Richard Rhodes and the most extensive unclassified technical history by Lillian Hoddeson et al. See also the very thorough “Brotherhood of The Bomb,” by Gregg Herken. Here, we limit ourselves to only briefly discussing Teller’s role in the effort. After the initial organization of Los Alamos, Oppenheimer selected Bethe to be head of the theoretical group. This choice was a deep disappointment to Teller for he had worked longer on the atomic bomb project, had helped in recruiting, and helped Oppenheimer in getting Los Alamos launched. Perhaps this was instrumental in 30 determining Teller’s role at Los Alamos, for one would have to characterize him, during the war years, as somewhat outside the main effort. He declined, when asked by Bethe to lead the effort on detailed implosion calculations (crucial to a plutonium bomb). He did attend meetings and often made significant suggestions, contributed significantly to the lab’s criticality test reactors, and was credited by Bethe for coming up with a crucial idea, but his main activity during the war was almost exclusively on the H-Bomb or “Super.” With Oppenheimer’s support, Teller assembled a small group of researchers who focused on this project. They included Emil (Kayski) Konopinski, Egon Bretscher, Cloyd Marvin Jr., Geoff Chew, Stan Ulam, Stan and Mary Frankel, Eldred Nelson, Nick Metropolis, Harold and Mary Argo, Henry Hurwitz, and Rolf Landshoff. One well-known result of his group was the verifying calculation that the atmosphere would not be ignited by the atomic bomb. By the end of the war, Teller’s group had produced a preliminary design for the “Super.” Ironically this early work, which likely was secretly transmitted by to the Soviets, would not have resulted in a weapon.

6. The Hydrogen Bomb

There is no question that the most important event in Teller’s life was the concept, design, construction, and successful operation of the thermonuclear, or ‘hydrogen’ bomb. Teller was, with out question, the true “father of the hydrogen bomb”, for Teller’s interest in a fast fusion reactions, goes back at least to the summer study in Berkeley in 1942. And, of course, he spent the war years thinking about and directing a small effort on the “Super”. Subsequently, he was relentless in his pursuit to construct a bomb far more powerful than the uranium or plutonium bombs of WWII. There have been many books written on the genesis of the hydrogen bomb (see for example, “Dark Sun: The Making of the Hydrogen Bomb” by Rhodes) and we shall not go into those details that are described in these books. Suffice it to note that Teller spent vacations from the University of Chicago (where he had gone after spending the war years at Los Alamos) visiting at Los Alamos. Then in 1950 he went there to make the hydrogen bomb a reality. He 31 recruited Emil Konopinski, Marshall Rosenbluth (just a few years after being a student of Teller), John Wheeler, Ken Ford, John Toll, and others. In addition, Conrad Longmire and Freddie de Hoffman worked with the group. Soon Johnny von Neumann, Stan Ulam, and Cornelius Everett had independently showed that the original Super would not work. Teller then had the crucial idea of radiation driven compression which, when coupled with Stan Ulam’s independent idea of ‘staging’, produced a practical design for a thermonuclear device. Together they wrote a report on this idea. It was this new idea for the hydrogen bomb that changed the view of the General Advisory Committee and the Atomic Energy Commission and led to the decision by President Truman to proceed with the development of the hydrogen bomb. Of course, the rapidly changing world political situation from 1948-1950, beginning with the Berlin crisis, the communist victory in the Chinese civil war, the successful Soviet atomic bomb test, and the communist invasion of South Korea also played a role in Truman’s decision. There were tests of parts of the idea, a lot of theoretical work at Princeton when John Wheeler returned there in 1951 (bringing along with him a number of distinguished physicists and recruiting others), and finally the culminating test of Richard Garwin’s detailed design, at Bravo near Bikini atoll. There are many details of the story, which are left out here. We have only presented the bare outlines of the story, but it should be clear that the hydrogen bomb was the result of many individuals’ efforts, over several years. Teller acknowledged this in a 1955 article in Science entitled “The Work of Many People.” However, the driving force was, without question, that of Teller, who had key ideas and was involved with the pure and applied science, sociology, administration and politics, all at the very highest level.

7. In the Matter of J. Robert Oppenheimer

There is no doubt that the single most important event in Teller’s post war emotional life was the security hearing for J. Robert Oppenheimer. Though surely significant for Oppenheimer, it was perhaps even more so for Teller. One can readily see this in Teller’s Memoirs, where relatively little space is devoted to scientific 32 accomplishments, but the most space is devoted to political matters and the security hearings, and their consequences. In fact, the only Appendix in that book is devoted to a transcript of Teller’s testimony. It seems that Teller changed his view even during the interview. He was — he says — very much influenced by the evidence presented to him just before the testimony, that Oppenheimer (many years earlier) had not told the truth to security agents. Teller uttered the damning words, “I would like to see the vital interests of this country in hands which I understand better and therefore trust more”. And later in the interview, “one would be wiser not to grant clearance”. However, he did not question Oppenheimer’s loyalty to the country, stating an earlier part of the testimony “Dr. Oppenheimer’s character is such that he would not knowingly and willingly do anything that is designed to endanger the safety of this country”. Most would have thought that this was the subject of the hearing, and if Teller had stopped there, his future world would have been very different. Perhaps Teller did not want to see, in a powerful position, a person whose views were different from his own and who had actively opposed the development of the Hydrogen Bomb, and he went on with those damning words. The consequences — ostracism and insults from many of his friends (but not all) and general alienation by the community, came as a surprise to Teller. The effect was a change in his life. To be sure, he gathered, in the many years after 1954 many new friends (especially younger people), and some of his old friends — such as von Neumann, Szilárd, Wigner, Fermi, Maria Mayer, Luis Alvarez, John Wheeler, and Ernest Lawrence — remained friends, but many did not and Teller became quite isolated from most of the American scientific community. Teller describes, in his memoir, his testimony as “stupid”. In retrospect, probably everyone would agree, for it seems likely that Oppenheimer would have been stripped of his clearance even without Teller’s testimony; whereas the testimony did great harm to Teller, probably more harm than it did to Oppenheimer.

8. Livermore

Immediately after the early promising results applying the Teller– Ulam concept to the creation of a workable hydrogen bomb, Lawrence 33 and Teller advocated the founding of a second nuclear weapons lab to accelerate its development. In 1952, the Lawrence Radiation Lab branch at Livermore (later the Lawrence Livermore National Laboratory) was founded about 50 miles east of San Francisco on the site of a square mile Naval air station built during the war. The Livermore lab was established under the auspices of the University of California for the Atomic Energy Commission as part of the Lawrence Radiation Laboratory, which up until that time had exclusively been in Berkeley, except for some small activity at the very location selected for the Livermore site. Beyond Lawrence and Teller, the founding and early prominent figures included Herbert York (who was the first director), Harold Brown (later Livermore Director, President of CalTech, and Secretary of Defense) John S. Foster Jr., (later Livermore Director and subsequently serving in several senior defense positions), Michael May (Later Lab Director and then Professor of Management Science and Engineering at Stanford), Roger Batzel (later Lab Director), John Nuckolls (later Lab director), Duane Sewell (who managed lab operations), and many other talented scientists and engineers, often with University of California pedigrees. From the beginning the Livermore lab was characterized by an entrepreneurial, can-do stance. This approach reflected both Teller and Lawrence’s personal philosophy that melded a deep interest in basic science and the desire to discover and push through important applications of that science. Probably also reflecting a kind of West Coast, ‘frontier’ egalitarianism in a manner similar to its ‘cousin,’ the Lawrence Berkeley Lab, the Livermore lab was quick to seize on the talents of its diversely educated population. The Livermore lab was soon competing with Los Alamos in the development of thermonuclear devices. An important break point occurred in 1956 at the ‘Nobska’ meeting called by the Navy to explore concepts for submarine launched ballistic missiles. There, Teller famously shocked his new Livermore colleagues into action by forcefully arguing the feasibility of building lightweight thermonuclear weapons that could be carried by a practical submarine launched missile. The lab succeeded in developing the warhead for the Polaris missile system — the first of many innovative contributions to the US nuclear deterrent. 34

As was true of Los Alamos, the Livermore lab, under Teller’s guidance was a trailblazer in the application of computers to scientific simulations. As the thermonuclear effort required the development of radiation hydrodynamics codes that could do useful calculations, an early spin-off in the 1950’s was the application of computational physics to astrophysics and hydrodynamics. Early key papers were written at Livermore by May and Richard White, Jim Wilson, Chuck Leith, and Sterling Colgate. Likewise, in an outgrowth of their work on equations of state, and Tom Wainwright, doing molecular dynamics simulations in the early 1960’s made major discoveries in phase transitions of 2-D systems and in the behaviors of fluids. As has been noted above in our description of his scientific achievements, Teller had been fascinated by “high energy density physics” since his time at George Washington University. It was therefore natural that he strongly encouraged innovative, basic and applied work at Livermore in this area. Key examples are the development of the inertial fusion concept and x-ray . The idea of inertial fusion driven by high-energy lasers or particle beams was an outgrowth of defense activities in the 1960’s and quickly became a large program in its own right. Likewise, x-ray lasers were developed in innovative synergy between defense programs and the laser program. In 1971 there was a formal separation of the two branches of the Radiation Laboratory. The lab in Berkeley was to do no classified work and was re-named The Lawrence Berkeley Laboratory. The lab at Livermore was called the Lawrence Livermore Laboratory. Both labs now reported directly to the president of the University of California.

9. The Plowshare Project

Many of those who were at Los Alamos were interested in three general areas in which nuclear energy might be applied. The first was nuclear weapons; the second generation of power and the third was in civil engineering. Teller was certainly interested in nuclear power, and made some interesting suggestions (such as putting nuclear power plants underground). However, his main interests in nuclear matters were in nuclear weapons and the possible peaceful 35 applications of nuclear explosives such as civil engineering. That Teller was very interested in using nuclear explosives for peaceful purposes one could psychoanalyze, but it is also true that Teller had a great faith in technology and deeply believed that nuclear explosives could be used to make life better. With this motivation he created a program, in 1958, at the Lawrence Livermore National Laboratory, called “Plowshares”. This program was rather controversial and aspects of the story are detailed in a critical book by O’Neill (“The Firecracker Boys” by O’Neill). After some successful tests in Nevada, Teller explored various possible sites for earthworks using Plowshare explosions. One possibility explored was a new canal to replace the Panama Canal, another was a harbor in Alaska. The latter idea was well received by the officials in Alaska, but certainly not by the ecologists, geologists, and biologists at the University of Alaska or by the local (Inuit) population. The fall-out, the ecological damage and the social disruption had been grossly underestimated, while the economic benefit of the harbor had been exaggerated. Attention was given to various overseas uses, such as a project in Australia, one in Israel (bringing sea water to the Dead Sea), and others in Thailand, Singapore and Japan. However, Teller soon learned that no site in other countries was possible. Attention then went in a very different direction; namely, using underground nuclear explosions to increase the production of gas and oil wells. Here there were a number of demonstrations and technically the results were very positive. One Utah test, in 1967, called Gasbuggy, increased gas production by a factor of six, another test, in Colorado, in 1969, called Rulison, increased well production by a factor between 10 and 15. Again, public concern about radiation (in this case quite unfounded) brought the activity to a halt. Soon, the Plowshares Program, without ever having accomplished its original goal of moving nuclear explosions into a program that would directly benefit society (rather than, at best, protect it) was terminated. All in all, the very idea of using nuclear explosions in a peaceful way was not one of Teller’s best initiatives. Perhaps the underground use will someday become a reality, but the effect of radioactive fall-out from the application of surface explosions was seriously — some would say even disingenuously — underestimated, 36 while the inattention to public opinion eventually proved fatal to the overall program.

10. The Strategic Defense Initiative

While the President Reagan’s “Strategic Defense Initiative” (SDI) of the 1980’s grew from many sources and motivations, Teller certainly played a significant role in its advocacy. Teller’s own motivations were consistent with the aspects of his philosophy already discussed: a desire to try new approaches to hard problems, certainty that organizations such as the Livermore lab needed new challenges in order to thrive, and his already mentioned desire to generate novel applications for nuclear explosives. The basic problem of strategic defense against nuclear weapons had existed since the weapons themselves were invented, and quite a lot of work had been done over the decades by both the US and USSR, up to the fielding of anti-ballistic missile (ABM) systems. The rapidly developing Soviet nuclear arsenal and the general increase of tensions added urgency in the early 1980’s. In the meantime, at Livermore, considerable innovative work was being done on the development of a nuclear pumped x-ray laser that offered the potential of rapidly striking targets at vast distances. Teller was very interested in this breakthrough, significantly because it represented a novel path forward in his quest to use nuclear devices not merely as explosives, but as ‘engines.’ Very controversial from the start, the Strategic Defense Initiative was widely criticized by many defense experts as being technically unworkable, particularly in the face of the enormous numbers of Soviet weapons. Ironically, the work at Livermore on the X-ray laser, because its intrinsic use of nuclear explosives contradicted Reagan’s desire for the defense to be non-nuclear, never commanded a significant portion of the SDI budget. The great bulk of the national program, under the auspices of the Department of Defense, (over 95%) was devoted to other projects at other institutions (e.g. sensors, computer software, optical lasers, and so on). Later, also with Teller’s encouragement, Livermore scientists were also to contribute an innovative non-nuclear ballistic missile defense concept: “.” This was based on the idea of 37 fielding cheap, maneuverable spacecraft that could intercept ballistic missiles. Ultimately, with the end of the cold war, this project also ended but it did contribute several innovative technologies. While it is difficult to objectively analyze the global role SDI may have played in the ultimate end of the cold war, one can certainly say that its challenges did invigorate the Livermore lab, engendering significant developments in computer codes, materials science, and fast experimental techniques and detectors in addition to engaging a new generation of highly talented scientists. On the other hand, for Teller personally, the advocacy of yet another unpopular position further increased his isolation from the broader scientific community. (See, “Edward Teller in the Public Arena’’ by Brown and May)

11. Teller as an Educator (1932–1975) and “Teller Tech” (1961–1975)

An aspect of Teller that is not widely appreciated, but most appropriate in this Memoir, was his devotion to education. Not only is this aspect not widely known, but his later impact upon the higher education of applied scientists and engineers, which was indeed very large, is not adequately recognized and appreciated. Throughout his life, Teller had a deep interest in education. As has been mentioned above, during the primarily academic phase of his career, he mentored the early Ph.D. research of many young scientists in Germany, England, and in the US at George Washington, Columbia, Chicago, and Berkeley. Many of these young scientists went on to illustrious careers. Examples already mentioned in this narrative include Chen Ning Yang, Marshall Rosenbluth, Arthur Kantrowitz, Marvin Goldberger, Lincoln Wolfenstein, Walter Selove, Julius Ashkin, Charles Critchfield , and Bruno Renner. Other students included Harold and Mary Argo, Anne Bonney, Hans Peter Duerr, and Balazs Rosnyai. Teller was also interested in basic scientific education, which he rightly regarded as a crucial part of the informed literacy of any civilization worthy of the name. For many years he taught, in the physics department in Berkeley, an elementary course on science appreciation. The course was highly regarded and although the 38 lecture hall held only 600, often more than 1,000 signed up to take the course. Starting in the early 1960’s, Teller felt the growing need for applied scientists trained in an innovative way that would combine sophisticated awareness of the latest developments in basic science with the ability to carry out advanced engineering projects. He therefore worked to develop a Department of Applied Science at Livermore under the University of California. The initial plan was to have students do their research at Livermore, but obtain their degree in Berkeley. Despite the support of the university president, Clark Kerr, there was sufficient opposition from the Berkeley faculty that after two years of trying Teller gave up on Berkeley. He then turned to the Davis campus (60 miles from Livermore) and there he had success, for the Department was incorporated into the Davis College of Engineering. The Department had excellent staff from amongst the scientists at Livermore and soon was turning out fine graduates, many of who have, subsequently, had outstanding careers, both in staying at Livermore and going on to other things at other places. In fact, Teller Tech (as it was called by the students) has become a major source of highly trained applied scientists and engineers; to date the program has trained more than 200 PhDs and more than 200 Masters of Science. Teller’s second major activity, with its first awards in 1963, was the establishment of the Hertz Fellowship for study in applied science. This fellowship was founded with support from John Hertz, a fellow Hungarian and founder of Yellow Cabs and Hertz Rent-a-Car. Through the years over 1050 fellowships to very able students have been awarded. This is about half of all the fellowships in applied science ever given in the USA. Management of the original bequest has allowed the Hertz Foundation to spend over 40 million dollars through the years. Later, starting in 1966, Hertz prizes were also awarded.

12. Conclusion

Edward Teller was simultaneously one of the great physicists of the twentieth century and a major, but often controversial figure in the development and advocacy of American defense technologies. 39

Courageously willing to push ideas persistently against the prevailing wisdom of the day, even at great personal cost, Teller was often very successful as with his development of the hydrogen bomb, the founding of the Livermore lab, and his role in the development of submarine launched missiles. However, in other cases he was less successful. As was true of his fellow ‘Martians,’ Teller believed that much of the best, intellectually dynamic science grew synergistically with applications and acted accordingly. As is true of his peers’ work from the heroic, early days of the development and application of quantum mechanics, his science continues to grow in influence, particularly in the deepening understanding of the microscopic properties of materials and their applications. He was, also, interestingly enough — perhaps almost surprisingly — a great advocate of openness in defense science and technology and frequently opposed secrecy, which he considered corrosive and damaging to America’s interests. Let us end this Memoir with a few selected quotations, by others, on Teller: For Teller’s memorial commemoration done in late 2003, his old friend Hans Bethe described their evolving relationship this way: describing Teller’s early work in Munich (he was two years Bethe’s junior under Sommerfeld in 1928) — “One student stood out — that was Edward Teller.” Moving to their early collaboration on defense research in the early days of the Manhattan project: ”We then began to map out the work needed at Los Alamos…Edward spent the remainder of the war primarily working on the ‘Super,’ but he made one very important contribution to the A-Bomb”…. Then, referring to the period from the end of the war through the 1980’s and on to 2003: “Teller was a hawk and I was, and still am, a dove. Our once close relationship strained and then broke. When I read Edward’s Memoirs, I was reminded of the good times. They were very good — among my most treasured memories. And that is how I prefer to remember my friend.” Andrei Sakharov, who has been compared to both Oppenheimer and Teller, gave the following interesting evaluation in his Memoirs: “I cannot help but feel deeply for and empathize with Oppenheimer whose personal tragedy has become a universal one. Some striking 40 parallels between his fate and mine arose in the 1960’s and later I was to go even further than Oppenheimer had. But in the 1940’s and 1950’s my position was much closer to Teller’s, practically a mirror image…so that in defending his actions, I am also defending what I and my colleagues did at the time. Unlike Teller, I did not have to go against the current in those years, nor was I threatened by ostracism by my colleagues. I had to overcome some resistance on technical questions, but I was not without support; the struggle for the “Third Idea” arose for different reasons and was conducted in different circumstances than in Teller’s case.” (“Memoirs” by Sakharov, p. 99– 100). Finally George Schultz, Secretary of State in the Reagan Administration, and later a colleague of Teller’s at the Hoover Institution at Stanford University, evaluating Teller’s role in the 1980’s said, at Teller’s memorial commemoration: “…SDI, as it turned out, played a critical role in bringing that to pass the successful negotiations at Reykjavik and the end of the cold war. Edward Teller played a key role in strengthening ’s resolve. Edward Teller made quite a contribution to the end of the cold war…” Then describing Teller’s characteristic manner of participation in his seminar at the Hoover institution at Stanford: “After all the obvious questions were asked, then Edward comes into play and he thinks of things that no one else thought of… So creative, so much fun, such a stimulating colleague. I’ll miss him…. He didn’t just make a difference, he made a gigantic difference.”

References

Harold Brown and Michael May, Edward Teller in the Public Arena, Physics Today, 2004, 8, p. 51. Istvan Hargittai, “The Martians of Science, Five Physicists Who Changed the Twentieth Century,” Oxford University Press, , 2006. Gregg Herken, Brotherhood of the Bomb, Henry Holt & Co., New York, 2002. Lillian Hoddeson, Paul Henriksen, Roger A. Meade, and Catherine Westfall, Critical Assembly, a Technical History of Los Alamos during 41 the Oppenheimer Years 1943-1945, Cambridge University Press, Cambridge, Great Britain, 1993. Stephen B. Libby and Morton S. Weiss, Edward Teller’s Scientific Life, Physics Today 2004, 8, p.45. Dan O'Neill, "The Firecracker Boys", New York: St. Martin's Press, 1994. Richard Rhodes, The Making of The A-Bomb, Simon and Shuster, New York (1986). Richard Rhodes, Dark Sun: The Making of the Hydrogen Bomb, Simon and Schuster, New York (1995). Andrei Sakharov, Memoirs, Knopf, New York, 1990. Edward Teller and Judith Shoolery, Memoirs, Publishing, Cambridge, Massachusetts, 2001.

Appendix A: Significant Dates of Teller’s Life

15 January 1908, Born in Budapest, Hungary 4 March 1941 Naturalized as a US citizen 9 September 2003, died in Palo Alto, California

1926–1928 Karlsruhe Institute of Technology, Germany 1928 University of Munich 1928–1930 University of Leipzig, Ph.D. under Werner Heisenberg 1929–1930 Research Associate, University of Leipzig 1930–1933 Research Associate, University of Göttingen 1934 Rockefeller Fellow, Institute for Theoretical Physics, Copenhagen, Denmark 1934–1935 Lecturer, City College of London, United Kingdom 1935–1946 Professor of Physics, George Washington University, Washington, D.C., USA 1941–1942 Professor Physics, Columbia University 1942–1943 Physicist, Manhattan Engineering District 1942–1943 Physicist, , University of Chicago 1943–1946 Physicist, Los Alamos Scientific Laboratory 1946–1952 Professor of Physics, University of Chicago 1949–1952 Assistant Director, Los Alamos Scientific Laboratory 42

1952–1953 Consultant and Cofounder, Livermore Radiation Laboratory, University of California 1953–1960 Professor of Physics, University of California, Berkeley 1954–1958 Associate Director, Lawrence Livermore Laboratory 1958–1960 Director, Lawrence Livermore Laboratory 1960–1975 Associate Director, Lawrence Livermore Laboratory 1960–1970 Professor of Physics at Large, University of California 1963–1966 Chairman, Department of Applied Science at Livermore, University of California at Davis 1970–1975 University Professor, University of California 1975–2003 Director emeritus, Lawrence Livermore National Laboratory 1975–2003 Senior research fellow, Hoover Institution, Stanford University

Appendix B: Honors (selected)

1948: National Academy of Sciences - elected 1955: Harrison Medal, American Ordnance Association 1957: Joseph Priestly Memorial, Dickinson College 1958: Albert Einstein Award, Lewis and Rosa Strauss Memorial Fund 1962: Enrico Fermi Award, Atomic Energy Commission 1974: Leslie R. Groves Gold Medal 1975: Harvey Prize, Technion Institute of Israel 1977: Semmelweiss Medal 1977: Albert Einstein Award, Technion Institute of Israel 1978: Henry T. Heald Award, Illinois Institute of Technology 1980: American College of Nuclear Medicine Gold Medal •Man of Science, Achievement Rewards for College Scientists •Paul Harris Fellow, Rotary •A. C. Eringen Award, Society of Engineering Science, Inc 1981: Distinguished Scientist, National Science Development Board •Distinguished Scientist, Phil-American Academy of Science and Engineering 1982: American Academy of Achievement Gold Medal • Jerusalem College of Technology 1983: National Medal of Science for 1982 43

1983: Joseph Handleman Prize, Jewish Academy of Arts and Sciences: Award, Association of Graduates, U.S. Military Academy, West Point 1988: Shelby Cullom Davis Award, Ethics and Public Policy 1988: Fannie and John Hertz Foundation Award 1989: Presidential Citizens Medal, President Reagan 1990: Ettore Majorana Erice Scienza Per La Pace, Science Peace Prize, Ettore Majorana Centre for Scientific Culture, Erice, Sicily 1990: Order of Banner with Rubies of the Republic of Hungary, President of the Republic of Hungary, Foreign Minister of the Republic of Hungary 1994: Middle Cross with the Star of the Order of Merit of the Republic of Hungary 1998: A Magyarsag Hirneveert Dij, (highest official Hungarian government award), Prime Minister of the Republic of Hungary 1999: Edward Teller Chair endowment, University of California at Davis's Department of Applied Science 2002: Department of Energy Gold Award, Energy Secretary Spencer Abraham 2003: Presidential Medal of Freedom, President George W. Bush

Honorary Degrees

Doctor of Science 1954: Yale University 1959: University of Alaska 1960: Fordham University 1960: George Washington University 1960: University of Southern California 1960: St. Louis University Doctor of Natural Science 1962: Rochester Institute of Technology 1964: University of Detroit 1964: Mount Mary College (Doctor of Humane Letters) 1966: Clemson University 1969: Clarkson College of Technology 1972: Tel Aviv University (Doctor of Philosophy) 44

1981: De La Salle University, Philippines 1983: Medical University of South Carolina (Doctor of Medical Science, honoris causa) 1987: Adelphi University Doctor of Law 1961: Boston College 1961: Seattle University 1962: University of Cincinnati 1963: University of 1974: Pepperdine University 1977: University of Maryland, Heidelberg1987: Defense Intelligence College (Doctor of Strategic Intelligence) 1991: Eötvös University, Budapest (Honorary Professorship)

Appendix C: Publications Scientific Papers (selected)

1. Über das Wasserstoffmolekülion (Hydrogen Molecular Ion). E. Teller. Zeits. f. Physik, 61 7–8, pp. 458–480 (1930) (Disser- tation). 2. Bemerkung zur Theorie des Ferromagnetismus (Remarks on the Theory of Ferromagnetism). E. Teller. Zeits. f. Physik, 62 1–2, pp. 102–105 (1930). 3. Der Diamagnetismus von freien Elektronen (The Diamagne- tism of Free Electrons). E. Teller. Zeits. f. Physik, 67 5–6, pp. 311–319 (January 31, 1931). 4. Zur Deutung des ultraroten Spektrums mehratomiger Moleküle (Infra-Red Spectra of Polyatomic Molecules). E. Teller and L. Tisza. Zeits. f. Physik, 73 11–12, pp. 791–812 (1932). 5. Bemerkungen über Prädissoziationsspektren dreiatomiger Moleküle (Remarks on the Predissociation Spectra of Triatomic Molecules). J. Franck, H. Sponer, and E. Teller. Zeits. f. Phys. Chem. 18, Abt. B1, pp. 88–101 (1932). 6. Eine für die Valenztheorie geeignete Basis der binären Vekto- rinvarianten (A Basis for Binary Vector Invariants Suitable for the Valence Theory). G. Rumer, E. Teller, and H. Weyl. Nachr. 45

Ges. Wiss. Gottingen, Math-Physik Klasse, 5, pp. 499–504 (1932) (German). 7. Modellmässige Berechnung von Eigenschwingungen organi- scher Kettenmoleküle (Calculation of the Characteristic Vibra- tions of Organic Chain-Molecule Models). E. Bartholome and E. Teller. Zeits. f. Phys. Chem. 19, Abt. B. 5, pp. 366–388 (1932). 8. Die Rotationsstruktur der Ramanbanden mehratomiger Mole- küle (Rotation Structure of the Raman Bands of Polyatomic Molecules). G. Placzek and E. Teller. Zeits. f. Physik 81 3–4, pp. 209–258 (1932). 9. Die spezifische Wärme des gehemmten eindimensionalen Rota- tors (Specific Heat of the Restricted One-Dimensional Rotator). E. Teller and K. Weigert. Gottengen Nachrichten, Math. Phys. Klasse 2, pp. 218–231 (1932). 10. Bemerkungen zur Quantenmechanik des anharmonischen Oszillators (Quantum Mechanics of the Anharmonic Oscillator). G. Poschl and E. Teller. Zeits. f. Physik 83 3–4, pp. 143–151 (1933). 11. Schwingungsstruktur der Elektronenübergänge bei mehrato- migen Molekülen (Oscillation Structure of Electron-Transfer in Polyatomic Molecules). G. Herzberg and E. Teller. Zeits. f. Phys. Chem. 21. Abt. B. 5–6, pp. 410–446 (1933). 12. Molekül- und Kristallgitterspektren. Bd. IX, Abschnitt 2 of Hand- und Jahrbuch der ehemischen Physik. W.W. Finkelnburg, R. Mecke, O. Reinkober, and E. Teller. 2. Theorie der langwelligen Molekülspektren by E. Teller. Leipzig: Akad. Verlagsges. pp. 43–160 (1934). 13. Molekül- und Kristallgitterspektren. Bd. IX, Abschnitt 2 of Hand- und Jahrbuch der ehemischen Physik. W. W. Finkelnburg, R. Mecke, O. Reinkober, and E. Teller. 3. Theorie der Kirstallgitterspektren by E. Teller. Leipzig: Akad. Verlagsges. pp. 161–188 (1934). 14. Theory of the Catalysis of the Ortho-para Transformation by Paramagnetic Gases. F. Kalckar and E. Teller. Roy. Soc. Proc. 150A. pp. 520–533 (1935). 15. Vibration Frequencies of Ethylene and Ethane. E. Teller and B. Topley. Chem. Soc., J. pp. 885–889 (1935). 46

16. Time Effects in the Magnetic Cooling Method. Part I. W. Heitler and E. Teller. Roy. Soc. Proc. 155A. pp. 629–639 (1936). 17. Zur Theorie Der Schalldispersion (Theory of Sound Dispersion). L. Landau and E. Teller. Phys. Zeits. d. Sowjetunion, 10 1, pp. 34–43 (1936). 18. Selection Rules for the Beta-Disintegration. G. Gamow and E. Teller. Phys. Rev. 49 12, pp. 895–899 (1936). 19. Some Generalizations of the Beta-Transformation Theory. G. Gamow and E. Teller. Phys. Rev. 51 p. 289 (1937) (Letter to Editor). 20. Heat of Sublimation of Graphite. G. Herzberg, K. F. Herzfeld, and E. Teller. J. Phys. Chem. 41 pp. 325–331 (1937). 21. Stability of Polyatomic Molecules in Degenerate Electronic States. I. Orbital Degeneracy. H. A. Jahn and E. Teller. Proc. Roy. Soc. A161, pp. 220–235 (1937). 22. The Scattering of by Ortho- and Parahydrogen. Julian Schwinger and E. Teller. Phys. Rev. 51. p. 775 (1937) (Letter to Editor). 23. The Scattering of Neutrons by Ortho- and Parahydrogen. Julian Schwinger and E. Teller. Phys. Rev. 52 pp. 286–295 (1937). 24. Crossing of Potential Surfaces. E. Teller. J. Phys. Chem. 41 pp. 109–116 (1937). 25. Structure of Benzene. Pt. X. Intensities of Raman Lines in Benzene and Hexadeuterobenzene. R. C. Lord and E. Teller. Chem. Soc. J. pp. 1728–1737 (1937). 26. Fluctuations of Composition in a System of Molecules in Chemical Equilibrium. F. G. Donnan. E. Teller, and B. Topley. Phil. Mag. 24 pp. 981–1001 (1937). 27. The Rate of Selective Thermonuclear Reactions. G. Gamow and E. Teller. Phys. Rev. 53 pp. 608–609 (1938) (Letter to Editor). 28. Adsorption of Gases in Multimolecular Layers. S. Brunauer, P. H. Emmett and E. Teller. Am. Chem. Soc. J. 60 pp. 309–319 (1938). 29. Rotation of the Atomic Nucleus. E. Teller and J. A. Wheeler. Phys. Rev. 53 pp. 778–789 (1938). 30. On the Saturation of Nuclear Forces. C. Critchfield and E. Teller. Phys. Rev. 53 pp. 812–818 (1938). 47

31. Electrical Breakdown of Alkali Halides. R. J. Seeger and E. Teller. Phys. Rev. 54 pp. 515–519 (1938). 32. Alpha-Particle Model of the Nucleus. L. R. Hafstad and E. Teller. Phys. Rev. 54 pp. 681–692 (1938). 33. Role of Free Radicals in Elementary Organic Reactions. F. O. Rice and E. Teller. J. Chem. Phys. 6, pp. 489–496 (1938). 34. Migration and Photochemical Action of Excitation Energy in Crystals. J. Franck and E. Teller. J. Chem. Phys. 6, pp. 861– 872 (1938). 35. Vapor Pressure of Isotopes. Karl. F. Herzfeld and E. Teller. Phys. Rev. 54 pp. 912–915 (1938). 36. Origin of Great Nebulae. G. Gamow and E. Teller. Phys. Rev. 55, pp. 654–657 (1939). 37. Energy Production in Red Giants. G. Gamow and E. Teller. Phys. Rev. 55 p. 791 (1939) (Letter to Editor). 38. Corrections to Paper “The Role of Free Radicals in Elementary Organic Reactions.” F. O. Rice and E. Teller. J. Chem. Phys. 7, p. 199 (1939). 39. On the Application of the Franck-Condon Principle to the Absorption Spectrum of HgCl2. H. Sponer and E. Teller. J. Chem. Phys. 7, p. 382 (1939) (Letter to the Editor). 40. Specific Heat and Double Minimum Problem of NH3. R. F. Haupt and E. Teller. J. Chem. Phys. 7, pp. 925–927 (1939). 41. Analysis of the Near Ultraviolet Electronic Transition of Benzene. H. Sponer, G. Nordheim, A. Sklar and E. Teller. J. Chem. Phys. 7, pp. 207–220 (1939). 42. Remarks on the Dielectric Breakdown. R. J. Seeger and E. Teller. Phys. Rev. 56 pp. 352–354 (1939). 43. Electron-Positron Field Theory of Nuclear Forces. E. P. Wigner, C. L. Critchfield and E. Teller. Phys. Rev. 56, pp. 530–539 (1939). 44. Ionic Depression of Series Limits in One-Electron Spectra. D. R. Inglis and E. Teller. Astrophys. J. 90, pp. 439–448 (1939). 45. Electric Breakdown of Alkali Halides. R. J. Seeger and E. Teller. Phys. Rev. 58. pp. 279–280 (1940) (Letter to Editor). 46. Metastability of Hydrogen and Helium Levels. G. Breit and E. Teller. Astrophys. J. 91, pp. 215–238 (1940). 48

47. Note on the Ultraviolet Absorption Systems of Benzene Vapor. G. Nordheim, H. Sponer and E. Teller. J. Chem. Phys. 8, pp. 455–458 (1940). 48. On a Proposed Thermoelectric Origin of the Earth's Magnetism. D. R. Inglis and E. Teller. Phys. Rev. 57, pp. 1154–1155 (1940). 49. Theory of the van der Waals Adsorption of Gases. S. Brunauer, L. S. Deming, W. E. Deming and E. Teller. Am. Chem. Soc. J. 62, pp. 1723–1732 (1940). 50. Scattering of Fast Electrons in Helium. J. B. H. Kuper and E. Teller. Phys. Rev. 58, pp. 602–603 (1940). 51. The Role of Ions in Surface Catalysis. P. H. Emmett and E. Teller. Twelfth Report of the Committee on Catalysis, National Research Council, John Wiley & Sons, Inc., pp. 68–81 (1940). 52. Energy Loss of Heavy Ions. J. Knipp and E. Teller. Phys. Rev. 59, pp. 659–669 (1941). 53. Polar Vibrations of Alkali Halides. R. H. Lyddane, R. G. Sachs and E. Teller. Phys. Rev. 59, pp. 673–676 (1941). 54. Electronic Spectra of Polyatomic Molecules. H. Sponer and E. Teller. Rev. Mod. Phys. 13, pp. 75–170 (1941). 55. Angular Distribution of Alpha-Particles Produced in the Li7- Reaction. C. L. Critchfield and E. Teller. Phys. Rev. 60, pp. 10–17 (1941). 56. Scattering of Slow Neutrons by Molecular Gases. R. G. Sachs and E. Teller. Phys. Rev. 60, pp. 18–27 (July 1, 1941). 57. On the Momentum Loss of Heavy Ions. J. H. M. Brunings, J. K. Knipp and E. Teller. Phys. Rev. 60, pp. 657–660 (1941). 58. Asymmetric Vibrations Excited by an Electronic Transition. E. Teller. Annls. of NY Acad. of Sci. XLI, Art. 3, pp. 173–186 (1941). 59. Deviations from Thermal Equilibrium in Shock Waves. H. A. Bethe and E. Teller. (Undated Memorandum) Distributed by Defense Technical Information Center; Rept. No. ATI-18278; NP-4898; BRL-X-117. 60. The Inelastic Scattering of Neutrons by Crystal Lattices. R. J. Seeger and E. Teller. Phys. Rev. 62, pp. 37–40 (1942). 61. X-ray Interference in Partially Ordered Layer Lattices. S. Hendricks and E. Teller. J. Chem. Phys. 10, pp. 147–167 (March 1942). 49

62. Interpretation of the Methyl Iodide Absorption Bands Near λ 2000. R. S. Mulliken and E. Teller. Phys Rev. 61, pp. 283–296 (1942). 63. Interaction of the van der Waals Type Between Three Atoms. B. M. Axilrod and E. Teller. J. Chem. Phys. 11, pp. 299–300 (June 1943). 64. Statistics of Two-Dimensional Lattices with Four Components. J. Ashkin and E. Teller. Phys. Rev. 64, pp. 178–184 (1943). 65. Neutron Emission by Polonium Oxide Layers. M. Argo and E. Teller. Los Alamos Scientific Laboratory Rept. LAMS-121. (August 8, 1944) (Declassified 1956). 66. Critical Amounts of Uranium Compounds. E. Konopinski, N. Metropolis, E. Teller, and L. Woods. Los Alamos Scientific Laboratory Rept. CF-548. (March 19, 1943) (Declassified 1956). 67. Theory of Water-Tamped Water Boiler. Work done by E. Teller, et al.; report written by E. Greuling. Los Alamos Scientific Laboratory Rept. LA-399. (September 27, 1945) (Declassified 1958). 68. Critical Dimensions of Water-Tamped Slabs and Spheres of Active Material. Work done by E. Teller, et al.; report written by E. Greuling. Los Alamos Scientific Laboratory Rept. LA-609. (August 6, 1946) (Declassified 1956). 69. Ignition of the Atmosphere with Nuclear Bombs. E. Konopinski, C. Marvin and E. Teller. Los Alamos Scientific Laboratory Rept. LA-602 (August 14, 1946) (Declassified 1974). 70. Neutron Spectrum from a Cold Parahydrogen Radiator. Work done by T. Hall, F. de Hoffman, and E. Teller; report written by T. Hall and F. de Hoffman. Los Alamos Scientific Laboratory Rept. LADC-111 (February 11, 1946) (edited to conform to security regulations). 71. The Decay of Negative Mesotrons in Matter. E. Fermi, E. Teller and V. Weisskopf. Phys. Rev. 71, pp. 314–315 (March 1, 1947). 72. On the Production of Mesotrons by Nuclear Bombardment. W. G. McMillan and E. Teller. Phys. Rev. 72, pp. 1–6 (1947). 73. The Capture of Negative Mesotrons in Matter. E. Fermi and E. Teller. Phys. Rev. 72, pp. 399–408 (1947). 74. On the Change of Physical Constants. E. Teller. Phys. Rev. 73. pp. 801–802 (1948). 50

75. Theoretical Considerations Concerning the D + D Reactions. E. J. Konopinski and E. Teller. Phys. Rev. 73, pp. 822–830 (1948). 76. On Nuclear Dipole Vibrations. M. Goldhaber and E. Teller. Phys. Rev. 74, pp. 1046–1049 (1948). 77. Equations of State of Elements Based on the Generalized Fermi-Thomas Theory. R. P. Feynman, N. Metropolis and E. Teller. Phys. Rev. 75, pp. 1561–1573 (1949). 78. On the Origin of Cosmic Rays. R. D. Richtmyer and E. Teller. Phys. Rev. 75, pp. 1729–1731 (1949). 79. The Origin of Cosmic Radiation. E. Teller. Phys. Today 2, pp. 6–13 (1949). 80. On the Origin of Elements. M. G. Mayer and E. Teller. Phys. Rev. 75, pp. 1226–1231 (1949). 81. On the Abundance and Origin of Elements. M. G. Mayer and E. Teller. Particules Elementaires, Institut International de Chimie Solvay, Burxelles (1950). 82. Magneto-Hydrodynamic Shocks. F. de Hoffman and E. Teller. Phys. Rev. 80, pp. 692–703 (1950). 83. The Assumptions of the B.E.T. Theory. W. G. McMillan and E. Teller. J. Phys. Chem. 55, pp. 17–20 (1951). 84. The Role of Surface Tension in Multilayer Gas Adsorption. W. G. McMillan and E. Teller. J. Chem. Phys. 19, pp. 25–32 (1951). 85. Equation of State Calculations by Fast Computing Machines. N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. H. Teller and E. Teller. J. Chem. Phys. 21, No. 6, pp. 1087–1092 (1953). 86. Theory of Origin of Cosmic Rays. E. Teller. Rep. Progr. Phys. 17, pp. 154–172 (1954). 87. Proton Distribution in Heavy Nuclei. M. H. Johnson and E. Teller. Letter in Phys. Rev. 93, No. 2, pp. 357–358 (1954). 88. Comments on Plasma Stability and on a Constant-pressure Thermonuclear Reactor. E. Teller. Paper submitted to Confe- rence on Thermonuclear Reactions, Princeton University, October 1954 (Declassified January 23, 1959). 89. Opening Remarks - Symposium on Plasma Instabilities. E. Teller. Paper submitted to Conference on Thermonuclear Reactions, University of California Radiation Laboratory, February 1955 (Declassified January 23, 1959). 51

90. The Work of Many People, Edward Teller; Science, pp. 267– 275, (1955). 91. Classical Field Theory of Nuclear Forces. M. H. Johnson and E. Teller. Phys. Rev. 98, No. 3, pp. 783–787 (1955). 92. Interaction of Antiprotons with Nuclear Fields. H. P. Duerr and E. Teller. Phys. Rev. 101, pp. 494–495 (1956). 93. Deep Underground Test Shots. D. Griggs and E. Teller. University of California, Lawrence Radiation Laboratory Rept. UCRL-4659 (1956). 94. General Problems of the Controlled Thermonuclear Process. E. Teller. Nucl. Sci. Engng. 1, pp. 313–324 (1956). 95. General Problems of the Controlled Thermonuclear Process. E. Teller. Paper submitted to Conference on Controlled Thermo- nuclear Reactions, June 1956 (Declassified January 23, 1959). 96. Peaceful Uses of Fusion. E. Teller. Reprinted from “Progress in Nuclear Energy, Series XI, Volume 1 — Plasma Physics and Thermonuclear Research,” pp. 56–65 (1958). 97. Seismic Scaling Law for Underground Explosions. A. L. Latter, E. A. Martinelli and E. Teller. Phys. Fluids. 2, No. 3, pp. 280– 282 (1959). 98. Peaceful Uses of Atomic Explosives. E. Teller. Fifth World Petroleum Congress Proceedings, Symposium on the Applica- tions of Atomic Energy to the Petroleum Industry, New York, pp 11–20 (1959). 99. Stability of the Adiabatic Motion of Charged Particles in the Earth's Field. T. G. Northrop and E. Teller. Phys. Rev. 117, pp. 215–225 (1960). 100. Nuclear Power Potential for Space Vehicles. E. Teller. Procee- dings of the Bureau of Naval Weapons Missiles and Rockets Symposium, Concord, CA., pp. 15–17 (April 1961). 101. Der quantenmechanische Mebprozeb und die Entropie. E. Teller. Werner Heisenberg und die Physik unserer Zeit, pp. 90–92 (1961). 102. On the Speed of Reactions at High Pressures. E. Teller. J. Chem. Phys. 36, No. 4, pp. 901–903 (1962). 103. On the Stability of Molecules in the Thomas-Fermi Theory. E. Teller. Rev. Mod. Phys. 34, No. 4, pp. 627–631 (1962). 52

104. The Hazards of Radiation. E. Teller. J. Nuclear Med. 3, No. 5, pp. 1–9 (1962). 105. Plowshare. E. Teller. Nucl. News 6, pp. 1–13 (March 1963). 106. Proposal of Experiments on Electromagnetic Radiation from a Distant Nuclear Explosion. W. K. Talley and E. Teller. Proceedings of the Third Plowshare Symposium, Engineering with Nuclear Explosives, University of California/Davis, pp. 31– 35 (April 1964). 107. Energy from Oil and from the Nucleus. E. Teller. J. Pet. Tech., pp. 505–508 (May 1965). 108. On a Theory of Quasars. E. Teller. From Perspectives in Modern Physics, Essays in Honor of Hans A. Bethe, R. E. Marshak (Ed.), Interscience Publishers, pp. 449–462 (1966). 109. Monte Carlo Study of a One-Component Plasma. I. S. G. Brush, H. L. Sahlin and E. Teller. J. Chem. Phys. 45, No. 6, pp. 2102– 2118 (1966). 110. On the Adiabatic Compression of a Light Packet. E. Teller. Sci of Light (Japan), Vol. 16 No. 1, pp. 22–25 (May 1967). 111. Some Remarks on Time Reversal. E. Teller. Proceedings of Symmetry Principles at High Energy, Fifth Coral Gables Confe- rence, University of Miami, pp. 1–6 (1968). 112. Prehistoric Safety Studies. E. Teller. Proceedings of the Livermore Array Symposium, Livermore, CA, pp. 1–5 (1968). 113. Atomic Explosives: Solved and Unsolved Problems. E. Teller. The Physics Teacher, Vol. 6, #5 (May 1968). 114. Internal Conversion in Polyatomic Molecules. E. Teller. Twentieth Farkas Memorial Symposium. Israel Journal of Chemistry, Vol. 7, No. 2, pp. 227–235 (1969). 115. Thermonuclear Energy. E. Teller. Center for Theoretical Studies, University of Miami Rept. CTS-HS-69-2 (1969). 116. Absorption of K- Mesons in Nuclear Surfaces. E. Teller, M. H. Johnson and S. D. Bloom. Phys. Rev. Lett. 23 1, pp. 28–30 (1969). 117. General Remarks on Electronic Structure. E. Teller and H. L. Sahlin from Physical Chemistry, an Advanced Treatise, Vol. V, (Ed.), Academic Press, pp. 1–34 (1970). 118. The Hydrogen Molecular Ion and the General Theory of Electron Structure. E. Teller and H. L. Sahlin. From Physical 53

Chemistry, An Advanced Treatise, Vol. V, Henry Eyring (Ed.), Academic Press, pp. 35–124 (1970). 119. Some Thoughts About High Energy Densities. E. Teller. Physics of High Energy Density, Academic Press, Inc., pp. 1– 6 (1971). 120. Relativistic Hydrodynamics in Supernovae. E. Teller. Physics of High Energy Density, Academic Press, Inc., pp. 402–418 (1971). 121. Die Verantwortlichkeit des Wissenschaftlers in der Gesell- schaft. E. Teller. Quanten und Felder, Physikalische und philosophische Betrachtungen zum 70. Geburtstag von Werner Heisenberg, pp. 93–100 (1971) . 122. An Effective Potential Calculation for the Ground State of Excited States of H2. H. Sahlin, R. Speed and E. Teller. University of California, Lawrence Radiation Laboratory Rept. UCRL-73338 (April 1971) for submission to the Journal of Chemical Physics. 123. General Shock Conditions. E. Teller and M. H. Johnson. Geophysical Monograph Series, Vol. 16, pp. 313–318 (1972). 124. A Future Internal Combustion Engine. E. Teller. University of California, Lawrence Livermore Laboratory Rept. UCRL-74487. For presentation at the 7th International Quantum Electronics Conference, Montreal, Canada (May 1972). 125. Concerning Strong Convergent Compression of Thermonuclear Fuel in Laser-Fusion CTR Schemes. E. Teller. University of California, Lawrence Livermore Laboratory Rept. UCRL-74117. 1972 Annual Meeting of the Division of Plasma Physics of the American Physical Society (1972). 126. Lasers in Chemistry. E. Teller. Proceedings of The Robert A. Welch Foundation Conferences on Chemical Research, XVI. Theoretical Chemistry, Houston, TX (November 1972). 127. The Dirac Hypothesis. E. Teller. Fundamental Interactions in Physics and Astrophysics, A Volume Dedicated to P. A. M. Dirac on the Occasion of his Seventieth Birthday, pp. 351–352, Plenum Press, New York (1972). 128. K--Mesic Atoms and Capture in the Nuclear Surface. S. D. Bloom, M. H. Johnson and E. Teller. W. H. Freeman & Co., pp. 89–111 (1972). 54

129. Are the Constants Constant? E. Teller. Cosmology, Fusion & Other Matters, George Gamow Memorial Volume, Colorado Associated University Press, pp. 60–66 (1972). 130. Thermonuclear Energy. E. Teller. Impact of Basic Research on Technology, Plenum Publishing Corp., New York, pp. 181– 192 (1973). 131. A Future ICE (thermonuclear, that is!). E. Teller. IEEE Spectrum 10, pp. 60–64 (1973). 132. Introductory Remarks to International Conference on Photo- nuclear Reactions and Applications. E. Teller and M. S. Weiss. Asilomar Conference Grounds, Pacific Grove, CA, March 26–30, 1973. Lawrence Livermore Laboratory Rept. CONF-730301 (1973). 133. Highly Excited Nuclear Matter. G. F. Chapline, M. H. Johnson, E. Teller and M. S. Weiss. Phys. Rev. D 8, No. 12, pp. 4302– 4308 (1973). 134. Die grundsätzliche Antwort. E. Teller. Einheit und Vielheit, Festschrift für Carl Friedrich v. Weizsäcker, Vandenhoeck & Ruprecht in Göttingen, (1973). 135. Futurology of High Intensity Lasers. E. Teller. Laser Interac- tions and Related Plasma Phenomena, Vol. 3, pp. 3–10, Plenum Press (1974). 136. Isotope Separation by Resonance Scattering. A. F. Bernhardt and E. Teller. Appl. Phys. Lett. 30, pp. 550–552 (1977). 137. Electromagnetism and Gravitation. E. Teller. Proc. Nat. Acad. Sci. 74 7, pp. 2664–2666 (1977). 138. Technical Initiatives on Early Sufficiency in Energy. E. Teller. Energy Research 2, pp. 3–7 (1978). 139. Remarks on the Thorium Cycle. E. Teller. Thorium and Gas Cooled Reactors. A seminar for the 65th birthday of Dr. Peter Fortescue. Annals of Nuclear Energy 5, pp. 287–296 (1978). 140. Is the Muon a Multipole Meter? E. Teller and M. S. Weiss. A Festschrift for Maurice Goldhaber, Transactions of the New York Academy of Sciences, Series II, Vol. 40, pp. 222–229 (1980). 141. Introduction. E. Teller. Fusion, Volume 1, Part A, pp. 1–29. Academic Press. (1981). 55

142. The Jahn-Teller Effect — Its History and Applicability. E. Teller. Physica 114A, pp. 14–18, North-Holland Publishing Co., (1982). 143. Intensity Changes in the Doppler Effect. M. H. Johnson and E. Teller. Proc. Natl. Acad. Sci. Vol. 79, p. 1340 (1982). 144. The Fusion Breeder--An Early Application of Nuclear Fusion. J. A. Maniscalco, D. H. Berwald, R. W. Moir, J. D. Lee and Edward Teller. University of California, Lawrence Livermore Laboratory Rept. UCRL-87801. For submission to Science, (June 1983). 145. On the Extragalactic Origin of Gamma-Ray Bursts. M. H. Johnson and E. Teller. University of California, Lawrence Livermore Laboratory Report UCRL-91744, Rev. 1. Presented at the Quantum Theory and the Structures of Time and Space, 6th Symposium, Tutzing, Germany, July 2–5, 1984. 146. Remarks on Stellar Clusters, E. Teller, contribution to a Festschrift volume in honor of Yuval Ne'eman's 60th birthday. Festschrift entitled, From SU (3) To Gravity (January 16, 1985). 147. Some Generalizations of the Virial Theorem. E. Teller. submitted to Foundations of Physics in honor of John A. Wheeler's 75th birthday (1986). 148. The Lunar Laboratory by Edward Teller published in the volume New Directions in Physics: The Los Alamos 40th Anniversary Volume. Academic Press, Inc., 1986 149. An Introduction To Equations of State: Theory and Applications (Foreward) by Edward Teller. Equations of State authored by Shalom Eliezer, A. K. Ghatak and Heinrich Hora, Cambridge University Press, 1986. 150. Remarks About Fields of High Intensity. E. Teller. For submission to Nuclear Instruments and Methods in Physics Research (Netherlands). (April 1987). 151. On The Chemistry of Superconductivity. R. More and E. Teller. University of California, Lawrence Livermore National Labo- ratory Report UCRL-98684. Presented at the International Conference on Lasers '87, December 1987. 56

152. Explosive Fusion Devices by Edward Teller published in Encyclopedia of Physical Science and Technology, Academic Press, Vol. 5, 1987, pp. 723–726. 153. Adaptation of the Theory of Superconductivity to the Behavior of Oxides, E. Teller. To appear in Proceedings of the NATO Advanced Study Institute on The Nuclear Equation of State, Peniscola, Spain, May 1989. 154. Theory of Superconductivity at High Temperatures by A. A. Broyles, E. Teller and B. G. Wilson published in the Journal of Superconductivity, Vol. 3, No. 2, pp. 161–169, 1990. 155. Lecture in connection with The Edward Teller Medal Award, published in Laser Interaction and Related Plasma Phenomena, Plenum Press, Vol. 10, pp. 1–4, 1992. Procee- dings of the Tenth International Workshop on Laser Interaction and Related Plasma Phenomena held November 11–15, 1991 at the Naval Postgraduate School, Monterey, California. 156. Space Propulsion By Fusion in a Magnetic Dipole, Edward Teller, Alexander J. Glass and T. Kenneth Fowler. Published in Fusion Technology, V. 22, August 1992, pp. 82–97 (a publicca- tion of the American Nuclear Society). Also presented at the 1st International A. D. Sakharov Conference on Physics, , USSR; May 27–31, 1991. 157. Fusion Devices, Explosive, Edward Teller. Published in Encyc- lopedia of Physical Science and Technology, Vol. 7, 1992 by Academic Press, Inc. 158. Introduction by Edward Teller, published in Advances in Spectroscopy in Hungary (Spectrochimica Acta) by Pergamon Press, Vol. 48A, No. 1, p. 1, 1992. 159. The Miracle of Superconductivity; Materials Science Forum Vols. 105–110 (1992) pp. 161–170. 160. Foreword by Edward Teller, published in the Textbook of Hyperbaric Medicine by Dr. K. K. Jain, American College of Hyperbaric Medicine, 1993; pp. XI–XII. 161. Yang, A Great Physicist. E. Teller, contribution to a Festschrift volume in honor of Professor C. N. Yang's 70th birthday. (1995) 162. Cosmic Bombardment V: Threat Object-Dispersing Approaches To Active Planetary Defense by Lowell Wood, Rod Hyde, Muriel Ishikawa and Edward Teller. Paper prepared for submittal to 57

the Planetary Defense Workshop, May 22-26, 1995, Livermore, CA; Report UCRL-JC-Draft (May 1995). 163. Completely Automated Nuclear Reactors for Long-Term Operation II: Toward A Concept-Level Point-Design Of A High- Temperature, Gas-Cooled Central Power Station System by Edward Teller, Muriel Ishikawa, Lowell Wood, Roderick Hyde and John Nuckolls. Prepared for submittal to 1996 Interna- tional Conference on Emerging Nuclear Energy Systems (ICENES '96), Obninsk, Russian Federation; 24–28 June 1996. UCRL-JC-122708 Pt. 2, June 20, 1996. 164. High Energy-Density Physics: From Nuclear Testing to the Superlasers. E. M. Campbell, N. C. Holmes, S. B. Libby, B. A. Remington, and E. Teller. 1996 American Institute of Physics No. 370; pp. 21–26. 165. The Evolution of High Energy-Density Physics: From Nuclear Testing to the Superlasers; E. M. Campbell, N. C. Holmes, S. B. Libby, B. A. Remington and E. Teller. Lasers and Particle Beams 4, pp. 607–626, (1997). 166. Nuclear Energy for the Third Millennium; Edward Teller. UCRL-JC-129547, prepared for submittal to the International Conference on Environment and Nuclear Energy, Washington, D.C., 27–29 October 1997. 167. Global Warming and Ice Ages: I. Prospects for Physics-Based Modulation of Global Change; Edward Teller, Lowell Wood, Roderick Hyde. UCRL-JC-128715, prepared for submittal to the 22nd International Seminar on Planetary Emergencies, Erice (Sicily), Italy, 20–23 August 1997. 168. Three Problems: Nuclear Energy, National Defense and International Cooperation by Edward Teller; UCRL-JC-135608 prepared for submittal to the Second International Symposium on the “History of Atomic Projects — The 1950s: Sociopolitical, Environmental and Engineering Lessons Learned” (HISAP ’99), Laxenburg,, Austria, October 4–8, 1999. 169. Long Range Weather Prediction III: Miniaturized Distributed Sensors for Global Atmospheric Measurements by Edward Teller, Cecil Leith, Gregory Canavan and Lowell Wood; UCRL- JC-146204, Part 3 prepared for presentation at the 26th 58

International Symposium on Planetary Emergencies, Majorana Centre for Scientific Culture, Erice, Italy, 20–23 August 2001. 170. Five Issues by Edward Teller and Dr. Behram N. Kursunoglu, Global Foundation, Inc.; UCRL-JC-142054 submitted to Global Warming and Energy Policy Conference, Fort Lauderdale, Florida, November 26–28, 2000. 171. Thorium Fueled Underground Plant Based on Molten Salt Technology, E. Teller and R. Moir, Nuclear Technology 151 (3), pp. 334–340, (2005).

Other Articles in Newspapers and Magazines

1. The Evolution and Prospects for Applied Physical Science in the United States. E. Teller. Reprinted from Applied Science and Technological Progress, A Report to the Committee on Science and Astronautics, U. S. House of Representatives, by the National Academy of Sciences (1967). 2. Can a Progressive be a Conservationist? E. Teller. New Scientist, February 19, 1970, pp. 346–349. 3. University Role in Nuclear Explosives Engineering Research. E. Teller. Education for Peaceful Uses of Nuclear Explosives, University of Arizona Press, pp. 293–298 (1970). 4. The Necessity of Strategic Defense by Edward Teller as presen- ted to The New York Academy of Sciences Conference on the High Technologies and Reducing the Risk of War. Published in High Technologies, Vol. 489, pp. 146–151, 1986. 5. Why I Am in America by Edward Teller published in The San Jose Mercury News, July 4, 1986. 6. Defense and the NATO Alliance by Edward Teller. Published in The National Interest, spring 1986. 7. Die Waffenabwehr (The Anti-Weapons) by Dr. Edward Teller published in Physikalische Blätter (Physikalische und technische Aspekte von Teilchenstrahl- und Laserwaffen), Vol. 42, No. 8, pp. 289–292, 1986. 8. Scientists and National Defense, An Open Letter to Hans Bethe by Edward Teller published in Policy Review, No. 39, pp. 18–23, Winter 1987. 59

9. In the Worst Event . . . by Edward Teller published as a book review on The Medical Implications of Nuclear War & A World Beyond Healing: The Prologue and Aftermath of Nuclear War.. Book review published in Nature magazine, Vol. 328, pp. 23–24, July 1987. 10. Defense Is The Best Defense by Edward Teller published in The New York Times Magazine, April 5, 1987, pp. 47–48. 11. The Question of Strategic Defense by Edward Teller published in Information Week, September 28, 1987, Issue 136, pp. 72. 12. Deterrence? Defense? Disarmament? The Many Roads Toward Stability by Edward Teller published in Thinking About America: the United States in the 1990s by Annelise Anderson and Dennis L. Bark, editors, pp. 21–32, September 1988 . 13. Widespread After-Effects of Nuclear War. E. Teller, Nature (London), Vol. 310, No. 5979, pp. 621–624 (August 23, 1984). 14. Science, Technology and Policy in the 1980's; Harvard International Review 10th Anniversary Issue; 1989; pp. 114– 118. 15. Survivability and Effectiveness of Near-term Strategic Defense by Gregory Canavan and Edward Teller. Published in Los Alamos as a technical paper: LA-11345-MS, UC-700, issued January 1990. 16. The Role of LLNL in the Education Process by Edward Teller published in The Quarterly at Lawrence Livermore National Laboratory: Looking Toward the 21st Century: Laboratory Leaders Share Their Vision of the Future. Vol. 21, No. 2, pp. 15– 17, November 1990. 17. Strategic Defence for the 1990s by Gregory Canavan and Edward Teller published in Nature magazine, Vol. 344, No. 6268, pp. 699–704, April 19, 1990. 18. The Future of Defense and Technology by Edward Teller. Formal paper presented at the Lawrence Livermore National Laboratory workshop: The Role of Nuclear Weapons in the Year 2000 sponsored by the Center for Technical Studies on Security, Energy and Arms Control. UCRL-JC-105925, CTS-11- 90, January 10, 1991. 60

19. Nuclear Glasnost by Edward Teller published in The Bulletin of the Atomic Scientists, Vol. 47, No. 9, pp. 34–35, November, 1991. 20. Low-Level Satellites Expand Distributed Remote Sensing; Dr. Gregory Canavan and Dr. Edward Teller; SIGNAL Magazine; Vol. 45, No. 12, August 1991; pp. 99–103. 21. The Laboratory of the Atomic Age by Edward Teller, published in Los Alamos Science, Number 21, pp. 32–37, 1993. Published for the Laboratory's 50th Anniversary. 22. U.S. Needs Fresh Approach to Nuclear Energy; The Christian Science Monitor, 1994; pp. 66–67. 23. Who's Afraid of Science? And Why? National Review, October 10, 1994; pp. 72.

Books (selected)

The Structure of Matter, Francis Owen Rice and Edward Teller, John Wiley and Sons, NY, 1949. Our Nuclear Future, Edward Teller and Albert L. Latter, Criterion Books, NY, 1958. The Legacy of Hiroshima, Edward Teller with Allen Brown, Doubleday and Co., Garden City, NY, 1962. The Reluctant Revolutionary, Edward Teller, University of Missouri Press, Columbia, MO, 1964. The Constructive Uses of Nuclear Explosives, Edward Teller, Wilson K. Talley, and Gary H. Higgins, McGraw Hill, NY, 1968. Great Men of Physics, Emilio G. Segrè, Joseph Kaplan, Leonard I. Schiff, and Edward Teller, Tinnon-Brown, Los Angeles, CA, 1969. Energy: A Plan for Action, Edward Teller, available from the Commission on Critical Choices for Americans, NY, 1975. Critical Choices for Americans: Power and Security, Edward Teller, Hans Mark, and John S. Foster, Lexington Books, Lexington, MA, 1976. Nuclear Energy in the Developing World, Edward Teller, Mitre Corporation, Metrek Division, McLean, VA, 1977. 61

Energy from Heaven and Earth, Edward Teller, W. H. Freeman and Co., San Francisco, CA, 1979. Better a Shield Than a Sword, Edward Teller, Free Press/MacMillan, New York, NY, 1987. Conversations on the Dark Secrets of Physics, Edward Teller, Wendy Teller, and Wilson Talley, Plenum Press, NY, 1991. Memoirs: A Twentieth-Century Journey in Science and Politics, Edward Teller and Judith Shoolery, Perseus Publishing, Cambridge, MA, 2001.

November 10, 2009 8:53 WSPC - Proceedings Trim Size: 9in x 6in 07˙Teller

62

CONICAL INTERSECTIONS, LIGHT CONES, AND MODE CONVERSION

R. G. LITTLEJOHN Department of Physics, University of California, Berkeley, California 94720-7300 USA ∗E-mail: [email protected]

This article presents a modern perspective on E. Teller, “The Crossing of Po- tential Surfaces,” J. Phys. Chem. 41, 109–116 (1937), in which the “conical in- tersection” was first described. It also provides a generalization of the Landau- Zener-St¨uckelberg formula for the probability of nonadiabatic transitions at avoided crossings or conical intersections, also called “mode conversion.”

Keywords: Conical intersection; mode conversion.

1. Introduction In 1937, Edward Teller published a paper1 on molecules that first described the object that is now called a “conical intersection.” Teller viewed this object as an intersection between potential energy surfaces in the Born- Oppenheimer approximation, and so it is usually regarded nowadays. It can, however, also be seen as a version (i.e., a pull-back) of a light cone in a space with a Minkowski metric. Moreover, the Minkowski metric plays an important role in the calculation of the transition probability and other quantities relevant for dynamics in the neighborhood of the cone. This talk concerns generalizations of conical intersections and Landau- Zener-St¨uckelberg transition probabilities in systems of coupled wave equa- tions. The generalization consists of allowing the equations to be coupled by arbitrary operators (not only potential energy couplings).

2. Historical Perspective

The title of Edward Teller’s 1937 paper is “The crossing of potential energy surfaces.” This has to be understood in the context of the “no-crossing rule,” which was first enunciated in a reasonably complete form by von November 10, 2009 8:53 WSPC - Proceedings Trim Size: 9in x 6in 07˙Teller

63

Neumann and Wigner in 1929.2 Briefly stated, this rule says that potential energy surfaces do not cross. More precisely, it says that when a Hermitian matrix or operator depends on a single parameter, then, as the parameter is varied, the eigenvalues do not cross. As the parameter is varied, a pair of eigenvalues may look as if they are going to cross, but when they get close together they tend to “repel” and bounce off one another, creating two branches of a small hyperbola. The rule is not absolute, but rather it states what is most likely to happen in a generic Hermitian matrix that depends on one parameter. The main application of this rule in molecular physics is the case of diatomic molecules, in which the electronic eigenvalues depend on one parameter, the interatomic distance. When a diatomic molecule passes through an avoided crossing, under the adiabatic approximation the system remains on the potential energy curve it started on. The adiabatic approximation is most likely to break down, however, when energy levels are close to one another, something that happens precisely at an avoided crossing. Therefore there is in fact some probability for the system to make a transition to the other potential energy curve, that is, to “jump the gap” between the two branches of the hyperbola. This probability was worked out independently by Landau,3 Zener4 and St¨uckelberg5 in 1932. Of the three, St¨uckelberg did the best job and receives the least credit. This transition probability is 2 γ = 12 , (1) ~vq

where 12 is the minimum energy differnce in the gap, where v is the velocity at the gap, and q is the difference between the slopes of the two adiabatic curves. The point of Teller’s title is that in polyatomic molecules, in which there is more than one parameter that can vary, not only can electronic eigenval- ues cross, but they are likely to do so. For example, in triatomic molecules there are three interatomic distances, which are enough parameters that intersections of electronic eigenvalues as a function of these distances (i.e., the potential energy surfaces) is to be expected. Teller examined this case, showed that the surfaces look like cones in the neighborhood of the intersec- tion, and generalized the Landau-Zener-St¨uckelberg transition probability, realizing that it could be applied on a ray-by-ray basis of the WKB wave functions. He also did a partial WKB analysis of the wave fields near a conical intersection, but missed the fact that the transmitted wave has the form of a Gaussian beam, at least initially, while the wave field that remains on the original potential energy surface develops a Gaussian shadow.6 November 10, 2009 8:53 WSPC - Proceedings Trim Size: 9in x 6in 07˙Teller

64

3. Coupled Wave Equations

I shall now present three examples of coupled wave equations that will put the problem of conical intersections or mode conversion into a broader context. The first is the problem of a neutral, spinning particle, say, a neutron, in an inhomogeneous magnetic field, as in the Stern-Gerlach experiment. The

wave function is the 2-component spinor ψ = (ψ1, ψ2), and the Hamiltonian is p2 H = µ B(x), (2) 2m − · where

Bz Bx iBy µ B(x) = µ0 σ B(x) = µ0 − . (3) · · B + iB B  x y − z  Writing out the time-dependent Schr¨odingerequation as a matrix in spinor space, we have p2 ∂ 1 0 B B ψ i~ µ z − 1 = 0. (4) 2m − ∂t 0 1 − 0 B B ψ      + − z   2  It looks like a 2 2 version of the Schr¨odingerequation, with a “potential × energy” that is a matrix. Unlike the potential energy matrices that occur in the Born-Oppenheimer approximation, this one is not real symmetric, it is complex Hermitian.

The second example is the H3 molecule. See Fig. 1, which shows the coordinates used. Vectors r1 and r2 are Jacobi vectors describing the posi- tions of the hydrogen nuclei in the center-of-mass frame, while vectors xi, i = 1, 2, 3 give the positions of the electrons relative to the nuclear center of mass. Now let uα(x1, x2, x3) be a fixed basis of electronic wave functions, for example, harmonic oscillator eigenfunctions centered at the nuclear cen- ter of mass. These eigenfunctions are fixed in the sense that they do not depend on the nuclear positions. Then expand the total wave function Ψ according to

Ψ(r1, r2; x1, x2, x3) = ψα(r1, r2)uα(x1, x2, x3). (5) α X Then the time-independent Schr¨odingerequation for the molecule can be written ∞ p2 p2 1 + 2 E δ + V (r , r ) ψ (r , r ) = 0, (6) 2m 2m − αβ αβ 1 2 β 1 2 βX=1    November 10, 2009 8:53 WSPC - Proceedings Trim Size: 9in x 6in 07˙Teller

65

where

V (r , r ) = u H (r , r ) u . (7) αβ 1 2 h α| elec 1 2 | βi This is the exact Schrdinger¨ equation for the molecule after the neglect of spin and fine structure, that is, no Born-Oppenheimer approximation has

been made as yet. Notice that the potential energy matrix Vαβ is real and symmetric. e

H x3 e r2 x1 e

x2 H

r1 H

Fig. 1. Coordinates for the H3 molecule.

The third example concerns the propagation of electromagnetic waves in the ionosphere. Waves are launched from the ground at a certain latitude and propagate into the ionosphere, a layer in which there is a nonzero density of free electrons. Since the earth’s radius is large compared to the thickness of the atmosphere, the latter is modeled as a slab, with z-axis vertical. The magnetic field B of the earth is directed at an angle α to the vertical, as shown in Fig. 2. November 10, 2009 8:53 WSPC - Proceedings Trim Size: 9in x 6in 07˙Teller

66 z

B α 0

y

x

Fig. 2. Coordinates for wave propagation in the ionosphere.

Let the electron number density be ne = ne(z), and let ωe and Ωe be the electron plasma frequency and gyrofrequency, respectively, so that 4πn e2 eB ω2 = e , Ω = 0 . (8) e m e mc Due to the translational invariance in the x- and y-directions, we can assume a wave field of the form, E(x, t) = E(z)ei(kxx+ky y−ωt), (9)

where kx, ky and ω are given. The frequency ω is the frequency of the transmitter, and kx and ky determine the launch direction of the waves. We introduce the dimensionless parameters, Ω ω2(z) Y = e ,Z(z) = e , (10) ω ω2 and then the Stix parameters,7 Z Z P = 1 Z,L = 1 ,R = 1 . (11) − − 1 + Y − 1 Y − Next we introduce the index of refraction vector, c N = (k xˆ + k yˆ + k ˆz), (12) ω x y z November 10, 2009 8:53 WSPC - Proceedings Trim Size: 9in x 6in 07˙Teller

67

where kx and ky are real parameters as described above (they are c- numbers), and where kz is understood as the operator (or q-number), ∂ k = i . (13) z − ∂z Next we transform the electric field to the helicity basis, B ˆ 0 1 ˆ b = , eˆ = [xˆ i(b xˆ)]. (14) B0 √2  × Then the wave equation can be written,

2 2 L N+N− Nb N+ N+Nb E+ − 2 − 2 N R N N− N N−N E− = 0. (15)  − − + − b b    N−Nb N+Nb P 2N+N− Eb  −    The components of the matrix are now second order differential operators, with a z-dependence on the diagonal.

4. Common Notation for Coupled Wave Equations Let us adopt a common notation that will cover all three of these examples and others as well. We will write these equations in the form,

N ˆ ˆ Dαβ(xˆ, k) ψβ(x) = 0, (16) βX=1 where

x = (x1, . . . , xn), k = (k1, . . . , kn). (17)

Wave functions live on Rn, which is topologically trivial. “Spinor” indices are α, β = 1,...,N. In the Stern-Gerlach example, N = 2 and n = 4, with coordinates (x, t); in the H example, N = and n = 6, with coordinates 3 ∞ (r1, r2); and in the ionosphere example, N = 3 and n = 1, with coordinate z. Operators (q-numbers) are indicated with a hat, while the absence of a hat indicates an ordinary number (a c-number). For example,

ˆ ∂ xˆi = multiplication by xi, ki = i . (18) − ∂xi We choose units so that ~ = 1, giving us a uniform notation for quantum ˆ and classical operators (and so thatp ˆi = ki). November 10, 2009 8:53 WSPC - Proceedings Trim Size: 9in x 6in 07˙Teller

68

ˆ 5. Properties of Dαβ ˆ The matrix Dαβ is a matrix of operators. It is Hermitian in the sense that ˆ † ˆ (Dαβ) = Dβα, (19) ˆ although in general the individual components of Dαβ are not Hermitian. ˆ In the Stern-Gerlach and H3 problems, Dαβ is a multiple of the identity plus a “potential energy” matrix, ˆ ˆ Dαβ = (fn of k) δαβ + Vαβ(xˆ). (20) ˆ For the H3 problem, Dαβ is “real,” that is, ˆ † ˆ (Dαβ) = Dαβ. (21) ˆ It turns out that in cases N > 2, the matrix Dαβ can be reduced to a 2 2 matrix by adiabatic means. See the references for how and under what × circumstances this can be done. In the following we will henceforth assume that N = 2. (The Stern-Gerlach example already has N = 2.) Assuming that N = 2, the wave equation becomes Dˆ (xˆ, kˆ) Dˆ (xˆ, kˆ) ψ (x) 11 12 1 = 0. (22) Dˆ (xˆ, kˆ) Dˆ (xˆ, kˆ) ψ (x) 21 22 !  2  ˆ ˆ ˆ † ˆ Note that D11 and D22 are Hermitian, and that (D12) = D21. The number of dimensions in x-space, denoted n, can at this point be anything.

6. Elements of the Semiclassical Analysis

We will be interested in analyzing Eq. (22) by semiclassical, that is, short- wavelength, means. This will involve converting operators, that is, functions of (xˆ, kˆ), into “classical” functions, that is, functions of (x, k). This is also referred to as “dequantization.” The opposite process, that of converting functions into operators, is “quantization.” The most familiar method for quantization is the Dirac prescription, which makes the replacements, x xˆ = multiplication by x , (23) i → i i ˆ ∂ ki ki = i . (24) → − ∂xi Dirac quantization is not unique because of issues of operator ordering, that ˆ is, xi and ki commute under ordinary multiplication, but [ˆxi, kj ] = i δij . As a result, Dirac dequantization is not invertible (a given operator corresponds to more than one function, depending on how noncommuting products of ˆ xˆi and ki are written). November 10, 2009 8:53 WSPC - Proceedings Trim Size: 9in x 6in 07˙Teller

69

A better method of quantization and dequantization for our purposes is that due to Weyl.8 If Aˆ is an operator and A(x, k) the corresponding function under Weyl quantization, then the two are connected by invertible integral transforms:

k s s s A(x, k) = dns e−i · x + Aˆ x , (25) h 2| | − 2i Z and n n n 0 0 d k d x d x k x x0 x + x Aˆ = ei ·( − ) A , k x x0 . (26) (2π)n 2 | ih | Z   The function A(x, k) is said to be the Weyl symbol of the operator Aˆ. The Weyl symbol correspondence is identical with Dirac quantization in cases where there are no operator ordering issues. Another useful property is that if A(x, k) is the Weyl symbol of Aˆ, then the Weyl symbol of Aˆ† is A(x, k)∗. In particular, Hermitian operators are mapped into real symbols by the Weyl symbol correspondence.

7. The Dispersion Tensor and the Dispersion Surface ˆ The matrix of Weyl symbols of the operator matrix Dαβ will be called the dispersion tensor. It will be denoted Dαβ(x, k) (without the hat): D (x, k) D (x, k) D = 11 12 . (27) D (x, k) D (x, k)  21 22  ˆ Since Dαβ is a Hermitian matrix of operators, the dispersion tensor is a Hermitian matrix of functions,

∗ Dαβ(x, k) = Dβα(x, k). (28)

There are two main cases that occur in our examples. In the H3 example, Dαβ is real and symmetric, while in the Stern-Gernach and ionospheric problems, it is complex Hermitian. ˆ Since the wave equation is β Dαβ ψβ = 0, it is logical that the semi- classical solution is supported on the surface in the (x, k) phase space given P by

det Dαβ(x, k) = 0, (29)

and that, moreover, the wave function ψβ is somehow proportional to the eigenvector of Dαβ on this surface with eigenvalue 0 (that is, ψβ must somehow lie in the kernel of the dispersion tensor). Equation (29) is one November 10, 2009 8:53 WSPC - Proceedings Trim Size: 9in x 6in 07˙Teller

70

constraint on 2n variables, so it specifies a (2n 1)-dimensional (codimen- − sion 1) surface in phase space. This surface is called the dispersion surface. What does the dispersion surface look like?

D-map B0

k1 k2

3 x2 B B2 B1 x1

Phase Space Hermitian Matrix Space

Fig. 3. The dispersion tensor defines a map from phase space to Hermitian matrix space.

The dispersion tensor defines a map from phase space to Hermitian matrix space, what we shall call the “D-map.” This just the meaning of the functions Dαβ(x, k). The map is illustrated in the case n = 2 (with a 4-dimensional phase space) in Fig. 3. Real coordinates on Hermitian matrix space can be constructed as fol- lows. We use the fact that the three Pauli matrices σ and the identity I span the space of all 2 2 matrices. We write σ = (I, σ) for a kind of × µ 4-vector of Pauli matrices, and we expand Dαβ according to

3 0 i µ D(x, k) = B (x, k) + B (x, k) = B (x, k)σµ, (30) i=1 X where in the final form we adopt a kind of relativistic notation for the contraction of two 4-vectors. The expansion coefficients Bµ are real, since D is Hermitian, and form coordinates on “Hermitian matrix space.” Since σ2 is pure imaginary, the µ = 2 coordinate is not needed for real, symmetric November 10, 2009 8:53 WSPC - Proceedings Trim Size: 9in x 6in 07˙Teller

71

matrices, and we see that real, symmetric matrix space is 3-dimensional with coordinates (B0,B1,B3), while complex Hermitian matrix space is 4-dimensional with coordinates (B0,B1,B2,B3). Although of course this expansion has nothing to do with relativity in a physical sense, nevertheless the relativistic notation is deliberate. That is because the Minkowski metric plays an important role in matrix space. In particular,

µ det D = B Bµ, (31)

µ so singular matrices det D = 0 lie on the light cone B Bµ = 0 in matrix space. Moreover the rank of the dispersion matrix can be determined by the position on the light cone. That is, at the origin of matrix space (the vertex of the light cone), the rank of D vanishes (that is, the whole matrix vanishes), while at other points on the light cone the rank is 1.

D-map B0

k

B3 x B1

2d Phase Space 3d Matrix Space

Fig. 4. The D-map in the case n = 1, with a real, symmetric dispersion tensor.

Thus the dispersion surface is the preimage of the light cone under the D-map. Assuming the D-map is generic, that is, assuming that its compo- nents are “randomly chosen” functions of (x, k), the geometrical structure of the dispersion surface is largely determined by a count of the dimensions (the number of dimensions of phase space and of matrix space). November 10, 2009 8:53 WSPC - Proceedings Trim Size: 9in x 6in 07˙Teller

72

8. D-map and Dispersion Surface in One Dimension The simplest case is n = 1, that is, a 2-dimensional phase space that is mapped onto a 3- or 4-dimensional matrix space. This case is illustrated in Fig. 4 for the case of a real-symmetric dispersion tensor, for which matrix space is 3-dimensional. The D-map maps a 2-dimensinal space into a 3- dimensional space.

B0

Π

k

B3

x

B1

Fig. 5. Intersection of the image of phase space Π under the D-map and the light cone in matrix space.

The image of phase space under the D-map is some 2-dimensional sur- face in matrix space. The light cone is also a 2-dimensional surface in ma- trix space, and the two surfaces are likely to intersect. If they do so, they are likely to intersect in a one-dimensional curve. The dispersion surface in phase space is the preimage of this curve under the D-map, that is, it November 10, 2009 8:53 WSPC - Proceedings Trim Size: 9in x 6in 07˙Teller

73

is also a one-dimensional curve. It is unlikely, however, that the image of phase space will pass through the origin, so the dispersion tensor, while singular on the dispersion surface, is not likely to vanish on it. This is a more modern version of the no-crossing rule formulated by von Neumann and Wigner.

1.5

P 1.0 L

0.5 R Nz 0.0

-0.5

-1.0

-1.5 0.0 0.5 1.0 1.5 Z

Fig. 6. Avoided crossing in the propagation of waves in the ionosphere.

The geometry of these surfaces and curves in matrix space is illustrated in Fig. 5. The image of phase space is denoted Π. On it are illustrated the images of the x- and k-axes in phase space. Both the surface Π and the axes are curved, since the D-map is in general nonlinear. In the illustration the surface Π does not pass through the origin (something it is unlikely to do), November 10, 2009 8:53 WSPC - Proceedings Trim Size: 9in x 6in 07˙Teller

74

but it ia assumed that it passes close to the origin. Otherwise, mode conver- sion (the generalization of Landau-Zener-St¨uckelberg transitions) will not occur. Assuming the D-map is generic, a small portion of the image Π will be approximately a plane, which will intersect the light cone in curves that are approximately the two branches of a hyperbola. (Other conic sections are also possible.) The dispersion surface in phase space is the preimage of these approximate hyperbolas. This explains the small hyperbolas at an avoided crossing.

B0

∂Bµ ∂x ∂Bµ ∂k

(x0, k0)

B3

µ B0 Π

B1

Fig. 7. Geometry of the mode conversion point, where the vector from the origin is Minkowski orthogonal to surface Π.

Figure 6 illustrates these conclusions for the problem of ionospheric wave propagation. A diagram of phase space is shown, not in the co-

ordinates (z, kz), but in the dimensionless coordinates Z(z),Nz) where N = (c/ω)k . The dispersion surface is a set of curves labelled with the z z symbols L, R and P , which indicate the physical nature of the wave at various points on the surface (left and right circularly polarized waves, and November 10, 2009 8:53 WSPC - Proceedings Trim Size: 9in x 6in 07˙Teller

75

plasma or electrostatic waves). The arrows show the direction of propaga-

tion of waves on the curves. The parameters of the problem (ω, kx, ky, B0 etc) have been chosen so that an avoided crossing occurs (inside the circle, what we call a “mode conversion region”). At an avoided crossing, there is some probability to “jump the gap” and make a transition. For example, a wave entering the mode conversion region on the L branch will make a tran- sition to a P -wave with some probability. This is what happens when waves are launched from the ground at the right frequency and in the right direc- tion. That probability is a generalization of the Landau-Zener-St¨uckelberg probability given in Eq. (1).

9. The Mode Conversion Point The calculation of that probability involves the Minkowski geometry of ma- trix space in a fundamental way. We begin by defining the “mode conversion point,” which is basically the center of the circle seen in Fig. 6, that is, it is the point of phase space that is the center of the hyperbolas. Since the hyperbolas are only approximate, we must formulate a precise definition. Suppose a plane intersects a cone in a hyperbola. What is the geomet- rical characterization of the center of the hyperbola? It is the point on the plane such that the vector from the origin (the apex of the cone) is Minkowski orthogonal to the plane. In our problem, the image of phase space (surface Π in Fig. 5) is not flat, but assuming it is approximately flat, we can define the “center” of the hyperbola as the point of Π where the vector from the origin is Minkowski orthogonal to Π. This is illustrated in Fig. 7. In that figure, the mode conversion point is designated with a 0 subscript, for example, the vector from the origin at the mode conversion µ point is B0 , and the phase space coordinates of the mode conversion point µ µ are denoted (x0, k0). The vectors ∂B /∂x and ∂B /∂k, evaluated at the mode conversion point, lie in the tangent plane to the surface Π at the mode conversion point, and span it; thus, they are themselves orthogonal µ to B0 . Thus, in analytic terms, we define the mode conversion point as the point at which

∂B ∂B Bµ µ = Bµ µ = 0. (32) ∂x ∂k

µ This in turn implies that det D = B Bµ is stationary at the mode conver- sion point. November 10, 2009 8:53 WSPC - Proceedings Trim Size: 9in x 6in 07˙Teller

76

10. Symmetries of the Transition Probability

The transition probability (the generalization of the Landau-Zener- St¨uckelberg formula) can be almost uniquely determined by the symme- tries it possesses. There are three of these (three symmetry groups), related to the ways the given set of wave equations (16) can be transformed into other equations with the same transition probability. We use the intuitive fact that the transition probability must be a function of the dispersion tensor and its derivatives, evaluated at the mode conversion point. The first symmetry group consists of scaling transformations, that is, we multiply the wave equation (16) through by some real constant c = 0, 6 resulting in the transformation D cD . (33) αβ → αβ We require c to be real so that the new dispersion tensor will be Hermitian, as was the old one. The new equations obviously have the same physical content as the old ones, so the mode conversion probability cannot change. This implies that the transition probability must be a homogeneous function of degree 0 of the dispersion tensor and its derivatives. The second symmetry group comes about by performing a change of

basis in spinor space. That is, we define a new wave function φα by

ψα = Sαβ φβ, (34) Xβ where S is a constant (independent of x), invertible, complex, 2 2 matrix. × One might suppose that unitary matrices would suffice to bring about the normal form, but this is not the case. After this transformation, we multiply the wave equation from the left by S†, in order to preserve the Hermiticity of the dispersion tensor. The transformation of the dispersion tensor is D S†DS. (35) → The determinant of S is some nonzero, complex number, but since S only enters in the transformation above in the combination S†S, we can, without loss of generality, assume that this determinant is real. Then, by applying the scaling transformation already considered, we can make this determi- nant +1. Altogether, without loss of generality, we can restrict S to the group SL(2, C) of complex, 2 2 matrices of unit determinant. × When we transform D according to Eq. (35), what happens to the ex- pansion coefficient Bµ in terms of the 4-vector of Pauli matrices? The an- swer is that it gets multiplied by a Lorentz transformation Λ, that is, Bµ Λµ Bν , (36) → ν November 10, 2009 8:53 WSPC - Proceedings Trim Size: 9in x 6in 07˙Teller

77

where 1 Λµ = tr(σµS†σ S). (37) ν 2 ν These formulas are expressions of the (well known in relativistic quan- tum mechanics) fact that SL(2, C) is the double cover of the proper Lorentz group (the identity component of O(3, 1)). Actually, in our applications, the Lorentz group is O(2, 1) for real symmetric dispersion tensors, and O(3, 1) for complex Hermitian ones. We conclude that the transition probability must be invariant under Lorentz transformations, that is, it must be a function of Minkowski scalar products of Bµ and its derivatives. The third symmetry group consists of canonical (or symplectic) trans- formations in the (x, k) phase space. Symplectic covariance is a fundamental principle of semiclassical analysis, as has been appreciated on many levels through the years. One example is the beautiful work of Miller9 on semi- classical matrix elements in integrable systems. Another aspect involves the unitary double cover of the group Sp(2n) of classical, linear canonical transformations, consisting of the so-called metaplectic operators.10 For a mathematical perspective on some of these issues, see the book by Guillemin and Sternberg.11 The implication of this symmetry group for the present discussion is that the mode conversion probability must be a symplectic or canonical invariant, that is, it must be possible to express it in terms of Poisson brackets of Bµ and its derivatives, evaluated at the mode conver- sion point. Another way to see the same thing is to note that the transition probability is a loop integral of k dx around a closed loop on a complex Lagrangian manifold—this aspect of the problem was seen intuitively by Landau in 1932. Such loop integrals are canonical invariants. The importance of canonical invariants in mode conversion was first appreciated by Kaufman and Friedland , who presented expressions for the mode conversion probability in terms of Poisson brackets.12 Using these three invariance principles, we can almost uniquely deter- mine the transition probability. Let us begin by constructing simultaneous Lorentz and canonical invariants. Everything is evaluated at the mode con- µ version point. The simplest canonical and Lorentz invariant is B Bµ. It is obviously a Lorentz invariant, and it is a canonical invariant because it is evaulated at a given point. This invariant is, however, of degree 2 in the dis- persion tensor, not degree 0. We must construct another degree 2 invariant and divide. Another simultaneous Lorentz and canonical invariant is Bµ,B , { µ} November 10, 2009 8:53 WSPC - Proceedings Trim Size: 9in x 6in 07˙Teller

78

where the curly brackets are the Poisson bracket. This quantity, unfor- tunately, vanishes, by the antisymmetry of the Poisson bracket. So also does the quantity B B Bµ,Bν , because of the condition (32). The next µ µ{ } simplest simultaneous Lorentz and canonical scalar is Bµ,Bν B ,B , (38) { }{ µ ν } which is of degree 4 and does not vanish. Therefore we guess that the transition probability is a function of BµB µ . (39) Bµ,Bν B ,B 1/2 |{ }{ µ ν }| In fact, the probability is P = exp( 2πγ), where − BµB γ = µ . (40) 2 Bµ,Bν B ,B 1/2 |{ }{ µ ν }| 11. Conclusions This outline shows the importance of Minkowski and symplectic geome- try in the problem of one-dimensional mode conversion. This geometry is equally important in higher dimensions. I will now provide some references to the literature on this subject. The references are not inteded to be ex- haustive, rather they provide entry points. The subject of Landau-Zener-St¨uckelberg transitions and intersections of surfaces in Born-Oppenheimer theory has an enormous literature going back to the 1937 Teller article and beyond. The field has taken on new dimensions in the last 30 years because of the geometric phase. In this area I will just mention the review articles by Yarkony13 and Mead14 and the book by Nikitin and Umanskii.15 As for generalizations to other systems of coupled wave equations, the themes developed in this article began with the work of Kaufman and Friedland.12,16 My students and I made further contributions somewhat later.17–22 This work was put on a firmer math- ematical foundation by Emmrich and Weinstein,23 a paper that has had quite an influence in mathematical circles since then, as a search on cita- tions will show. For more recent mathematical work in this area, I mention some papers by Colin de Verdi`ere.24–26 Meanwhile, Tracy, Kaufman and Jaun have continued to make developments and applications mode conver- sion theory.27,28

References

1. E. Teller, J. Phys. Chem. 41, 109 (1937). November 10, 2009 8:53 WSPC - Proceedings Trim Size: 9in x 6in 07˙Teller

79

2. J. von Neumann and E. Wigner, Phys. Z. 30, 467 (1929). 3. L. Landau, Sov. Phys. 1, 89 (1932). 4. C. Zener, Proc. R. Soc. A 137, 696 (1932). 5. E. C. G. St¨uckelberg, Helv. Phys. Acta 5, 369 (1932). 6. Robert G. Littlejohn, in Path Integrals from meV to MeV, proceedings of the fourth international conference, Tutzing, Bavaria, May 18–21, 1992, edited by Hermann Grabert et al. (World Scientific, Singapore, 1993). 7. Thomas H. Stix, The Theory of Plasma Waves (New York, McGraw Hill, 1962). 8. N. L. Balazs and B. K. Jennings, Phys. Reports 104, 347. 9. W. H. Miller, Adv. Chem. Phys. 25, 69 (1974). 10. Robert G. Littlejohn, Phys. Rep. 138, 193 (1986). 11. Victor Guillemin and Shlomo Sternberg, Symplectic Techniques in Physics (New York: Cambridge University Press, 1984). 12. A. N. Kaufman and L. Friedland, Phys. Lett. A 123, 387 (1987). 13. David R. Yarkony, Rev. Mod. Phys. 68, 985 (1996). 14. C. Alden Mead, Rev. Mod. Phys. 64, 51 (1992). 15. E. E. Nikitin and S. Ya. Umanskii, Theory of Slow Atomic Collisions, (Springer-Verlag, New York, 1984). 16. L. Friedland and A. N. Kaufman, Phys. Fluids 30, 3050 (1987). 17. Robert G. Littlejohn and William G. Flynn, Phys. Rev. A 44, 5239 (1991). 18. Robert G. Littlejohn and William G. Flynn, Chaos 2, 149 (1992). 19. Robert G. Littlejohn and William G. Flynn, Phys. Rev. Lett. 70, 1799 (1993). 20. Stefan Weigert and Robert G. Littlejohn, Phys. Rev. A 47, 3506 (1993). 21. Robert G. Littlejohn and Stefan Weigert, Phys. Rev. A 48, 924 (1993). 22. William G. Flynn and Robert G. Littlejohn, Ann. Phys. (N.Y.) 234, 403 (1994). 23. C. Emmrich and A. Weinstein, Commun. Math. Phys. 176, 701 (1996). 24. Y. Colin de Verdi`ere,M. Lombardi and J.Pollet, Annales de l’Institut Henri Poincar (Physique thorique) 71, 95 (1999). 25. Y. Colin de Verdi`ere, Annales de l’Institut Fourier, 53, 1023 (2003). 26. Y. Colin de Verdi`ere, Annales de l’Institut Fourier, 54, 1423 (2004). 27. E. R. Tracy, A. N. Kaufman, and A. Jaun, Physics ofPlasmas 14, 82102/1 (2007). 28. A. Jaun, E. R. Tracy, and A. N. Kaufman, Plasma Physics and Controlled Fusion 49, 43 (2007). November 10, 2009 8:55 WSPC - Proceedings Trim Size: 9in x 6in 08˙Haxton

80

EDWARD TELLER AND NUCLEI: ALONG THE TRAIL TO THE NEUTRINO

W. C. HAXTON∗ Institute for Nuclear Theory and Department of Physics, University of Washington, Box 351550, Seattle, WA 98195 ∗E-mail: [email protected] www.int.washington.edu/haxton.html

I discuss two of Edward Teller’s contributions to nuclear physics, the intro- duction of the Gamow-Teller operator in β decay and the formulation of the Goldhaber-Teller model for electric dipole transitions, in the context of efforts to understand the weak interaction and the nature of the neutrino.

Keywords: Edward Teller; beta decay; neutrino properties; axial currents; elec- tric dipole nuclear responses.

1. Introduction It is a great pleasure to take part in the Edward Teller Centennial Sym- posium and to have this opportunity to describe Dr. Teller’s contributions to electroweak nuclear physics. His career in physics began just at the time that the nature of β decay and the likely existence of the neutrino were first becoming clear. Edward’s own contributions to this story are very signifi- cant and involve both neutrino properties and the role of weak interactions in astrophysics. Experiments on radioactive nuclei had, by the late-1920s, demonstrated that the positrons emitted in β decay were produced in a continuous spec- trum, carrying off on average only about half of the nuclear decay energy.1 James Chadwick first obtained this result in 1914 from studies of the beta decay of 214Pb. A particularly definitive calorimetry measurement was done by Ellis and Wooster in 1927 and confirmed and improved by Meitner and Orthman in 1930. Speculative explanations included Niels Bohr’s sugges- tion that Einstein’s mass/energy equivalence might not hold in the “new quantum mechanics,” and Chadwick’s observation that perhaps some un- observed radiation accompanied the positron. August 13, 2008 15:6 WSPC - Proceedings Trim Size: 9in x 6in LLNL˙teller November 10, 2009 8:55 WSPC - Proceedings Trim Size: 9in x 6in 08˙Haxton

2 81 In 1930 Wolfgang Pauli, who Bohr had once described as a “genius, In 1930 Wolfgang Pauli, who Bohr had once described as a “genius, comparable perhaps only to Einstein himself,” hypothesized that an unob- comparable perhaps only to Einstein himself,” hypothesized that an unob- served,served, neutral, neutral, spin-1/2 spin-1/2 “neutron,” later later renamed renamed the the neutrino neutrino by by Fermi, Fermi, accountedaccounted for for the the apparent anomaly – – a a new new particle particle with with a a mass mass less less than than 1%1% that that of of the the proton. proton. His suggestion came came in in a a letter letter to to the the participants participants of of aa conference conference in in T¨ubingen T¨ubingenthat that began with with “Liebe “Liebe radioaktive radioaktive Damen Damen und und Herren!”Herren!” Reflecting Reflecting perhaps the more conservative conservative nature nature of of theorists theorists of of thatthat era, era, he he later later worried: “I have done done a a terrible terrible thing. thing. I I have have postulated postulated aa particle particle that that cannot cannot be detected.” Pauli’s Pauli’s first first public public presentation presentation on on the the 2 neutrinoneutrino did did not not come until the 1933 7th 7th Solvay Solvay Conference. Conference.2

FigFig.. 1. 1. The The four-fermion four-fermion interaction Fermi proposed proposed as as a a model model for forββdecadecay,y, an an analog analog ofof the the electromagnetic electromagnetic interaction apart from from the the absence absence of of the the electromagnetic electromagnetic field. field. PhotoPhoto of of Fermi Fermi (note (note the blackboard error) courtesy courtesy of of Argonne Argonne National National Laboratory. Laboratory.

Today’sToday’s neutron neutron was found by Chadwick Chadwick in in 1932. 1932. Fermi, Fermi, who who had had fol- fol- lowedlowed Pauli’s Pauli’s suggestion suggestion and other developments developments in inββdecay,decay, in in 1934 1934 pro- pro- posedposed a a model model of of the weak interaction, based based on on an an analogy analogy with with electro- electro- 3 magnetism.magnetism.3 AsAs shown in Fig. 1, a proton proton bound bound in in a a nucleus nucleus is is transformed transformed into a neutron, with the emission of a positron and νe. The interaction oc- into a neutron, with the emission of a positron and νe. The interaction oc- curs at a point, so Fermi’s model has no counterpart to the electromagnetic curs at a point, so Fermi’s model has no counterpart to the electromagnetic field. Remarkably, apart from axial currents and the associated parity vio- field. Remarkably, apart from axial currents and the associated parity vio- lation, this description is the correct low-energy limit of today’s standard lation, this description is the correct low-energy limit of today’s standard model. It anticipated future developments in which the electromagnetic model. It anticipated future developments in which the electromagnetic and weak interactions would be unified, in the standard model and in the and weak interactions would be unified, in the standard model and in the nuclear response to these interactions. nuclear response to these interactions. November 10, 2009 8:55 WSPC - Proceedings Trim Size: 9in x 6in 08˙Haxton

82

2. Teller4 and Gamow6 Edward Teller completed his PhD in Leipzig in the same year, 1930, that Pauli made his suggestion of the neutrino. Teller worked with Werner Heisenberg on the quantum mechanics of molecular hydrogen, and had benefited from the many visitors attracted to the university. One of special note was George Gamow, who visited in 1930, accompanied by Lev Landau. Gamow had described barrier penetration in 1928 to explain α decay, set- ting the stage for later treatments of nuclear astrophysics and the Gamow peak. Teller became an assistant at G¨ottingenin 1931, helping Eucken and Franck. Through his friendship with Czech physicist George Placzek, Teller received an invitation to visit Fermi in the summer of 1932. Teller describes the circumstances:5 Placzek wanted to continue with his work in the holidays while G¨ottingenwas closed. I wanted to go home to Budapest and he said: “No. I, Placzek, want to visit with Fermi in Rome and you come along.” In a way, I was interested but I had just started to make my own money, needed little help from home. Didn’t know quite how to pay for my stay in Rome. “Oh said Placzek – I will take care of that. I’ll ask Fermi.” Here I get a copy of a letter from Fermi, that he has written to appropriate authorities in Hungary – I hear that Dr. Teller is considering to visit Rome for a few weeks. He is a very famous physicist, and I want his cooperation. Could you please help him to get to Rome and to stay there? Fermi and I had never met. That he had reason to consider me as a famous physicist was, to say the very least, an impudent exaggeration. But what makes the story particularly enjoyable for me is that together with the copy of the letter to the Hungarian authorities, I got, at- tached, a little note from Fermi: Dear Dr. Teller, I am sending you this copy. I want you to know that actually I would be really very happy to see you in Rome. So he took back the exaggeration but replaced it with a, a premature offer to friendship which, of course, became a very real friendship in the course of time. This must have been an exciting summer to have visited Fermi. A third visitor, Hans Bethe, had also been invited. The neutron had been discovered a few months earlier. (Teller later notes that Fermi’s studies of neutron interactions with nuclei, begun in 1934 and revealing the odd activation of uranium, could have profoundly affected world politics, had Fermi correctly November 10, 2009 8:55 WSPC - Proceedings Trim Size: 9in x 6in 08˙Haxton

83

interpreted the results.) Teller’s friend Gamow had resolved to leave Russia by this point. In 1932 he made two attempts to defect by kayak with his wife, Lyubov Vokhminzeva, first via the Black Sea to Turkey, and later from Murmansk to Norway. Both attempts failed because of poor weather conditions. But in 1933 a simpler opportunity arose when both were granted visas to leave Leningrad to attend the 7th Solvay Conference – the same conference where Pauli finally discussed the neutrino. By 1934 Gamow had moved to the US to join the faculty at George Washington University. Teller’s path led him, after two years in G¨ottingen,to England in 1933, a move facilitated by the Jewish Rescue Committee. He soon arrived in Copenhagen to spend a year with Niels Bohr. In February 1934 he mar- ried Augusta Maria Harkanyi, the sister of a friend. In 1935, at the behest of Gamow, Teller was invited to become a professor at George Washing- ton University. He remained there for the next six years. In March 1936 Gamow and Teller submitted a paper on β decay to the Physical Review arguing that a spin-dependent interaction – an axial current – was required to account for observed selection rules.

3. Gamow-Teller Transitions The Gamow-Teller paper’s abstract reads7 1. The selection rules for β-transformations are stated on the basis § of the neutrino theory outlined by Fermi. If it is assumed that the spins of the heavy particles have a direct effect on the disintegration these rules are modified. 2. It is shown that whereas the original § selection rules of Fermi lead to difficulties if one tries to assign spins to the members of the thorium family the modified selection rules are in agreement with the available experimental evidence. Fermi’s treatment of β decay in analogy with electromagnetism predicts that weak transitions will obey the selection rules of a vector current, which in contemporary notation are displayed in Table 1. In the nonrelativistic, long-wavelength limit – the allowed limit – only the µ = 0 charge operator arises, with selection rules ∆J = 0 ∆π = 0, e.g., 0+ 0+. ↔ The Gamow-Teller paper also notes that Fermi had introduced, to ensure relativistic invariance, the velocity operator ~p/M, with selection rules + ∆J = 0, 1 but no 0 0 ∆π = 1, e.g., 0 1−. ± ↔ ↔ November 10, 2009 8:55 WSPC - Proceedings Trim Size: 9in x 6in 08˙Haxton

84

These operators are shown in the first row of Table 1.

Table 1. Long-wavelength vector-current operators, first-order corrections pro- portional to k~r, and long-wavelength axial-vector operators. µ=0 µ=1,2,3 V Jr µ (~) 1 ~p/M V i~k ~r Jr µ (~) e · k~r kr[~ ~p/M]J=0,1,2 A ⊗ Jr (~) gσA~ ~p/M gσA~ µ ·

Gamow and Teller considered an additional operator arising from the three-momentum transfered to the nucleus, obtained from a spherical har- i~k ~r monic expansion of e · . The first entry in the second row of Table 1, the dipole operator, is first-forbidden, suppressed by one power of ~k, with the same selection rules as the velocity operator. Its matrix elements can be re- lated to those of the velocity operator through current conservation. (This operator is the subject of another famous Teller paper, discussed later in this talk.) Gamow and Teller argued that β-decay rates for such an operator 3 would be suppressed typically by 10− . They did not discuss explicitly ∼ the second-forbidden operator appearing in the second row, which could mediate 0+ 1+ transition, but would be suppressed by an additional ↔ 2 factor of 10− due to relativity, as nucleon velocities in the nucleus are ∼ of order ~v/c 0.1. But certainly they would have recognized that this | | ∼ operator exists and is numerically insignificant. Because the selection rules for allowed and first-forbidden operators built on the vector current could not explain strong magnetic transitions seen in β-decay experiments, Gamow and Teller introduced second allowed operator, the spin operator corresponding to the space-like part of an axial- A vector current Jµ (~r), as shown in the third row of Table 1. The selection rules for this operator are

∆J = 0, 1 but no 0 0 ∆π = 0, e.g., 0+ 1+. ± ↔ ↔ Gamow and Teller designated the Fermi operator – the vector charge operator – M1 and the new Gamow-Teller operator - the axial three-current – M2, noting

Either the matrix element M1 or the matrix element M2 or finally a linear combination of M1 and M2 will have to be used to calculate the probabilities of the β-disintegrations. If the third possibility is the correct one, and the two coefficients in the linear combination have the same order of magnitude, then all transitions [satisfying November 10, 2009 8:55 WSPC - Proceedings Trim Size: 9in x 6in 08˙Haxton

85

the selection rules] would now lie on the first Sargent curve.

The first Sargent curve is the term then used to designate a strong, allowed transition. This observation is remarkable in several ways. It gives the correct al- lowed rate in the absence of polarization ω f 1 i 2 + g2 f ~σ i 2. ∼ |h | | i| A|h | | i| Gamow and Teller suggested that the vector and axial coupling might be similar in magnitude. Today’s standard model describes the coupling to the underlying quarks as V A. Also, while the following issue does not arise − for rates – the focus of the Gamow-Teller paper – one could accomplish the suggested generalization of Fermi’s theory in two ways. In a modern notation, J V J V µ + J AJ Aµ J V J V µ  µ µ µ → (J V J A)(J V µ J Aµ) µ − µ − That is, one could add an axial current-current interaction to Fermi’s vector-vector interaction, or alternatively generalize the current to V A. − The latter would have anticipated by 20 years parity violation in the weak interaction. While Gamow and Teller do not comment explicitly on this issue or mention parity violation, their description of the matrix elements M1 and M2 is curious. They speak of a linear combination of M1 and M2 – that is, a sum of vector and axial-vector amplitudes, which they suggest would be of comparable importance. They were remarkably close to the standard model. The introduction of the Gamow-Teller operator was critical to efforts in the 1930s to understand the mechanisms for hydrogen burning in main- sequence stars. The initiating step in the pp chain synthesis of 4He

+ p + p (L = 0 S = 0 T = 1) d (L = 0 S = 1 T = 0) + e + νe → is a Gamow-Teller transition. The structure of the weak interaction – the amplitudes that might be constructed from vector (V), axial-vector (A), scalar (S), pseudoscalar (P), and tensor (T) terms at low energies – was not fully resolved until 30 years later. Teller had another connection with this story, through his University of Chicago student C. N. Yang (1946-9). In 1957 Lee and Yang pointed out that parity conservation was poorly established in the weak interaction, and that its violation might explain puzzling decay properties of neutral kaons. Quickly following this suggestion Wu, Ambler, Hayward, Hoppes, November 10, 2009 8:55 WSPC - Proceedings Trim Size: 9in x 6in 08˙Haxton

86

and Hudson found an angular asymmetry in the βs produced in the decay of polarized 60Co, and Garwin, Lederman, and Weinrich found highly po- larized muons in pion β decay. Finally, Goldhaber, Grodzins, and Sunyar demonstrated that β decay neutrinos are left-handed, ruling out possibili- ties like S+T in favor of V-A.

4. Particles, Antiparticles, and Neutrino Mass While the V A nature of the weak interaction may seem an old story, it has − a modern connection to some very important open questions regarding the neutrino. The neutrino is unique among standard model fermions in that it lacks a charge or any other additively conserved quantum number. Such quantum numbers reverse sign under particle-antiparticle conjugation, and thus distinguish particles from their antiparticles. Thus we know that the electron has a distinct antiparticle, the positron with its opposite charge. But in the case of the neutrino, the need for a distinct antiparticle is unclear: it is possible that the neutrino is its own antiparticle. This might prompt one to do the gedanken experiment illustrated in the top panel of Fig. 2. The first step is to define the νe as the particle that accompanies the positron produced by a β+ source. The second step is to determine what that particle does when it strikes a target. One finds

it produces e−s. Next define theν ¯e as the particle that accompanies the electron pro- duced by a β− source. Then one finds that this particle, on striking a target, produces an e+. From a comparison of the two experiments it appears that the νe andν ¯e are distinct particles: they produce different final states when they interact in targets. As there is no obvious quantum number distinguishing the νe andν ¯e, would would then be tempted to introduce one, the lepton number le, re- quiring it to be additively conserved:

lepton le e− +1 + e 1 le = le. − ⇔ X X νe +1 in out ν¯e 1 − This would account for the results of the “experiments” illustrated in Fig. 2. Historically this issue was connected with the early development of the Cl detector famous in solar neutrinos. After Pontecorvo suggested using Cl, Alvarez investigated various background issues, as he was considering August 13, 2008 15:6 WSPC - Proceedings Trim Size: 9in x 6in LLNL˙teller November 10, 2009 8:55 WSPC - Proceedings Trim Size: 9in x 6in 08˙Haxton

8 87

Fig. 2. An operational test of the identity of the νe and ν¯e, prior to the discovery of Figparity. 2. nonconservation. An operational testIf one of were the identity to define of the theνeνeasand theν ¯e partner, prior ofto the the positron discovery in of + parityβ decay nonconservation. and theν ¯e as If the one partner were to of definethe electron the νe inasβ− thedecay, partner then of these the positron neutrinos in + − βwoulddecay appear and tothe beν ¯e distinctas the operationally, partner of the when electron their in interactionsβ decay, in then targets these are neutrinos tested. wouldThis would appear seem to be to distinct require operationally,the introduction when of a their quantum interactions number in like targets lepton are number tested. Thisto distinguish would seem the toν requirefrom the theν ¯. introduction of a quantum number like lepton number to distinguish the ν from theν ¯.

testing ν/¯ν identity, using reactorν ¯es. Later Davis placed a Cl detector testingprototypeν/¯ν nearidentity, the Savannah using reactor Riverreactorν ¯es. Later to search Davis for placed a Cl detector prototype near the Savannah River reactor to search for 37 37 Cl +ν ¯ Ar + e− 37 e 37 − Cl +ν ¯e → Ar + e

but found no Ar, indicating that the νe andν ¯e are distinct at the level of but5%. found no Ar, indicating that the νe andν ¯e are distinct at the level of ∼ ∼ 5%.There is an elegant way to do the Savannah River experiment at the nuclearThere level, is an with elegant neutrinoless way toββ dodecay. the Savannah8 In this River process experiment a nucleus (N,Z) at the 8 nucleardecays throughlevel, with a second-order neutrinoless weakββ decay. interactionIn this process a nucleus (N,Z) decays through a second-order weak interaction

(N,Z) (N 2,Z + 2) + e− + e− (N,Z) → (N − 2,Z + 2) + e− + e−

with the emission of two electrons. If the νe andν ¯e are identical if the with the emission of two electrons. If the ν andν ¯ are identical−− if the neutrino is a Majorana particle then the neutrinoe emittede in one neutron − neutrinoβ decay is can a Majorana be reabsorbed particle on− athen second the neutron, neutrino as emitted shown in in one the neutron upper βpaneldecay of can Fig. be 3. reabsorbed But we do not on a see second this process neutron, in asnature. shown Thus in the it seems upper panel of Fig. 3. But we do not see this process in nature. Thus it seems once again that the νe andν ¯e must be distinct, carrying opposite lepton oncecharges. again As that the middle the νe panelandν ¯ illustrates,e must be neutrinoless distinct, carrying double oppositeβ decay would lepton charges. As the middle panel illustrates, neutrinoless double β decay would then be strictly forbidden: the final state of two electrons (le = 2) cannot then be strictly forbidden: the final state of two electrons (l = 2) cannot result from the decay of an initial state with le = 0. e result from the decay of an initial state with le = 0. August 13, 2008 15:6 WSPC - Proceedings Trim Size: 9in x 6in LLNL˙teller November 10, 2009 8:55 WSPC - Proceedings Trim Size: 9in x 6in 08˙Haxton

88 9

Fig. 3. Panel a) neutrinoless double beta decay in the case of a Majorana neutrino Fig.appears3. Panelnaively a) to neutrinoless be in conflict doublewith experiment, beta decay as it in produces the case a of substantial a Majorana decay neutrino rate. appearsIn the Dirac naively case to (Panel be in b))conflict the decay with isexperiment, strictly forbidden as it produces by lepton a number substantial conservation: decay rate. In the Dirac case (Panel b)) the decay is strictly forbidden by lepton number conservation: theν ¯e produced in the first decay is the wrong neutrino to complete the second step. theA Diracν ¯e produced neutrino in is the thus first allowed decay by is experiment,the wrong neutrino as it is consistent to complete with the the second absence step. Aof Dirac neutrinoless neutrino double is thus beta allowed decay, bya process experiment, so far asnot it seen is consistent in nature. with Panel the c) shows absence ofthe neutrinoless Majorana case, double including beta decay, the effects a process of neutrino so far handedness.not seen in nature.A Majorana Panel neutrino c) shows theis allowed Majorana by experiment,case, including provided the effects the mass of neutrino is sufficiently handedness. small (so A the Majorana handedness neutrino is issufficiently allowed by exact). experiment, This requires provided the the Majorana mass is neutrino sufficiently mass small to be (so< the1 eV, handedness a result is sufficiently exact). This requires the Majorana neutrino mass to be < 1 eV, a result compatible with other tests of mass, such as neutrino oscillations. ∼∼ compatible with other tests of mass, such as neutrino oscillations.

But there is a hidden assumption in the above arguments, one that startsBut with there the is axial a hidden current assumption introduced in by the Gamow above and arguments, Teller. We one can that remove all references to lepton number so that ν¯e = νe but suppress starts with the axial current introduced− by Gamow| i | andi − Teller. We can double β decay with a different label, the handedness of the neutrino. As the remove all references to lepton number − so that |ν¯ei = |νei − but suppress doubleGoldhaber,β decay Grodzins, with a different and Sunyar label, experiment the handedness would show of the in neutrino. 1957, because As the Goldhaber,the Gamow Grodzins, and Teller and spin Sunyar interaction experiment does appear would show with in Fermi’s 1957, vector because interaction in the combination V-A, the (anti)neutrino emitted in β decay the Gamow and Teller spin interaction does appear with Fermi’s− vector is righted-handed, while the neutrino that produces an e when scattering interaction in the combination V-A, the (anti)neutrino emitted− in β− decay in a target is left-handed. Thus, in the third panel of Fig. 3, we find another is righted-handed, while the neutrino that produces an e− when scattering mechanism for suppressing double β decay, without the assumption of a in a target is left-handed. Thus, in the third panel of Fig. 3, we find another conserved lepton number: the neutrino produced in the first beta decay has mechanism for suppressing double β decay, without the assumption of a conserved lepton number: the neutrino produced in the first beta decay has November 10, 2009 8:55 WSPC - Proceedings Trim Size: 9in x 6in 08˙Haxton

89

the wrong handedness to generate a neutrino by scattering off a second nucleon. These assignments do not forbid double β decay we eliminated lepton − number and its absolute conservation but only suppress it: the handed- − ness of the neutrino is not exact because of its mass. The amplitude in panel c) is proportional to the handedness admixture

mν 8 mν 3 10− , Eν ∼ × 1 eV

where we have estimated the energy of the exchanged neutrino to be Eν 1 1 ∼ R− 6f − for a typical heavy nucleus. The same arguments apply to nucleus ∼ the Savannah River experiment and other tests that naively suggest the ν must have a distinct antiparticle. Thus this discussion shows that there are two descriptions of massive neutrinos, and both are consistent with nature, for light neutrinos. These are illustrated in Fig. 4. The first is the two-component Majorana case: the neutrino is its own antiparticle, so that under CPT the νLH νRH . One | i → | i can also consider the constraints of Lorentz invariance. If one boosts to a frame moving faster than a massive neutrino, momentum is reversed but not spin. The handedness is then flipped: Lorentz invariance requires a right- handed counterpart to a left-handed state, and the reverse. Thus a two- component neutrino can satisfy the constraints of both particle-antiparticle conjugation and Lorentz invariance. Alternatively, one can introduce a lepton number to distinguish the ν andν ¯. Lepton number reverses under particle-antiparticle conjugation, but not under Lorentz boosts. Thus four neutrino components are required to satisfy the constraints of particle-antiparticle conjugation and Lorentz invariance. This is the Dirac case of Fig. 4. Our minimal standard model of particle physics does not allow neutrino mass: Dirac masses are absent because there is no right-handed neutrino field, and Majorana masses are absent because they require interactions that are poorly behaved at high energies. But neither of these standard-model restrictions is likely to hold in the more general models that will someday replace the standard model; nor is the second concern of any importance if one adopts a modern view that the standard model is an effective theory that should be restricted to lower energies. We now know a new, extended standard model is needed, because neu- trinos are massive. The Super-Kamiokande and SNO experiments have demonstrated that atmospheric and solar neutrinos oscillate. While oscil- lation experiments constrain differences in the squares of neutrino masses, August 13, 2008 15:6 WSPC - Proceedings Trim Size: 9in x 6in LLNL˙teller November 10, 2009 8:55 WSPC - Proceedings Trim Size: 9in x 6in 08˙Haxton

11 90

Fig. 4. The two-component (Majorana) and four-component (Dirac) neutrino schemes, Fig. 4. The two-component (Majorana) and four-component (Dirac) neutrino schemes, showing the relationships between the components under Lorentz boosts and particle- showing the relationships between the components under Lorentz boosts and particle- antiparticle conjugation. antiparticle conjugation.

those differences tell us that at least one neutrino has a mass m > 0.04 eV. > thoseWe also differences have the tellν mass us that bounds at least one neutrino has a mass m∼∼ 0.04 eV. We also have the ν mass bounds m < 6.6 eV (laboratory) m < 0.7 eV (cosmology) XX i X i i mi <∼∼6.6 eV (laboratory) i mi ∼<∼ 0.7 eV (cosmology) The formeri comes from combining tritiumi β decay mass limits with mass 2 2 2 Thedifferences former comesδm = frommi combiningmj known tritiumfrom oscillationβ decay experiments, mass limits while with massthe 2 2 − 2 differenceslater is derivedδm = frommi cosmological− mj known arguments, from oscillation that massive experiments, neutrinos while inhibit the laterthe is growth derived of fromstructure cosmological on large scales. arguments, that massive neutrinos inhibit the growthThis chain of structure of argument on large leads scales. to an interesting observation: while we mustThis look chain to extended of argument models leads for anto explanationan interesting of neutrino observation: mass, while it is at we mustfirst look not clear to extended how a more models unified for antheory explanation can account of neutrino for neutrino mass, masses, it is at firstsince not they clear are how so much a more smaller unified than theory thecan masses account of other for standardneutrino modelmasses, 6 sinceparticles. they Aare group so much theory smaller factor thanis not the going masses to generate of other the standard factor of 10model− particles. A group theory factor is not going to generate the factor of 10−6 November 10, 2009 8:55 WSPC - Proceedings Trim Size: 9in x 6in 08˙Haxton

91

or more to explain the ratio mνe /me. But a elegant resolution of this puzzle is provided by the special freedom available with neutrinos, the possibility of both Dirac and Majorana mass terms.9 Neutrinos and other standard- model fermions can share the same Dirac mass scale mD. But the seesaw mechanism, in addition, postulates a heavy right-handed Majorana neu- trino mass mR, yielding a mass matrix

0 mD light mD   ⇒ mν mD   mD mR diagonalize ∼ mR

Thus a natural “small parameter” mD/mR emerges that explains why neu- trinos are so much lighter than other fermions. The scale mR represents new physics. If one takes

2 mν δmatmos. 0.05 eV 15 ∼ p ∼  mR 0.3 10 GeV, mD mtop 180 GeV ⇒ ∼ × ∼ ∼ one finds an mR that is very close to the energy scale where supersymmetric Grand Unified theories predict that the strong, weak, and electromagnetic forces unify. Thus it is quite possible that tiny neutrino masses are giving us our first glimpse of physics that is otherwise hidden by an enormous energy gap.

5. The Goldhaber-Teller Model In 1946 Edward Teller left Los Alamos to join Enrico Fermi and Maria Mayer at the University of Chicago. In 1948 Maurice Goldhaber, then at the University of Illinois, approached Teller about the broad photoabsorp- tion resonances he had observed in (γ,n) nuclear reactions – the nuclear response was similar to related phenomena in crystal lattices that Teller had considered years earlier. Out of these discussions emerged a simple col- lective model of the giant dipole resonance in which the neutrons oscillate against the , with the nuclear symmetry energy generating a linear restoring force. This single harmonic mode could be constructed to satisfy the energy-weighted E1 sum rule A 2M τ3 2 A (Ef Eg.s.) f z(i) g.s. = . ~2 X − h | X 2 | i 4 f i=1 Figure 5 illustrates the mode. This celebrated paper10 also has a connection with neutrinos and with the Gamow-Teller suggestion of a semi-leptonic weak interactions mediated by a combination of vector and axial-vector currents. Once the model is August 13, 2008 15:6 WSPC - Proceedings Trim Size: 9in x 6in LLNL˙teller

November 10, 2009 8:55 WSPC - Proceedings Trim Size: 9in x 6in 08˙Haxton

13 92 constructed to saturate the E1 sum rule, it can be generalized algebraically toconstructed account forto thesaturate full 15-dimensional the E1 sum rule, super-multiplet it can be generalized of dipole algebraically resonances, ifto it account is assumed for the nuclear full 15-dimensional forces are independent super-multiplet of of spin dipole and resonances, isospin. This yieldsif it is a assumed set of SU(4) nuclear generalizations forces are independent of the E of1 spinmode and which isospin. saturate This the (L=1yields S a T) set responses of SU(4) generalizationsfor the allowed of choices the E1 of mode spin whichS andsaturate isospin T. the (L=1 S T) responses for the allowed choices of spin S and isospin T.

Fig. 5. Schematic illustrations of the original Goldhaber-Teller E1 mode, saturating the Fig.photoabsorption5. Schematicsum illustrations rule, and of of an the S=1 original generalization, Goldhaber-Teller one of the E1 giant mode, dipole saturating modes the photoabsorptionthat would be excited sum byrule, the and axial-vector of an S=1 current generalization, in inelastic one neutrino of the scattering. giant dipole modes that would be excited by the axial-vector current in inelastic neutrino scattering.

One can envision this pictorially as a generalization of the pro- ton/neutronOne can fluid envision oscillations this of pictorially the original as Goldhaber-Teller a generalization model of to the flu- pro- ton/neutronids that also carry fluid spin.oscillations For example, of the the original axial responses Goldhaber-Teller needed to model describe to flu- idsneutral that currentalso carry neutrino spin. For scattering example, involve the axialthe substitution responses needed to describe neutral current neutrino scattering involve the substitution τ3(i) z(i)τ3(i) [~r(i) ~σ(i)]   ⇒ ⊗ J=0,1,2 1τ (i)  z(i)τ (i) ⇒ [~r(i) ⊗ ~σ(i)] 3 3 J=0,1,2 1 An example of such a spin-dependent mode is given in Fig. 5: a fluid con- Ansisting example of spin-up of such protons a spin-dependent and spin-down mode neutrons is given oscillates in Fig. against 5: a fluid one con- with spin-up neutrons and spin-down protons. Thus this is an L=1 S=1 sisting of spin-up protons and spin-down neutrons oscillates against one T=1 mode. with spin-up neutrons and spin-down protons. Thus this is an L=1 S=1 Despite its great simplicity, this generalized Goldhaber-Teller model T=1 mode. captures enough of the basic physics of first-forbidden nuclear responses toDespite be a useful its tool great for simplicity, calculations. this One generalized “homework” Goldhaber-Teller problem11 that can model captures enough of the basic physics of first-forbidden nuclear responses to be a useful tool for calculations. One “homework” problem11 that can November 10, 2009 8:55 WSPC - Proceedings Trim Size: 9in x 6in 08˙Haxton

93

be solved with this model is “How did the galaxy make the fluorine found in toothpaste?” That data needed for the solution include: Fluorine has a single stable isotope, 19F, and is relatively rare. Its • galactic abundance relative to neon is 1/3100. Galactic core-collapse supernovae occur about once every 30 years. • Such supernovae are thought to be the primary source of Ne, which • is synthesized from “burning” oxygen in the supernova progenitor star during the long period of hydrostatic evolution, then ejected with the rest of the mantle during the explosion. Each supernova releases about 4 1057 muon and tauon νs. • × As these νs have an average energy of 25 MeV, most can excite • ∼ giant resonances when scattering off Ne. As the typical radius of the Ne shell is about 20,000 km, the to- • tal fluence of νs through this shell during the few seconds of the explosion is 1038/cm2. ∼ Although the average neutrino energy ω 25 MeV, cross section kine- ∼ matics yields makes neutrinos on the high-energy tail of the Boltzmann distribution much more important. Furthermore, neutrinos scattering back- ward can transfer a three-momentum ~q 2ω. Consequently the inelastic | | ∼ scattering is dominated by the first-forbidden responses, the giant reso- nances. While the original Goldhaber-Teller model was designed to satu- rate the sum rule for the (γ, n) nuclear response, its SU(4) generalization addresses the full set of giant resonances important to both axial and vector currents. That is, it provides a reasonable model for 20 19 19 20 19 Ne(Z0, n) Ne F or Ne(Z0, p) F. → where Z0, the boson mediating neutrino-nucleus scattering, is the analog of the γ in Goldhaber’s photoexcitation experiments. Summing over the spin and isospin modes yields 41 2 σ 3 10− cm 1/300 of Ne shell converted to F ∼ × ⇒ The direct synthesis of new elements by supernova neutrinos is called the neutrino process. When calculations only slightly more sophisticated than the above are combined with nuclear reaction networks that include the effects of the processing of the neutrons and protons coproduced with the 19Ne and 19F, as well as effects of shock-wave heating of the Ne shell, one finds that the correct ratio of 19F/20Ne is obtained for a heavy-flavor neutrino temperature of 6 MeV. This is very similar to the temperatures ∼ supernova modelers obtain from detailed hydrodynamic simulations. November 10, 2009 8:55 WSPC - Proceedings Trim Size: 9in x 6in 08˙Haxton

94

6. Summary Edward Teller’s career in nuclear physics spanned 70 years and encompassed many subjects not addressed here. However, the two papers chosen for discussion are notable for their physics insight and their historical setting. Gamow and Teller introduced a spin-dependent β decay amplitude that anticipated the axial-vector current of the standard model and the 1957 discoveries that established the V-A form of the weak interaction. The resulting handedness of the neutrino provides an explanation for suppressed double β decay rates, thereby keeping open the possibility of Majorana neutrino masses. Because neutrinos can have both Majorana and Dirac mass terms, a natural explanation arises for the difference between the neutrino mass scale and that of other fermions – but one not yet confirmed experimentally. Goldhaber and Teller introduced a simple nuclear model capable of saturating the E1 photoabsorption sum rule. This model has a natural generalization for weak charged- and neutral-current responses, if the nu- clear Hamiltonian is assumed be independent of spin and isospin. While the Gamow-Teller paper described for the first time the full set of opera- tors responsible for allowed transitions, and Goldhaber-Teller model and its SU(4) generalization provided a similar description for the first-forbidden responses. These two papers together provide a framework for tackling astrophysics problems that range from the pp-chain and Big-Bang nucleosynthesis to the interactions of neutrinos in the mantle of a supernova.

Acknowledgements This work was supported in part by the U.S. Department of Energy, Office of Nuclear Physics, under grant #DE-FG02-00ER41132.

References 1. For a discussion of the early history, see L. M. Brown, Physics Today, Septem- ber 1978, pp 23-28; also see “Celebrating the Neutrino,” Los Alamos Science 25, 1 (1997). 2. W.Pauli, Proc. VII Solvay Congress, Brussels, 324 (1933). 3. E. Fermi, Z. Phys. 88, 161 (1934). 4. See https://publicaffairs.llnl.gov/news/teller edward/teller bio.html for a bi- ographical summary. 5. E. Teller, Part 5 of the interviews from http://www.peoplesarchive.com/. 6. See, for example, http://wapedia.mobi/en/George Gamow. November 18, 2009 9:59 WSPC - Proceedings Trim Size: 9in x 6in 08˙Haxton

95

7. G. Gamow and E. Teller, Phys. Rev. 49, 895 (1936). 8. W. C. Haxton and G. J. Stephenson, Prog. Part. and Nucl.Phys. 12 (1984) 409; S. R. Elliott and J. Engel, J. Phys. G 30, R183 (2004). 9. M. Gell-Mann, P. Raymond, and R. Slansky, in Supergravity, ed. P. van Nieuwenhuizen and D. Z. Freedman (North-Holland, Amsterdam, 1979), p. 315; T. Yanagida, in Proc. Workshop on the Unified Theory and Baryon Number in the Universe, KEK Report No. 79-18 (1979). 10. M. Goldhaber and E. Teller, Phys. Rev. 74, 1046 (1948). 11. S. A. Woosley and W. C. Haxton, Nature 334, 45 (1988). 96

SURPRISES IN HIGH ENERGY DENSITY PHYSICS

S. J. ROSE Physics Department, Imperial College, London SW7 2BZ, UK

Edward Teller’s work on what is now called High Energy Density Physics (HEDP) is not so well known as some of his work in other areas of physics. Yet he made substantial contributions since the 1940s and the models that he developed and the problems that he worked on are still relevant today. In this talk we shall look at two major areas in HEDP with the first treated more historically and the second more with a view to recent work that the author and others have undertaken which perhaps indicates future directions.

1. Equation of State and Opacity of High Energy Density Plasmas The first major area is that of the calculation of material properties of high energy density plasmas, specifically the equation of state and opacity. A paper authored by Richard Feynman, Nick Metropolis and Edward Teller entitled ‘Equation of State of Elements Based on the Generalised Fermi-Thomas Theory’1 was seminal. Although pub- lished in 1949 the work was probably undertaken during the years of World War II. It developed the existing ‘Fermi-Thomas theory’ (although in more recent times it would be referred to as ‘Thomas- Fermi theory’) in two distinct ways. The existing Thomas-Fermi theory treated isolated atoms or ions by a method that gave the electron number density as a function of distance from the nucleus. Information on the phase of the wavefunction had been lost but in doing so had simplified the problem of calculating the electron distribution to a point which was tractable even for the computing available at the time. The first extension of the existing theory was to 97 remove the assumption of the isolated atom. In the paper by Feynman, Metropolis and Teller the concept of an ion sphere was introduced by associating the average volume occupied by the atom in the plasma with a sphere of radius R0. The potential V(r) has the boundary condition that it goes to zero at r = R0 and is zero beyond (in other words inside each ion sphere is a nucleus of charge Z at the centre and Z neutralising electrons. In addition V(r) tends to the potential due to the nucleus alone as r → 0. The second extension of the existing theory is to finite temperature where the probability that an electron at any radius has a specific energy is changed from the original model in which it is unity up to the Fermi energy, to a temperature-dependent Fermi factor. The model then solves Poisson’s equation to find the potential where the charge density depends on the potential through this Fermi factor. The effects of density and temperature are introduced through the two extensions to the original model described above.

Fig. 1. The electron number density (ne (r)) and the potential (V (r)) for the case of iron at a temperature of 50 eV and normal density (7.87 gcm−3). 98

The model of Feynman, Metropolis and Teller formed the basis of both the equation of state and opacity calculations at AWRE Aldermaston in the late 1970s when the author first worked there. Figure 1 shows the result of the solution of these equations for a specific case. The electron number density (ne (r)) is peaked at the nucleus but does not drop to zero at R0; it is this electron number density that gives the electron pressure (the majority part of the total pressure in the equation of state). The electron number density is a smooth curve and does not show modulations due to the presence of electron shells; it also represents the total number density of electrons as it does not discriminate between bound and free electrons. This total electron number density can be split into bound and free parts after the calculation, but this split is not necessary in the model. Whilst the approach outlined above provides the equation of state, to calculate the opacity, transition matrix elements are required which need wavefunctions. These do not come from the Feynman, Metropolis and Teller model1 as the phase information in the wavefunction has been lost. (It is this loss of phase information that is at the root of another insight by Edward Teller: that the original Thomas-Fermi model, if applied to a molecule — two or more nuclei — will not result in bonding2). To put back the phase information, the AWRE models of the 1970s (dating back to the 1950s) solved numerically the one-electron Schroedinger or Dirac equation using the potential from the Feynman, Metropolis and Teller model, resulting in a set of one-electron wavefunctions. Interestingly, unlike the pure Coulomb potential, an infinite number of wavefunctions cannot be found and although the low-lying orbitals (starting with 1s, 2s….) usually do exist, for the Feynman, Metropolis and Teller potential, solutions can only be found down to a certain level of binding energy. What is being seen is what is sometimes referred to as ‘continuum lowering’ where the presence of ions and electrons surrounding the ion in question ‘removes’ excited states. This has been approached by several methods, one of which concerns what would be seen in an absorption or emission spectrum and is due to Edward Teller and David Inglis.3 Using the one-electron orbitals, the opacity calculations at AWRE then constructed one-electron matrix elements and thereby calculated photon absorption cross- sections. The occupancy of the orbitals was then determined by 99 statistical mechanics and the two parts of the calculation were brought together for a calculation of the opacity. The generality of the Feynman, Metropolis and Teller model allows this to be applied to any element at any density and temperature for which the assumptions are valid (one important one being that there are no molecules in the plasma, hence temperatures of over 10 eV are needed). However bringing the quantum mechanical and statistical mechanical parts of the problem together using the one-electron orbitals presents a relatively small number of absorption lines and edges in the calculated opacity. Opacity calculations use averages over the absorption spectrum and the type of average appropriate to calculations of stellar structure where radiation transport occurs by diffusion of photons is due to Rosseland.4 This Rosseland mean opacity involves an average over the inverse of the absorption cross- section and thereby weights not its peaks (its highest values) but the troughs (the lowest values). Because the intrinsic line-broadening mechanisms result in a few narrow absorption lines in the one- electron picture which do not appreciably alter the underlying continuous absorption due to inverse bremsstrahlung and photoionisation, it would be tempting to conclude that bound-bound absorption could be ignored in calculating the Rosseland mean opacity. However in reality each of these one-electron transitions generally can take place in a huge number of bound electron configurations, as generally there will be more than one electron bound to a nucleus at any time, each at absorption energies close to that of the underlying one-electron transition energy. However now this ‘splitting’ coupled with the intrinsic line-broadening potentially alters the situation with the Rosseland mean (see Fig. 2) by allowing the lines to ‘fill in’ windows in the absorption spectrum and potentially, make a significant contribution to the Rosseland mean. This had been understood by AWRE scientists since the mid 1950s when the first opacity calculations were performed. However the first calculations of opacity including these full effects of line absorption were performed by Harris Mayer at Los Alamos and published in in 1948.5 Edward Teller is acknowledged in this document, but in a later paper6 Harris Mayer notes: ‘It was, however, Edward Teller who realised the great importance of line absorption in opacities under conditions where many electrons remain bound to their parent 100

Fig. 2. Schematic diagram of the frequency-dependent opacity showing that proper accounting for the effect of many-electron ions results in the potential for ‘filling in’ the absorption windows and thereby potentially increasing the Rosseland mean opacity. nucleus. …This method, first published in the open literature by Goody and now often referred to as the Mayer–Goody model, should most properly be credited to Teller’. This insight into the importance of line absorption was not, however, immediately apparent to workers in the former USSR. An interesting paper by Avrorin et al.7 notes that it was experimental evidence from nuclear tests that first showed that bound-bound absorption was important. Arnold Nikiforov8 was the first to include bound-bound absorption in opacity calculations of the former USSR and between 1955 and 1958 the values of opacity calculated in the USSR rose, in some cases by as much as a factor of 20 when this was included. Results from opacity experiments of the type referred to by Avrorin et al.7 were published 101

100 )

-1 experiment g

2 IMP (single shell open) IMP (K and L-shells open) cm

( 10 opacity opacity

1

0.50 0.75 1.00 1.25 temperature (keV) (a)

100

experiment )

-1 IMP (single shell open) g

2 IMP (K and L-shell open) 10 cm ( opacity opacity

1

0.50 0.75 1.00 1.25 temperature (keV) (b)

Fig. 3. Experimental10 and theoretical values of the Rosseland opacity for iron at 1 gcm−3. The theoretical calculations used the code IMP and have included electronic configurations either using a single open shell11 or an open K and L-shell. 102

100 Iron

10 Aluminium

(Carbon) κ

/ experiment κ opacityratio IMP (single shell open) Carbon IMP (open K- and L-shell)

1

5 10 15 20 25 30 nuclear charge (c)

Fig. 3. Experimental9 and theoretical values of the ratio of the Rosseland opacity to that of carbon at 1 gcm−3. The theoretical calculations used the code IMP and have included electronic configurations either using a single open shell11 or an open K and L- shell. by Eliseev et al.9 and Avrorin et al.10 and are compared to theoretical calculations in Fig. 3. The theoretical values in Fig. 3 are taken from an opacity code called IMP11 which was written by the author and is a development of the original AWRE opacity model, but still uses the Feynman, Metropolis and Teller potential within the ion-sphere. Theory and experiment are in reasonable agreement (as is found for the many other opacity models that have been compared to this experimental data). At around the time these papers were being published, other experimental measurements of opacity were starting to be published, in this case spectrally-resolved opacity was measured rather than the average (Rosseland mean) values and the experiments were being conducted in the laboratory where the plasmas were being produced using high-power lasers rather than in nuclear tests. These experiments were pioneered at AWRE and LLNL in the late 1980s and early 1990s and an early example of comparison of experimental 103

Fig. 4. Comparison12 between experiment and theory for germanium at a temperature of 76 eV and a density of 0.054 gcm−3. results with theory comes from Foster et al.12 The experiment involves heating a small sample of material with X-rays generated by a plasma which is itself heated using a high-power laser. A separate laser beam produces a plasma which generates X-rays and the spectrally-resolved transmission gives a measurement of the opacity. Although the code IMP was used for the theoretical calculations presented by Foster et al.12 (Fig. 4), more sophisticated opacity models were being developed at that time, in the sense that they either used a potential not derived from the Feynman, Metropolis and Teller method, such as the self-consistent field method13 or abandoned the single potential methodology and calculated the wavefunctions for each many-electron electronic state individually.14 Consequently the IMP model has not been developed since the 1990s. However opacity experiments continue to be performed and Fig. 5 shows a comparison between a recent experiment15 and IMP (still retaining its Feynman, Metropolis and Teller potential). Figure 5 shows that sixty years after the Feynman, Metropolis and Teller model was published it is still able to act as a credible basis for an opacity calculation. The spectrally-resolved opacity measurements shown are of material below 100 eV and this is close to the limit of what is achievable using high-power lasers. The Russian experiments gave much higher 104

1.0

0.8 experiment IMP

0.6

0.4 transmission

0.2

0.0 2300 2400 2500 2600 2700 2800 photon energy (eV) Fig. 5. Comparison between experiment15 and theory for niobium at a temperature of 30eV and a density of 0.028gcm-3. The calculations were performed by Mr Jim Gaffney as part of his PhD studies at Imperial College London.

3.5

3.0

experiment 2.5

2.0

1.5

1.0 emitted intensity (arb. units)

0.5

0.0 1400 1600 1800 2000 2200 photon energy (eV)

Fig. 6. Comparison between experiment15 and theory for germanium at a temperature of approximately 500eV and a density of 1–2 gcm −3. The calculations were performed by Mr Jim Gaffney as part of his PhD studies at Imperial College London. 105 temperatures (nearer 1 keV) but their driver is no longer available! However, recent developments in laser technology now allows the laser energies that were previously available only in nanosecond pulses (as was used for the opacity experiments we have described) to be delivered to target in much shorter (picosecond) pulses. This has allowed a new class of opacity experiment, on this occasion dependent on emission rather than absorption measurements, to be developed that can access much higher temperatures (around 500 eV). These experiments16 have the potential to provide new tests of opacity models under conditions only previously accessible using nuclear tests. Figure 6 shows a comparison between such experimental data and the IMP code. Once again the Feynman, Metropolis and Teller potential is still performing well enough to be valuable to the High Energy Density Physics community. I rate that as a surprise!

2. Fusion and High Energy Density Plasmas The second major area discussed in this paper is that of fusion energy generated in a high energy density plasma. The famous paper by Nuckolls et al.17 introduced the use of compression to high density to achieve inertially-confined fusion (ICF). However predating that paper, the idea was aired by Edward Teller in a paper he presented at the 7th International Quantum Electronics Conference in Montreal, Canada on 7th May 1972. The title of the talk was Modern Internal Combustion Engines and it appears as a LLNL report.18 The story of the development of ICF is well known, culminating most recently in the building of the US National Ignition Facility (NIF) at LLNL with the aim that fusion energy gain will be demonstrated on NIF in the next few years. We shall not look at that further, but note that in ICF schemes the fusion reactions take place between particles that have a thermal distribution (thermonuclear fusion). In this paper we shall consider whether it may be possible to produce a non-Maxwellian ion distribution with an enhancement at the part of the distribution where the fusion reaction cross-section is high. Taken to an extreme the distribution would involve a beam of fast ions (such as deuterons) hitting a target of cold ions (such as tritons). If the energy of the beam ions is adjusted so that the DT collision takes place at a value of energy close to the peak of the DT fusion reaction cross-section then it 106 might have been expected that this will produce a gain in energy as the fusion reaction provides a total of 17.6 MeV in energy from its product particles (3.6 MeV as kinetic energy of the α-particle and 14 MeV from the fast neutron) and the peak in the cross-section involves an ion energy of less than 100 keV. However it has been known for many years that this potentially appealing scheme won’t work because the cross-section for inelastic collisions between beam and target is much greater than the fusion cross-section. In other words the beam energy mainly ends up as heat in the target rather than creating a net fusion energy gain. However it was pointed out by Dawson et al.19 that this was not the case if, instead of the target being cold, it was a hot plasma. Dawson et al.19 showed that for plasma temperatures over a few keV and for deuteron energies of several hundred keV the energy produced by nuclear reactions can exceed the ions’ kinetic energy by a factor of up to around 5. This takes place because the inelastic cross-section is reduced for the case of a hot plasma. The plasma densities considered by Dawson et al.19 were so low, however, that the plasma was not of ‘high energy density’ and represented the conditions typical of magnetic confinement fusion devices. This work has been revived in a recent paper by Sherlock, Rose and Robinson20 where we have revisited Dawson’s idea but within the context of inertial confinement fusion. We have shown that injecting a deuteron beam into a hot plasma under the high density (and high energy density) conditions of inertial confinement fusion produces fusion reactions that produce energy amplification over the energy of the injected beam. The maximum amplification occurs for deuteron (beam) ion energies of several hundred keV and tritium (target) temperatures of over 10 keV (see Fig. 7). Using this idea it is possible in principle to consider using an ion beam injected into a burning plasma to increase the fractional burn-up of inertial confinement fusion targets. For this scheme to be of any value in terms of net energy gain, at least two practical problems need to be overcome. The first is the need to generate deuteron (or triton) beam ions of a few hundred keV at high efficiency. Fast ions have been generated in short-pulse laser-plasma interactions but as yet with relatively high energies (MeV range) and low efficiency (<10%), but this is a developing field. The second problem involves injecting the ions close to the burning fuel and for 107

5 20keV 4 10keV

5keV 3

gain 2 2keV

1 1keV

0 0 100 200 300 400 500 beam energy (keV) Fig. 7. The gain in energy for a deuteron beam interacting with a Tritium target at a number of different temperatures (taken from Sherlock, Rose and Robinson.10 this a modern development of inertial confinement fusion: cone- guided fast ignition, may be of help. Fast ignition was originally proposed by Tabak et al.21 Unlike conventional ICF, fast ignition uses a two-stage process to initially compress the thermonuclear fuel to high density but relatively low temperature, followed by a short (picosecond) high energy laser beam that heats one side of the fuel to high temperature initiating a thermonuclear burn wave across the target. One problem with this scheme involves the difficulty of propagation of a short-pulse beam through the plasma blown off by the long-pulse implosion. Kodama et al.22 demonstrated a solution to this problem by introducing a cone insert into the spherical target and in that way provided a clear channel for the short-pulse beam to propagate to the compressed core. Potentially the cone insert could also be used to inject the ion beam for the afterburner into the burning hot core plasma. This scheme is still at an early stage in its development, but it is interesting to see that new ideas for inertially- confined fusion are still emerging over 35 years since Edward Teller first described the benefit of implosion for fusion energy generation. By the time 40 years have elapsed (2011) we expect the National Ignition Facility at LLNL to have demonstrated a burning inertially- 8 10 confined plasma, a fitting culmination to the pioneering work in thermonuclear fusion that Edward Teller started in the 1940s.

3. Conclusions I wanted to bring the themes discussed in this paper together and for this I refer the reader to Fig. 8. In this figure we plot the position, in terms of temperature and density, of many high energy density plasmas that are produced in the laboratory or are found in astrophysical settings. The density-temperature track of the radiative flow region in the Sun is shown, together with conditions achieved in opacity experiments described earlier in the paper. In addition to the conditions achieved in radiative heating and short-pulse heating experiments, the potential for opacity experiments under more extreme conditions is also shown. Indeed in these experiments we hope to achieve density and temperature conditions similar to those

1010 early universe degeneracy boundary Si-burning 25Msolarcore D2 burning O-burning 109 Ne-burning C-burning DT burning

He-burning 108 H-burning radiative flow region in Sun 7 10 combined long/short-pulse opacity experiments temparture (k)

short-pulse opacity experiments 106

radiatively-heated opacity experiments

105 10-3 10-2 10-1 100 101 102 103 104 105 106 107 108 109 1010 1011 density (gm cm-3)

Figure 8. Temperature and density conditions for plasmas found both in the laboratory and in astrophysical settings. 109 at the Sun’s centre and expect to achieve that by using a variant of the fast-ignition technique described earlier, but without the need for the short-pulse beam to heat the plasma to thermonuclear conditions. The Sun centre has a temperature of roughly 1 keV, in contrast it is necessary to heat thermonuclear fuel to over 10 times that temperature. A preliminary design of such an experiment that could potentially be fielded on NIF is described by Rose.23 The conditions in inertially confined hot plasmas are also shown in Fig. 8. To burn pure (as opposed to a mixture of deuterium and tritium) higher temperatures would be needed. Looking further to the future, fuels that do not produce copious neutrons would be useful to substantially reduce neutron activation. Candidate reactions involving higher-Z ions have been considered, including the proton-boron-11 reaction that produces 3 alpha particles and these reactions would need higher temperatures still. It is interesting to note that the conditions predicted to occur at the centre of a massive 25 Mסּ star during different phases of its evolution as it burns higher-Z material do not follow the track that we envisage for the laboratory. Indeed the astrophysical case prefers to use a much higher density in which the free electrons are highly degenerate. In fact such conditions would have considerable benefit for inertially confined fusion within the laboratory. Degenerate free electrons radiate less, couple less strongly to the ions and take less energy from the charged fusion reaction products than non-degenerate electrons.24 In looking to the future perhaps a fruitful area for fusion research may be the exploration of the use of non-Maxwellian distributions of both electrons and ions. Of course this work is aimed at generating energy but the immediate effect of the use of fusion will be to provide energy density amplification that allows access within the laboratory to even higher energy densities than could otherwise be produced. The field of HEDP in which Edward Teller had such an influence at its beginnings and in its early development, is now a mature exciting field with huge prospects for future discovery.

References

1. R. P. Feynman, N. Metropolis and E. Teller, Phys. Rev. 75, 19 (1949). 110

2. E. Teller, Rev. Mod. Phys. 34, 627 (1962). 3. D. R. Inglis and E. Teller, Astrophysical J 90, 439 (1939). 4. J. I. Castor, Radiation Hydrodynamics (Cambridge University Press, 2007). 5. H. L. Mayer, Methods of Opacity Calculations, Los Alamos Scientific Laboratory, LA-647 (1948). 6. H. L. Mayer, J. Quant. Spectroscopy and Radiative Trans. 4, 585 (1964). 7. E. N. Avrorin, V. A. Simonenko and L. I. Shibarshov, Physics — Uspekhi 49, 432 (2006). 8. A. F. Nikiforov, V. G. Novikov and V. B. Uvarov, Progr. Math. Phys. 37, Birkhauser Verlag (2005). 9. G. M. Eliseev, I. Sh. Model’, A. T. Narozhnyi, A. Nikiforov, V. G. Novikov, V. B. Uvarov, A. I. Kharchenko and S. A. Kholin, Soviet Phys. Doklady 31, 635 (1986). 10. E. N. Avrorin, B. K. Vodolaga, V. A. Simonenko, and V. E. Fortov, Soviet Phys. Uspekhi 36, 337 (1993). 11. S. J. Rose, J. Phys B: Atom Molec Opt Phys. 25, 1667 (1992). 12. J. M. Foster, D. J. Hoarty, C. C. Smith, P. A. Rosen, S. J. Davidson, S. J. Rose, T. S. Perry and F. J. D. Serduke, Phys. Rev. Letts. 67, 3255 (1991). 13. B. F. Rozsnyai, Phys. Rev. A 5, 1137 (1972). 14. F. J. Rogers and C. A. Iglesias, Science 263, 50 (1994). 15. D. J. Hoarty, J. W. O. Harris, P. Graham, S. J. Davidson, S. F. James, B. J. B. Crowley, E. L. Clark, C. C. Smith and L. Upcraft, High Energy Density Phys. 3, 325 (2007). 16. D. J. Hoarty, S. F. James, H. Davies, C. R. D. Brown, J. W. O. Harris, C. C. Smith, S. J. Davidson, E. Kerswill,, B. J. B. Crowley and S. J. Rose, High Energy Density Phys. 3, 115 (2007). 17. J. Nuckolls, L. Wood, A. Thiessen and G. Zimmerman, Nature 239, 139 (1972). 18. E Teller, A Future Internal Combustion Engine, University of California, Lawrence Livermore Laboratory Report: UCRL- 74487. 19. J. M. Dawson, H. P. Furth and F. H. Tenney, Phys. Rev. Lett. 26, 1156, (1971). 20. M. Sherlock, S. J. Rose and A. P. L. Robinson, Phys. Rev. Lett. 99, 255003 (2007). 111

21. M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J. Woodworth, E. M. Campbell, M. D. Berry and R. J. Mason, Phys. Plasmas 1, 1626 (1994). 22. R. Kodama, P. A. Norreys, K. Mima, A. E. Dangor, R. G. Evans, H. Fujita, Y. Kitagawa, K. Krushelnick, T. Miyakoshi, M. Miyanaga, T. Norimatsu, S. J. Rose, T. Shozaki, K. Shigemori, A. Sunahara, M. Tampo, K. A. Tanaka, Y. Toyama, T. Yamanaka and M. Zepf, Nature 412, 798 (2001). 23. S. J. Rose, Plasma Phys. Contr. Fusion 47, B735 (2005). 24. P. T. Leon, S. Eliezer, J. M. Martinez-Val and M. Piera, Phys. Lett. A 289, 135 (2001). 112

PLASMA PHYSICS AND CONTROLLED NUCLEAR FUSION

N. J. FISCH Department of Astrophysical Sciences Princeton University, Princeton, NJ 08543

Already while making his famous contributions in uncontrolled nuclear fusion for wartime uses, Edward Teller contemplated how the abundant energy release through nuclear fusion might serve peacetime uses as well. His legacy in controlled nuclear fusion, and the associated physics of plasmas, spans both magnetic and inertial confinement approaches. His contributions in plasma physics, both the intellectual and the administrative, continue to impact the field.

1. Introduction

Edward Teller left a monumental legacy in controlled nuclear fusion and the associated physics of plasmas through his setting, people and institutions. The main ideas of controlled nuclear fusion are derived from his more famous contributions that have led the lay public to label him the “Father of the H-bomb.” The H-bomb is of course the hydrogen bomb, a device that explodes through the uncontrolled release of nuclear fusion energy. The controlled release of fusion energy and its conversion to a usable form is now the goal of the international controlled nuclear fusion program.1–3 Such a program was anticipated early on by Teller, who called for academic discussions at Los Alamos on peacetime uses of fusion energy as early as 1942.4 The key to controlling the release of fusion energy is to release the energy slowly, or possibly in many small explosions, but not in too big of an explosion. But releasing the energy slowly turned out to be harder than to release it all at once. The possibility for uncontrolled

113 release of this energy is not in doubt; on February 28, 1954, on the surface of the reef in the northwestern corner of Bikini Atoll, the U.S. detonated its first deliverable thermonuclear weapon, code named Bravo. The device, the hydrogen bomb, dramatically yielded 15 megatons of energy (see Fig. 1). The details of the H-bomb are still classified, but it is well known that the concept is based on the so-called Teller–Ulam design, in which, in a primary stage, radiation produced in a fission bomb is used to compress isotopes of hydrogen fuel which then fuse in a secondary stage. Teller is generally credited with the idea that gamma and x-ray radiation produced in the fission bomb, called the primary, could transfer enough energy into the fusion target or secondary, which would implode under the radiation pressure, attaining high temperatures and densities, thereby also achieving the necessary conditions for the release of fusion energy. Interestingly, while the project was conducted in secrecy, Teller himself was in favor of publicizing this information; in a letter to his fellow Hungarian physicist Leo Szilard (July 2, 19455), Teller wrote, “[o]ur only hope is in getting the facts before the people. This might help

Fig. 1. The Castle Bravo test.

114 convince everybody that the next war will be fatal. … This responsibility must in the end be shifted to the people as a whole and that can be done only by making the facts known.”

2. Controlled Nuclear Fusion

The fusing of deuterium and tritium, isotopes of hydrogen, results in a 3.5 MeV alpha particle and a 14 MeV neutron. The fusing ions do need to collide at high energy to overcome their mutual repulsion — the Coulomb barrier. To accomplish this, the fusing ions are heated to high temperatures, about 15 keV. Thus, devices based on high temperatures to achieve fusion are called thermonuclear. There are two major approaches to the controlled release of nuclear fusion suitable for peacetime use, inertial confinement fusion and magnetic confinement fusion. In each approach, the rate of energy released from the fusion reaction is purposefully kept small enough that the energy can be converted to electricity. In the case of inertial confinement fusion, a millimeter-sized pellet of frozen hydrogen is compressed to a thousand times solid density, creating an explosive release of fusion energy that is small enough to handle and convert to electricity. The high density allows the explosion to be small, yet efficient. Because the hydrogen fuel is not confined except by its own inertia, which means that it is confined only in that it takes a certain amount of time to leave the region in which it is heated, the approach is called “inertial confinement fusion,” sometimes abbreviated as ICF. This approach is inherently pulsed; these small explosions would occur several times a second to release millions of Joules of energy in each explosion, with average powers about a gigawatt. This is the concept behind the recently completed National Ignition Facility (NIF), a multi-billion dollar class experi- ment on the campus of the Lawrence Livermore National Laboratory. The other confinement approach is to employ a so-called “magnetic bottle.” Magnetic fields greater than a tesla are used to confine plasma, which is rarefied enough that the energy release occurs slowly but continuously. The powers contemplated are also about a gigawatt of electricity. In a strong magnetic field, charged particles tend to follow field lines, or in other words move in the direction of the magnetic field rather than across it. Hence, the

115 confinement problem is reduced from three dimensions to one dimension, the dimension along the field line. The one dimensional confinement problem is then solved basically in one of two ways: either particles follow the field lines around in a circle or particles are entrained in a region of basically straight magnetic field lines, except that the magnetic fields are stronger at the ends, causing particles to reflect at the ends of the region, like off a mirror. The former is the so-called toroidal confinement approach; the latter is the mirror confinement approach. The leading approach today is toroidal, and more specifically the approach, in which the plasma is entrained in toroidal magnetic fields that twist around poloidally as well as toroidally. The poloidal direction is the short way around a torus; the toroidal direction is the long way around. The poloidal twist in the magnetic field is the result of toroidal current. At present a consortium of countries, which includes the United States, is planning to build a $10B class tokamak in Cadarache, France. The project is now simply known as ITER, which was originally an acronym for International Thermonuclear Experimental Reactor.

3. Legacy in Inertial Confinement Fusion

Teller’s legacy in inertial confinement fusion (ICF) is direct in that the leading approach today in inertial confinement fusion uses important principles of the Teller–Ulam design for the H-bomb. In that design, a primary explosion produces x-rays. These x-rays then implode a hydrogen target, thereby triggering a secondary fusion reaction (see Fig. 2). The primary explosion for the H-bomb is a nuclear explosion based on fission, namely an atomic bomb, which releases a great deal of its energy in the form of x-rays. This radiation is trapped in a radiation shield and trained on the hydrogen fuel secondary. Together with Ulam, Teller is credited with recognizing that the x-ray radiation produced in the primary explosion could be used to compress a fuel of isotopes of hydrogen capable of nuclear fusion, and that the compressed fuel will react much more quickly than the uncompressed fuel, quickly enough that the mechanisms which might extinguish the reaction, such as heat losses, have no time to operate.

116

Fig. 2. Schematic of Teller-Ulam design.

Fig. 3. NIF target assembly consisting of a capsule inside a cm-sized hohlraum.

The primary in NIF is not an atomic bomb trigger producing x- rays, but rather a football-field sized laser facility that trains 2 MJ of laser power on a cm-sized cavity, called a hohlraum, that produces the x-rays (see Fig. 3). The X-Rays produced in the hohlraum alight on the mm-sized pellet and ablate the surface; this `secondary’ of frozen deuterium and tritium thereby implodes by a spherical rocket effect. What makes the compression by lasers different from the Teller–Ulam design is that the lasers are capable of compressing smaller amounts of material to higher densities, so that the energy released is small enough to be handled and converted to electricity.

117

The pellets in NIF are compressed to a thousand times solid density, which is the critical density required for the nuclear fusing of such small amounts of hydrogen fuel. The mission of the NIF facility is actually two-fold: First, it is an experiment to control the energy released in nuclear fusion. Second, in achieving the conditions relevant to nuclear fusion, the NIF experiment explores the physics of nuclear weapons without the building or testing of nuclear weapons, thereby contributing to a mission of national security, known as stockpile stewardship, for securing our nuclear weapons without actually testing them physically. The data gathered from NIF will enable the numerical simulation of these tests to be conducted with greater confidence. The square ports in the chamber are for converging laser beams of up to 2 MJ of ultraviolet light; the spherical ports are mainly for diagnostics. The NIF project was completed in 2009 and the experimental program is making excellent progress. Teller’s legacy in inertial confinement fusion also stems from his founding in 1952 of Lawrence Livermore National Laboratory

Fig. 4. The 10-meter diameter NIF target chamber which houses the target assembly depicted in Fig. 3. 118

(LLNL). LLNL began as a center for advancing nuclear fusion, both in developing the hydrogen bomb and in pursuing peaceful uses of nuclear fusion. Under the intellectual leadership of Edward Teller, LLNL invented the field of inertial confinement fusion and led the development of the high powered lasers required to pursue ICF. Livermore has been the leader in building and operating the world’s largest lasers from the 1970’s to the present, from Cyclops and Janus to NIF. While Director of the Lab from only 1958 to 1960, Teller was indeed a scientific and technical leader throughout the Lab’s entire history of both magnetic confinement fusion, as we will see below, as well as ICF.

3. Legacy in Magnetic Confinement Fusion

Apart from founding LLNL, Teller also supported an East Coast laboratory to pursue nuclear fusion research on the campus of Princeton University. The effort was first called Project Matterhorn, out of which evolved the Princeton Plasma Physics Laboratory (PPPL). PPPL became a leading laboratory for the pursuit of magnetic confinement concepts using toroidal fields for the control of nuclear fusion. In a famous meeting in 1954 at the now extinct “Gun Club” on the Forrestal Campus of Princeton University (attended by physicists, rather than the Gun Club members), Teller is remembered to have outlined the theory of chronic (or interchange) instabilities, saying something like, “trying to confine plasma with magnetic field lines is like trying to hold a blob of jelly with rubber bands,” or, alternatively, “if you try to confine high pressure gas with elastic bands, this is intuitively not a good thing to do.” His colorful analogy was based on his observation that the poor confinement properties of holding plasma pressure by a region of concave or bulging magnetic field lines was due to the fact that the field energy (like the rubber band energy) would be smaller if a long bundle of field lines were exchanged with a shorter bundle of plasma. Princeton Professor Russel Kulsrud, who attended the Gun Club meeting, remembers that Teller’s ideas stimulated to invent the important minimum-B geometry stellarator approach to magnetic confinement.

119

4. Legacy in Adiabatic Invariants of Particle Motion One of the very important contributions of Teller to controlled nuclear fusion was his work on the adiabatic invariants of single particle motion in plasma. In his Memoirs (1981), he wrote, “The functioning of magnetic mirrors and minimum-B configurations is due to remarkable approximate conservation laws, the conservation of adiabatic invariants.” Indeed, in magnetic confinement fusion, it is critical that particles be confined in the region of the magnetic field for hundreds of thousands of traversals of the magnetic field region, and this confinement is made possible by the strong conservation properties of certain invariants of the motion. However, Teller’s original interest in the matter stemmed not only from the advantageous possibility of long confinement times of charged particles in magnetic fields for controlled fusion. Working with Theodore Northrop,6 Teller was also curious about the lifetime of particles in the radiation belts around the Earth that had just recently been discovered by van Allen. In addition to belts of natural origin, there was the possibility of artificial radiation belts produced by small nuclear explosions. Indeed, there remains the worry, still present today, that even a small nuclear explosion might lead to a large number of charged particles remaining trapped for months in the magnetosphere. These energetic particles might, for example, damage satellites flying in low Earth orbit. What Northrop and Teller found was the possibility of unusually long retention in a magnetic field, or, in their words,5 “The motion of charged particles in a magnetic field such as that of the Earth or that of a is discussed…. These conservation laws lead to retention of particles in the magnetic field.” In characterizing the constraints on the motion, Northrop and Teller go on to state, “In case the oscillation along a line of force is fast compared to the effects of the drift, one will be primarily interested in the line on which the particle finds itself and what energy it possesses.” It is this last statement that anticipated my own personal debt to Teller, for here there is the recognition that breaking the adiabatic invariants leads to highly constrained motion in which the particle may find itself at a 120 different energy and at a different point in space. How this observation by Northrop and Teller in 1960 concerning the constrained motion of charged particles in magnetic fields led to a personal intellectual debt, I now explain.

5. A Personal Debt

In 1992, together with Jean Marcel Rax, now a professor at Ecole Polytechnique, I made use of the Northrop–Teller constraints in developing a concept for controlled nuclear fusion that has come to be known as alpha channeling.7 In magnetic confinement fusion, the charged energetic fusion by-products, the alpha particles, sustain the reaction by slowing down on electrons, which heat the fuel ions that produce the fusion reaction, in turn releasing more energetic alpha particles. The electrons, however, tend to lose much of this energy in radiation or transport prior to heating the ions. Moreover, if the electrons capture the alpha particle power before heating the ions, the electrons are necessarily at least as hot as the ions, so the high electron pressure necessitates even stronger magnetic fields to contain the electron pressure. Yet the electrons do not contribute directly to the production, so that pressure would be more valuably taken up by ions, which can release fusion energy. The idea of alpha channeling is to use plasma waves to catalyze the heating of the ions directly from the alpha particles, eliminating the electron heat channel, so that the electrons can be colder than the ions. How can this be done? Because of the Northrop–Teller constraints on the particle motion, even though the plasma waves diffuse particles in energy, the diffusion in energy can be linked to diffusion in space. Alpha particles that absorb wave energy might be forced to the interior of a magnetic confinement device, whereas alpha particles that lose energy might necessarily move to the periphery of the device. Thus, since only at the periphery are particles removed, by shining waves long enough, all alpha particles must exit with little kinetic energy, in other words, cold; the energy lost by the alphas is absorbed by the plasma wave. The energy of the wave might then be utilized to directly heat the fuel ions. Were this to work out as speculated, the cost of electricity derived from nuclear fusion could be significantly less.

121

The key to producing the cooling effect is to use external waves to link diffusion in energy to diffusion in space. To see how diffusion paths can be arranged in joint velocity-configuration space to produce cooling, consider for simplicity slab geometry, with ions immersed in a uniform magnetic field (pointing into the paper), following circular paths projected onto the x-y plane. Ions will rotate with frequency Ω (the gyro-frequency) on these paths in the counter-clockwise direction. Suppose now that a short-wavelength electrostatic wave propagates in the x-direction. When a particle encounters the wave, there is a particularly effective interaction if the wave phase velocity ω/kx matches νx, the particle velocity in the x-direction (like a surfer encountering a wave). When the resonance condition, νx = ω/kx, is satisfied, the particles gets an instantaneous kick in the x-direction, which depending on the phase of the wave could be either to increase its energy or to slow it down. Thus, the velocity in the x-direction changes instantaneously but randomly with νx  νx + ∆ νx. However, the change in the guiding center is related to the change in energy, with ygc  ygc +∆νx/Ω. Thus, in Fig. 5, an ion in the

Fig. 5. Coupling of kick in energy and gyrocenter. 122

middle orbit undergoes a velocity kick ∆νx at either point where the three orbits intersect, where the resonance condition, νx = ω/kx, is satisfied. If the ion gains energy from the kick, it goes into the top orbit, whereas if it loses energy it goes into the bottom orbit. Thus, the change in energy ∆ε is linked to the change in the gyro-center, with ∆ygc = ∆ε kx/Ωmω, where m is the ion mass. The wave-particle resonance recurs as the particle retraces its circular orbit, although possibly at different x-y coordinates. Repeated interactions with the wave result in diffusion, with the constraint that particles that diffuse to higher energy must go up; particles that diffuse to lower energy must go down. This links diffusion in energy to diffusion in space, forming the required path in energy-space coordinates. Although the analysis here is conducted in 2D, we can imagine that a similar analysis could be conducted in 3D. We further imagine that one end of this diffusion path points to the center of a confinement device, while the other end points to the periphery. The cooling effect is now obtained when two further conditions are satisfied: First, the diffusion path must connect hot particles at the core to cold particles at the periphery. Second, the cold particles must be removed at the periphery, while the particle diffusion to higher energy must be bounded. With the proper phasing of the waves, so that energetic in the center is connected to cold on the periphery, alpha particles born with 3.5 MeV near the center must eventually (upon repeated wave-particle interactions) exhaust cold at lower energy at the periphery. Here, the diffusion to higher energy is bounded since particles have limited excursion length to the center. Note that the diffusion occurs along highly constrained orbits; absent other effects such as collisions, ions must exhaust cold because there is no other way to leave the magnetic trap. In more complicated magnetic fields, there are similar constraints that relate the change in energy to the change in coordinate. In the Northrop–Teller picture, particle orbits lie on surfaces completely determined by invariants of the motion. One can think of the invariant values as labeling the surface. Thus, when a wave kicks a particle in both energy and momentum, the particle hops to the next orbit surface. Because the kicks in energy and momentum are related by the wave parameters (as in the 2D case examined here), the paths to the next orbit surface are similarly constrained. In this generalized

123 context, these orbit surfaces are nested in the particle invariant coordinate space, with the outer surfaces where the particles can be removed. The stochastic cooling effect then occurs when kicks to the outer surfaces in this space are accompanied by loss of particle energy. It turns out, however, that Rax and I owe another, related intellectual debt to Teller. The use here of microwave radiation to trap fusion energy in the first place parallels Teller’s approach to achieving inertial confinement fusion, controlled or uncontrolled. Within the Teller–Ulam framework, Teller’s personal contribution was to show how x-ray radiation could be used to compress and heat the DT target to many times solid density so that the fusion energy would not leak away through radiation before it could be useful in sustaining the reaction. Similarly, in alpha channeling, microwave radiation is used to capture the alpha particle energy quickly so as to avoid energy escaping through the electrons.

6. Teller’s Outlook — The Hybrid

Teller was the quintessential optimist on the ultimate use of fusion energy. During the wartime effort, he was an optimist on achieving the uncontrolled release of the energy, when others might have given up, and his optimism was ultimately vindicated. He was an optimist also on achieving the controlled release of fusion energy, but also a realist. About controlled nuclear fusion, he wrote in 1981,8 “It is likely that an economic impact of pure fusion cannot be realized before the year 2000.” In 1987 he updated that hope, saying, “I hope very much that the process of controlled fusion will become practical at some point in time, but … I do not expect that that time will come during my lifetime.” But in 1981, Teller was also imagining ways of utilizing fusion energy not by itself as the ultimate clean energy source, but rather together with fission. He wrote,3 “The best way to take advantage of this [inexhaustible source of energy] is to construct a fusion-fission hybrid. Combining Fusion and Fission is a natural marriage.” Recently, a quarter century after Teller’s pronouncement, the hybrid approach appears to be gaining traction, including at LLNL in the interesting Laser Inertial Fission-Fusion Energy (LIFE) Program.9 124

In a hybrid approach, Teller envisioned releasing atomic energy both through fusion and fission reactions. The fusion reactions, however, would be useful primarily for the neutrons produced rather than the energy released. The fission reactions would consume neutrons, but would release tremendous energy. Thus, the neutron- rich fusion reaction would be the natural complement to the energy- rich fission reaction. In this respect, it would be an ironic twist if the hybrid approach were eventually the best way to utilize fusion energy for peaceful uses. Although in an entirely different way, the breakthrough in the Teller–Ulam design for the hydrogen bomb also utilized the fission reaction to complement the fusion reaction. On the ultimate possibilities, in traditional Teller fashion, Teller retained his optimism and his belief in unintended consequences,3 “The final result may, indeed, be the availability of better, safer, cleaner, more abundant energy sources. It is equally possible that during the development of controlled fusion, other applications will be found. … The more adventurous the technology, the harder it is to predict the ultimate outcome.”

7. Legacy in People

Apart from the legacies that he left in ideas and institutions, Teller was a mover of individual people who would themselves push the field forward. He was persuasive in bringing policymakers to support nuclear fusion and he was a successful recruiter of top scientists to the field. In 1967, Teller visited the Princeton Plasma Physics Laboratory, which had that time was pursuing the stellarator approach to magnetic confinement fusion. With the clock in the background showing either 8 am or 8 pm, Teller was photographed in the Model C stellarator control room with the leaders of the magnetic confinement fusion program (see Fig. 6). In this illuminating photograph, Teller is captured together with many of the key people that he set in motion in the area of magnetic confinement fusion, including those he set in motion directly and others whom he set in motion through his general support of the magnetic fusion research carried out at PPPL. Teller’s impact on the field can be seen even from reviewing just these personages and Teller’s personal relationships with them. None of these people is

125

Fig. 6. Teller inside the Model C stellarator control room in 1967 (third from left). alive today, but their enormous collective impact in plasma physics and controlled nuclear fusion most certainly lives on. At the far right is Professor Melvin Gottlieb, the Director of PPPL, the institution whose founding Teller had strongly supported when it was called Project Matterhorn. Succeeding Lyman Spitzer, Gottlieb served as Director of PPPL from 1961 to 1981. Standing next to Gottlieb, is Professor Marshall Rosenbluth, who was Teller’s graduate student, colleague in the early days at Los Alamos, and a foremost figure in the field of plasma physics and controlled nuclear fusion. Recalling how he entered the field in the 1999 PBS film, “The Race for the Superbomb,” Rosenbluth said, “Well, I believe it was the summer of '48. I had been working — Teller was actually my thesis advisor, and he never sort of had any time because he was always running off to Los Alamos, or was doing fifty other things. So he said why don't you come out to Los Alamos and spend a summer there. There is interesting physics problems, and I will have more time then to look at your thesis and so on. I agreed ….” To the right of Rosenbluth, and standing next to Teller, is Lewis Strauss, the Atomic Energy Commission chairman from 1953 to 1958, 126 who was a powerful ally of Teller and strong advocate of both the hydrogen bomb and controlled nuclear fusion. On Teller’s right stands Professor Harold Furth, who would later build the landmark TFTR tokamak at Princeton and who in 1981 would succeed Gottlieb as Director of PPPL. Before coming to Princeton, Furth had been a Teller recruit at LLNL. To the right of Furth stands Professor Thomas Stix, who wrote the classic text, “The Theory of Plasma Waves.” Stix also directed the graduate program in plasma physics at Princeton University, a position he later relinquished to me. In 1956, while Teller was his boss, Furth published a very witty poem about Teller in The New Yorker Magazine. Called the “Perils of Modern Living,” the poem imagines a meeting between Dr. Edward Anti–Teller and a visitor from outer space (presumably) Teller. Their meeting, however, ends abruptly and thusly:

Then, shouting gladly o'er the sands, Met two who in their alien ways Were like as lentils. Their right hands Clasped, and the rest was gamma rays.

Teller enjoyed the joke, and promptly wrote a witty rejoinder, also published in The New Yorker, elucidating a number of the physics concepts. Teller signed his response saying, “ … I was pleased that the New Yorker mentioned me. Come to think of it, only Anti-Teller was mentioned by name in the poem, but I am confident that somewhere in an anti-galaxy, the Anti-New Yorker devoted some pleasant lines to Yours Sincerely, Edward Teller.” (Teller also enjoyed pointing out to Furth that his far more verbose response earned from the magazine much more than Furth’s cleverly crafted, but therefore concise, poem.) When I look at this picture, I see Teller’s legacy in the people who built the field. I see in the picture Teller at the center of many of the key players in plasma physics and controlled nuclear fusion, people who pushed the field forward, people who in one way or another were pushed by Teller or who pushed with Teller, and people with whom Teller could share not just scientific dreams, but also wit and humor, and the camaraderie of the scientific adventure.

127

Acknowledgment

I am indebted to , Greg Hammett, Will Happer, Robert Gross, Dale Meade, Ken Fowler, Steve Libby and Mordy Rosen for particularly useful conversations and recollections.

References

1. Robin Herman, Fusion: The Search for Endless Energy, Cambridge University Press (1990). 2. Joan Lisa Bromberg, Fusion: Science, Politics, and the Invention of a New Energy Source, MIT Press (1982). 3. T. Kenneth Fowler, The Fusion Quest, John Hopkins University Press (1997). 4. Richard Rhodes, Dark Sun: The Making of the Hydrogen Bomb, NY Simon and Schuster, 1995. 5. Edward Teller (with Judith L. Shoolery), Memoirs: A Twentieth Century Journey in Science and Politics, Perseus Publishing (2001). 6. T. G. Northrop and E. Teller, Stability of the Adiabatic Motion of Charged Particles in the Earth’s Field, Phys. Rev. 117, 215 (1960). 7. N. J. Fisch and J. M. Rax, Interaction of α Particles with Intense Lower Hybrid Waves, Phys. Rev. Letts. 69, 612 (1992). 8. Edward Teller, Introduction, in Fusion, edited by Edward Teller, Academic Press (1981). 9. E. I. Moses, T. D. de la Rubia, E. P. Storm, J. F. Latkowski, J. C. Farmer, R. P. Abbott, K. J. Kramer, P. F. Peterson, H. F. Shaw and R. F. Lehman II, A Sustainable Nuclear Fuel Cycle Based on Laser Inertial Fusion-Fission Energy, submitted to Fusion Science and Technology (2009). 128

MONTE CARLO METHODS

M. H. KALOS Lawrence Livermore National Laboratory, Livermore, CA 94551 CA, USA

Computation now plays an essential role in science, especially in theoretical physics. The greater depth of our understanding of physi- cal phenomena and the need to predict the behavior of complex de- vices demands a level of analysis that purely mathematical methods cannot meet. Monte Carlo methods offer some of the most powerful approaches to computation. They permit a simple transcription of a random process into a computer code. Alternatively, they give the only accurate approach to the many-dimensional problems of theo- retical physics. I will describe a number of complementary ap- proaches for Monte Carlo methods in treating diverse systems.

1. Introduction

Numerical computation now has an important role in both theoretical and experimental science. The design of a high-energy accelerator, of its complex detectors, or of an experiment demands computation often at a significant level. Analysis of the results is usually computationally demanding. In- ference from astronomical observations can require significant com- puter-aided modeling. In theoretical science quantitative prediction of many phenom- ena, chemical reaction rates,1 the behavior of a nuclear reactor, or the energy of an atomic nucleus from more fundamental information re- quire intensive computation, and Monte Carlo methods are often the techniques of choice. 129

The prediction of the response of a high-energy particle detector is most effectively analyzed by a Monte Carlo simulating the stochastic processes of creation, decay, transformation, transport and detection processes of particles. Such a calculation is straightforward on mod- ern computers, including parallel computers. Such a calculation simulates a stochastic process in many dimen- sions. An important advantage of Monte Carlo methods is that they offer efficient approaches to numerical calculations in many dimen- sions — calculations intractable by standard numerical methods. The earliest statistical theory of fluids — kinetic theory — infers their properties from the collisions of constituent atoms or molecules. A Monte Carlo treatment is natural and straightforward, following the pioneering work of G. A. Bird.2 A widely used model of non-equilibrium processes in solids, ki- netic Monte Carlo, assumes rates of configurational changes that de- pend on local or long-range structure. The system might be defined on a lattice in two or three dimensions, with sites occupied by one or more species of atoms or by vacancies. Rates are specified for proc- esses such as the migration or transformation of atoms, and a simu- lated stochastic process is followed on a computer. The model can aim for significant physical realism, say, in understanding the annealing of epitaxial growth, or it can be highly simplified to generate insight about equilibrium and non-equilibrium statistical physics and chem- istry. We will discuss one example in greater detail in the talk. Monte Carlo methods can be applied to a wide variety of compu- tations that do not derive from natural stochastic processes. Many of these more abstract procedures involve the evaluation of definite in- tegrals or of integrals derived from integral equations in many- dimensional spaces. A simple but important example — indeed the calculation that opened the possibilities of Monte Carlo methods in statistical physics — is the evaluation of the equation of state of hard discs in two dimensions or hard spheres in three. One needs to average some property of the positions of discs or spheres over all possible non- overlapping configurations. For an N-body system, this is a 2N- or 3N- dimensional integral, a natural problem for Monte Carlo treat- ment. The algorithm called the “Metropolis” or “” or M(RT)2 method was first devised for this application. 130

Credit for the essential invention — the idea of rejecting some moves of a random walk but returning to the previous position — is now obscure, but it is likely that Teller played an important role. The method has been generalized to an extremely wide variety of techniques and applied to an extremely wide variety of physical ap- plications. The statistical mechanics of hard discs or spheres is an idealized physical system, but the insight it brings to more realistic models is invaluable. Integrating the non-relativistic Schrödinger equation for an N- body system is another broad application that does not arise from a physically defined stochastic process. It has the form of a partial dif- ferential equation in a 3N-dimensional space plus time that offers ac- curate predictions of ordinary matter. Formally, if the physical time variable set to be imaginary, then the equation is a linear diffusion equation for a random walker in a 3N-dimensional space in which the physical potential produces a readily simulated process of birth and annihilation of walkers. Direct transcription of this process to a computer code is ineffi- cient, and grows more inefficient with increasing N. A mathematical reformulation of the method lends itself to effective computation. For certain significant physical quantum many-body systems, it is possi- ble to carry out a numerical treatment without uncontrolled approxi- mations as will be discussed further. A useful recent survey of Monte Carlo methods in the physical sciences is the Proceedings of the conference held in 2003 at Los Ala- mos to celebrate the fiftieth anniversary of the “Metropolis Algo- rithm”.3

2. Particle Transport Serious study of Monte Carlo methods was motivated by the chal- lenges of the transport theory for particles and radiation at Los Ala- mos. Ulam, von Neumann, and Fermi were among the pioneers. The interaction of particles such as neutrons or photons with matter is, of course, a natural stochastic process, but Ulam was first to note that it could also be effectively used for many other problems. The mathematicians contributed significant ideas about broad ranges of applications and about reduction of statistical error. The 131 theory of zero-variance Monte Carlo for linear transport was formu- lated in the late 1940s and has been the basis of particle computa- tions ever since.4 One starts with approximations to the “adjoint solution”, effec- tively the description of the stochastic process run backwards in time. This is, of course, no easier to calculate than the “forward” solution, but qualitatively reasonable approximations are often easy to estab- lish and very efficient in practice. A widely used general-purpose transport Monte Carlo program, MCNP (Monte Carlo N-Particle code5) from Los Alamos, includes an option for the automatic genera- tion of adjoint information from a deterministic approximation to the physical system.6

3. Kinetic Theory of Gases

Contemporary very large computers have permitted atomistic calcu- lations of gases with billions of particles. The method is widely used in the study of dilute gases, the atmosphere at high altitudes, and in general where atomistic effects in fluids need to be elucidated. An in- teresting and important application has been the study of the early development of instabilities in discontinuous fluids. I will show re- sults of such calculations that demonstrate agreement between the- ory and experimental measurements of instability growth rates.7 What is significant here is that the fluctuations on the atomic level — not described by the classical Navier–Stokes equation–decisively in- fluence the rates.

4. Kinetic Monte Carlo (kMC)

There are no effective computational methods to model the dynamic behavior of many-body systems taking into account their quantum character. Studies of the evolution of the structure of condensed phases like crystals use approximations — often very good approxi- mations — based on classical physics and on models of the potential energy functions or energetics of structural changes. Molecular dy- namics (MD) — the numerical solution of Newton’s equations of mo- tion — is a widely used methodology. But the computation of atomic trajectories by MD is necessarily limited to a relatively small number 132 of atoms for currently available computers and short times (several nanoseconds). Most crystal growth systems involve time scales up- ward of minutes and crystal sizes larger than microns. As described above, kMC is the realization of a class of diffusive models of atomistic behavior in condensed matter, especially in solids. Rates for different processes, including the migration of atoms, are specified. Often these are assumed to depend on the temperature of the system, T, proportional to exp ( −K/T), where K is an activation temperature. kMC models based on atomic motion between discrete lattice sites have provided valuable simulations for elucidating crys- tal growth processes involving large length and time scales. Atomic scale nucleation of new layers on close-packed surfaces, atomic-level step motion, surface roughening, and morphological instabilities in growing surfaces have been simulated in detail. The straightforward translation of such models is as a time- driven simulation, but it was noted8 that an event-driven simulation would be more efficient in many applications, and this method is now used very widely. Recently, still more sophisticated methodology — first-passage algorithms — have been shown to provide speed-ups of orders of magnitude for dilute systems.9 Early kMC simulations were the first to identify a surface rough- ening phase transition.10 Crystals grown below some temperature,

Tr , exhibit facets, whereas those grown at higher temperatures are rounded. This work has stimulated a large body of research on the nature of the transition and the detailed morphologies for crystals grown in the vicinity of Tr . The models have been extended to more complex systems, including the growth of polycrystalline thin films.11 Systems with grain boundaries show a tendency for the formation of voids during growth of thin films from the vapor. An important aspect of thin film growth on foreign substrates is the formation of texture; that is, the development of a preferred orientation of the grains of a polycrystalline film. Simulations using kMC have shown that texture results from anisotropic growth rates. These examples illustrate the usefulness of the kMC model because of its ability to treat the atomic level phenomena that control faceting and grain boundary properties, and still allow freedom to encompass aspects such as polycrystalline structures and void formation. 133

kMC is also used extensively for the study of irradiated materials. Energetic particles such as fission fragments or accelerated ions can cause considerable damage to crystalline materials. In reactor materials, the diffusion of the point defects produced by decay fragments can cause problems with the stability of structural steel, and also affect the fuel rods (2). Because the lifetime of a reac- tor is several decades, kMC models can provide predictions of the evo- lution of the fuel rods, and guide the development of structures that will extend the operational lifetimes.12 Implantation of impurities is essential in the manufacture of semiconductors. Energetic beams of dopant atoms are used to make p and n-type regions during the fabrication of silicon devices. kMC models predict the final distribution of dopant atoms, and can be used to optimize that distribution by modifying the processing steps. Simulations of the paths of the incoming ions and the recoils of silicon atoms are combined with KMC diffusion models to provide an atom- istic level of detail for use in predicting the final distribution of dopant atoms.13 I will show a video of the evolution of a process in which alumi- num atoms are deposited on an aluminum substrate at various tem- peratures. This is the work of G. Gilmer.14 The computations were confirmed by experiments. Simulations of this kind, including many with realistic detail of nanoscale features, are widely used for quality assurance in fabrication in the electronics industry.

5. Classical Statistical Mechanics Although its inventors (Metropolis, Rosenbluth, Rosenbluth, Teller, and Teller 1953) did not follow up on the M(RT)2 method, and al- though theoretical scientists at the time disdained the use of compu- tation, it proved to have a powerful impact on research on statistical mechanics in physics, chemistry, and biology.15 The basic idea is ele- gantly simple: A probability distribution, p(X), is to be sampled for variates X in a many-dimensional space. A random walk is estab- lished whose dynamics are the following: A proposed move from position X to position Y is generated from the pdf T (Y|X) and ac- cepted with probability min[1, p (Y) T (Y|X)/p (X) T (X|Y)]. Under very broad conditions, the asymptotic density is p (X). In classical 134 statistical mechanics, the function p (X) to be sampled is the Boltz- mann distribution, exp[ −V (r1,r2,…,rN)], where V is the potential en- ergy function of the coordinates rk. From a methodological point of view these applications have pro- vided a wealth of generalizations, such as the observation that T (Y|X) does not have to be a symmetric distribution. The method has been applied to liquids, alloys, magnetic systems, and polymers, yielding accurate numerical results for, among other parameters, critical temperatures and critical exponents. For a re- view, see the article by D. P. Landau16 and the book by Landau and Binder17 and references therein.

6. Quantum Monte Carlo

6.1. Variational quantum Monte Carlo Important progress in the study of many-body quantum systems was made by W. L. McMillan18 who observed that the function to be sam- pled in M(RT)2 need not be a classical Boltzmann distribution. In variational calculations a trial wave function, ψT (r1,r2,…,rN), is as- sumed, and the following quotient of integrals is to be computed:

ψ T 21 ,...,, N )( ψ T 21 N )( 1...,...,, drdrrrrHrrr N ∫ EV = 2 ψ ...),...,,( drdrrrr ∫ T 21 N 1 N

1 2 where H 2 +∇−= 1 rrV N ),...,( is the Hamiltonian operator. By set- ting the pdf p (X) in M(RT)2 to be ψ 2 , he showed that the ratio could easily be computed. Before this, expectations using even the simplest plausible many-body trial function, a “Jastrow product”

ψ J 1 N = Π − rrfrr ji |)(|),...,( , < ji could only be computed by making uncontrolled approximations. The combination of unknown approximation of variational energy with unknown overestimate of the variational energy itself led to signifi- cant uncertainty in the validity of the theory. Variational Monte Carlo is still widely used, but usually as an ad- junct to the more accurate methods discussed below. 135

6.2. Sign problem In a number of applications one seeks solutions that are not every- where positive. This is particularly true of “fermionic” systems, such as many-electron systems, for which the exclusion principle19 de- mands that the wavefunction be antisymmetric, which is to say that it transforms into its negative when the coordinates of like-spin elec- trons are interchanged. Another, even greater challenge arises in treating quantum systems in physical rather than imaginary time. Here the propagators are complex so that treatment by random walk is necessarily challenging. Some of these sign problems can be dealt with in straightforward technical ways, say by correlating negative and positive estimators, but others present deep challenges to the methodology. I will touch on some of these below.

6.3. Green’s function Monte Carlo The treatment of many-particle quantum systems by simulating the non-physical diffusion of a many-dimensional random walker in imaginary time is now well developed, and applied to many sys- tems.20,21,1 For “bosonic” systems — like a collection of 4He atoms at zero temperature, it provides a numerical method with no uncon- trolled approximations.22 The key to efficient sampling is an impor- tance sampling transformation, namely recasting the random walk so ψ that the density of walkers is biased by a trial function T , and modifying the transition probabilities accordingly. Unfortunately, many important applications involve fermions, and various fixes, usually approximate, have been applied. The most usual for many-electron systems is the “fixed-node” approximation. Here, an antisymmetric trial function is used, one that has nodes, i.e. subspaces of lower dimension on which they vanish. It can be shown that if the random walk is terminated when it reaches such a point, then the energy calculated for the system is an upper bound. This is widely used, and after at least a decade of development and optimiza- tion, very good results have been attained. Research into methods that are potentially as reliable as for bosonic systems continues.23 I will show striking results of calculations of this kind: for the homogeneous electron gas, by Ceperley and Alder24; for the low-lying 136 states of light nuclei, from the work of Pandharipande and collabora- tors25; and for some molecular dimers by Umrigar and Toulouse.26 The results for the electron gas are important for two reasons: they were the first highly reliable data for the equation of state of a many-electron system, and they form the basis of a very-widely used approximation method, “density-functional theory.” The calculations on the light nuclei are noteworthy in that the particle interactions here involve extremely complex nuclear forces. There are two-body forces derived from the study of nucleon-nucleon scattering, and which depend in complicated ways on the particles and their relative states. There are also three-body forces derived in a phenomenological way from the interactions of pions with nuclei. This means that a trial function for A = 8 comprises 17920 complex func- tions. Finally, the quality of the agreement with experiment validates our understanding of the structure of nuclei at this level. The last example is that of the energies of first-row dimers (i.e. Li2 through F2) as calculated by quantum Monte Carlo methods, in- cluding the fixed-node approximation. To appreciate the nature of this achievement one must first understand that the energy differ- ences that are important for chemistry are of the order of 10-5 or less of the total energy of the system. To attain this precision in a Monte Carlo calculation is evidence of highly sophisticated methodology. The second point is that the accuracy is very high, comparable or bet- ter than the “traditional” methods based on very large basis sets, an indication of the quality of the trial-function optimization now possi- ble.

6.4. Quantum Chromodynamics Quantum chromodynamics (QCD) is the theory of the strong force — that is, of how quarks interact via gluons to form heavy particles such as protons and neutrons.27 It is a field theory — that is, like quantum electrodynamics, the particles interact by way of fields that permeate space. Unlike electrodynamics where the intermediating particle is a photon, both the particles (quarks) and the quanta of the field (glu- ons) have many possible states. There are six types of quarks and eight gluons and the interactions of quarks and gluons and gluons with themselves are mediated by matrices that couple these different 137 states. The coupling is strong so that the kind of perturbation theory that works well for electrodynamics does not converge in QCD. For- tunately, a discretized version of the theory — lattice QCD — was formulated by Kenneth Wilson,28 which permits a numerical treat- ment. A four-dimensional lattice is set up and values of the quark fields are associated with the points. The gluon interactions are represented by the links. Here too, the computed result can be expressed as an average with respect to a weighting function. The quarks are fer- mions so that the weighting function is not positive, but reasonable approximation schemes can make it so. In either case, the numerical problem, for large enough lattices to approximate reasonably well to a continuum, requires a Monte Carlo treatment. Indeed, even after three decades of ingenious algorithmic development and more than 105 increase in computer speed, the lat- tice sizes attainable are still not quite large enough. Nevertheless, significant predictions are now available. I will show results of lattice QCD calculations for the masses and other pa- rameters of particles, including nucleons.

7. Conclusions It is my hope that the examples discussed have served to exhibit the range of techniques and scientific applications that are treated under the heading of Monte Carlo methods. Our understanding of the natu- ral world requires experiment, observation, and theory to connect them and to show their underlying unity. In the contemporary world, computation is essential for the quantitative prediction of observed phenomena. Monte Carlo methods extend our predictive capabilities in powerful ways.

Acknowledgments I am indebted to Cyrus Umrigar, Steven Pieper,29 George Gilmer, and Robert Sugar for unpublished data. This workwas performed under the auspices of the U. S. Department of Energy by Lawrence Liver- more National Laboratory under Contract DE-AC52-07NA27344. 138

References 1. J. B. Anderson, J. Chem. Phys. 65, 4122–4127 (1976). 2. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon, 1994). 3. J. E. Gubernatis, The Monte Carlo Method in thePhysical Sci- ences, ed. James E. Gubernatis, AIP Conference Proceedings, Volume 690 (2003). 4. M. H. Kalos, and P. A. Whitlock, Monte Carlo Calculations (Wiley, 1986). 5. MCNP 2007. Available via 6. J. Sweezy, F. Brown, T. Booth, J. Chiaramonte and B. Preeg, Radiation Protection Dosimetry 116, 508–515 (2005). 7. K. Kadau, C. Rosenblatt, J. L. Barber, T. C. Germann, Z. Huang, P. Carlès and B. J. Alder, The importance of fluctuations in fluid mixing, Proc. National Acad. Sci. 104, 7741–7745 (2007). 8. A. B. Bortz, Kalos M. H. and J. L. Lebowitz, J. Comput. Phys. 17, 10–18 (1975). 9. T. Oppelstrup, V. V. Bulatov, G. H. Gilmer, M. H. Kalos and B. Sadigh, First Passage Monte Carlo Algorithm: Diffusion without All the Hops, Phys. Rev. Lett. 97, 230602–230605 (2006). 10. G. H. Gilmer, and P. Bennema, Simulation of Crystal Growth With Surface Diffusion, J. Appl. Phys. 43, 1347–1360 (1972). 11. H. Huang, G. H. Gilmer and T. Diaz de la Rubia, An atomistic simulator for thin film deposition in three dimensions, J. Appl. Phys. 84, 3636–3649 (1998). 12. M. J. Caturla, N. Soneda, T. Diaz de la Rubia, M. Fluss, and M. Jaraíz, Kinetic Monte Carlo simulations applied to irradiated materials: The effect of cascade damage in defect nucleation and growth. J. Nuclear Materials 351, 78–87 (2006). 13. M. E. Law, G. H. Gilmer and M. Jaraíz, Simulation of Defects and Diffusion Phenomena in Silicon, MRS Bulletin, 45–50 (2000). 14. G. H. Gilmer, Private communication (2007). 15. N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller and E. Teller, J. Chem. Phys. 21, 1087–1092 (1953). 139

16. D. P. Landau, The Metropolis Monte Carlo Method in Statistical Physics. In The Monte Carlo Method in the Physical Sciences, ed. James E. Gubernatis, AIP Conference Proceedings, Volume 690, pp. 134–146 (2003). 17. D. P. Landau, and K. Binder, A Guide to Monte Carlo Simula- tions in Statistical Physics (Cambridge University Press, 2000). 18. W. L. McMillan, Phys. Rev. A 138, 442–445 (1965). 19. W. Pauli, Zeitschrift für Physik 43, 601–623 (1927). 20. M. H. Kalos, Phys. Rev. 128, 1791–1795 (1962). 21. M. H. Kalos, D. Levesque and L. Verlet, Phys. Rev. A 9, 2178– 2195 (1974). 22. K. E. Schmidt, P. Niyaz, A. Vaught and M. A. Lee, Phys. Rev. E 71, 016707 (2005). 23. M. H. Kalos, and F. Pederiva, Phys. Rev. Lett. 85, 3547–3551 (2000). 24. D. M. Ceperley, and B. J. Alder, Phys. Rev. Lett. 45, 566–569 (1980). 25. V. Pandaripande, Quantum Monte Carlo Simulations of Nuclei and Nuclear Reactions. In The Monte Carlo Method in the Physi- cal Sciences, ed. James E. Gubernatis, AIP Conference Proceed- ings, Volume 690, 261–268 (2003). 26. C. Umrigar and J. Toulouse, Private communication (2007). 27. C. Quigg, Theories of Strong, Weak, and Electromagnetic Interac- tions (Benjamin-Cummings, 1983). 28. K. Wilson, Phys. Rev. D 10, 2445–2459 (1974). 29. S. C. Pieper, Private communication (2007). 140

TELLER ON ENERGY

JANOS KIRZ Advanced Light Source, Lawrence Berkeley National Laboratory

1. Personal Introduction

I met Edward Teller on his 49th birthday. In fact I became a part of his family that day. I grew up in Budapest. During the war years, and during the subsequent years of the cold war that followed, it was not to our advantage, nor to his, to have any interaction. A letter sent through an intermediary every couple of years, written with the expectation that it will be intercepted and read by the “authorities” was the extent of the contact between the two parts of the family. I escaped from Hungary on foot at night after the events of 1956, in early December, and arrived in Berkeley on January 15, 1957. It was a leap of faith on the part of Edward and his family to take in this 19 year old stranger, who claimed to be his sister’s son. I lived in the Teller house for 2 ½ years. For my young cousins, Paul and Wendy, it was a surprise that they actually had a relative other than their parents. They adopted me, taught me English, and introduced me to American life. For me it was the first taste of what my grandfather had talked about, when he referred to his earlier existence, as “life without fear”. The first lesson Edward was eager to teach me was that in America one is expected to tell the truth. I guess, in full knowledge about all his political enemies, he wanted to make sure that I do not prove to be a major embarrassment. Being a physics student in the Teller house had its moments of agony and ecstasy. Being sent to the airport to pick up Leo Szilard 141 was of course among the many high points. But hearing Edward exclaim on a frequent basis that he was an “idiot”, (such as when one of his innumerable ideas did not work), had me question — if he is an idiot, what am I? I remember Edward talking fondly about his years at George Washington University with George Gamow. He described his friend as a most inventive scientist, who would come in every morning with a brilliant new idea. By noon 90% of these ideas were proven to be wrong, but the remaining 10% were of such importance, and the process so much fun as to having made a deep impression on him at the time. I remembered this story about a decade ago. The Stony Brook Physics Department (of which I was a member for nearly 40 years), hosted a group of prospective graduate students at a dinner. The after dinner speaker was Edward’s former Ph.D. student, C. N. Yang. Yang recalled his years as a grad student in Chicago. He related that he was brought up in his undergraduate years in China to talk only about results he had proven rigorously. On arriving at the University of Chicago he encountered Teller, a most inventive scientist, who would come in every morning with a brilliant new idea. By noon 90% of these ideas were proven to be wrong, but the remaining 10% were of such importance, and the process so much fun as to having made a deep impression on him at the time. In fact, he described it as liberating for the development of his own creative process.

2. Energy Issues

After World War II Edward made major contributions to nuclear reactor safety. He served as the first chair of the Reactor Safeguards Committee, the group that was tasked with setting standards for the nascent civilian nuclear energy industry. In the 1950’s, he, along with worked on the design of the TRIGA reactor. Many TRIGAs were built and used at hospitals and universities for isotope production, and training. Their safety and reliability has been extraordinary. Beyond nuclear power, Edward’s introduction to energy issues came about through his friendship with then New York governor Nelson Rockefeller. In 1965 there was a huge blackout affecting New York, the Northeast US and a large part of Canada. Rockefeller asked 142

Edward to investigate, and advise him what steps were necessary to avoid a repeat. Edward rapidly became an expert on the North American electricity grid, in all its complexity. In 1973 Rockefeller established his Commission on Critical Choices for Americans in preparation for his planned run for the 1976 presidential nomination. He assembled a star-studded cast for the Commission, including Teller, whose role was to lead the study on energy issues. 1973 was also the year of the Arab oil embargo, the year OPEC shocked the world by creating an acute oil shortage, triggering the first energy crisis. Teller put a lot of his time and energy into studying the various facets of the problem both in the context of the Commission, and on a much broader scale. In the next few years he wrote and lectured widely on the subject. In his article “The Energy Disease”, published in Harpers Magazine, February 1975 he writes: “The obvious symptom is the increase in the price of oil. To replace oil by another source of energy will be a long and costly procedure. In the meantime, oil at more than $10, a barrel has given the world economy an unprecedented shock”. (Note that $10, in 1975 is equivalent to $40, in 2008. The cost of a barrel today – 5/28/08 – is roughly $120). He goes on to express concern about too much money in the hands of oil producers, hands that one may not trust. In looking at potential solutions he predicts that neither fusion nor solar would cure the problem in the 20th century, and advocates conservation as the quickest and most effective way to reduce dependency on imported oil. How little has changed in the last 33 years! The end of the article is vintage Teller: “I like to define a pessimist as one who is always right but takes no pleasure in it, and an optimist as a person who imagines that the future is uncertain. To be an optimist is a duty, because with the imagined uncertainty there comes the will to act”. The same month Teller gave an interview to the San Francisco Chronicle. He advocated pursuing all alternatives to oil as an energy source. He suggested siting reactors underground, expanding the use of coal through gasification, and vigorous efforts at conservation, including the use of smaller cars. He went on to give series of lectures on the energy problem, and finally a few years later he collected his

143 conclusions in a book: `Energy from Heaven and Earth’ (W. H. Freeman, San Francisco, 1979). In re-reading this book thirty years later, it is remarkable how much ahead of his time many of Edward’s ideas were. There is much discussion on the concern about global warming and the melting of the polar ice caps; on the increasing energy needs of developing countries, and how this will affect future energy markets. The role of oil sands, oil shale, and methane clathrates is discussed. The need for carbon-neutral energy production is discussed, including cellulosic alcohol, and the concern about how energy oriented agriculture may affect food production, and create a water shortage. (He suggests looking into the use of algae, since they grow in salt water). He sees the in-depth understanding of photosynthesis as critical to the development of the best solar to chemical conversion processes. Regarding the broader implications, Edward expressed concern about the effects on international relations of the competition with our friends and allies for scarce energy resources, and reiterated his concern about the accumulation of huge profits in the hands of non- democratic oil producing regimes. He urged that the US vigorously develop new energy technologies, so as to be able to assert leadership in this area. Much of the world has changed since the first energy crisis, but the energy crisis came back this year, and is likely here to stay. Teller is unfortunately no longer with us to share his wisdom and insight. While he was alive, he followed his own admonition: He was an optimist, and in many ways he believed that whatever was not forbidden by the laws of physics could be achieved with ingenuity and hard work. He had the courage of his convictions. He was not always right, but was right on most things. I remember him with admiration and affection. 144

PROFESSOR EDWARD TELLER AND HIGHER EDUCATION

JOHN F. HOLZRICHTER Hertz Foundation & Lawrence Livermore Laboratory

Professor Edward Teller (1908–2003) was a remarkable individual who was shaped by and participated in the events of the most dramatic century in human history. He actively participated in those events through his intellectual contributions as a student, an educator, as an applied physicist, and through his technical leadership of the United States’ nuclear defense programs. One of his enduring contributions has been to demonstrate the power of thinking deeply about important problems and to deal directly with them–no matter what the consequences. This paper follows the outline of my talk given at the Teller Centennial, which took place in Livermore on May 28. The talk is

Fig. 1. Teller at age 17, graduating from the Minta Gymnasium. 145 available at https://tellercentennial.llnl.gov and at www.hertzfounda- tion.org. Its summary of Teller’s work, especially regarding education, is divided into six parts starting with Teller’s early years in Hungary, 1908 to 1926, and finishing with the period marking the end of the cold war 1991 and his death in 2003. Two recurring themes of Teller’s philosophy are echoed time and time again: ‘major technological advances are built on foundations of basic knowledge’ and ‘the pursuit of knowledge is important in its own right’.

1. The Hungarian Years: 1908–1926 Edward Teller was born in Hungary in 1908, into a professional family, which was multilingual, loving of its children, and demanding of excellence. He experienced an intellectual’s education in the best private gymnasiums of the Austro–Hungarian Empire. He recalls that many of his teachers were strict (i.e., Prussian), others Socratic, humanistic, and most importantly, they were able to stimulate his mathematical and scientific talents. With the peace treaties of WWI, upon the defeat of the German and Austro-Hungarian armies, Hungarian society collapsed, and Hungary ceased to be the state that it once was. Many of the former Hungarian lands, cities, and population were ceded to neighboring countries. Because of the disastrous war and the poorly considered peace treaties, Hungarian and other middle European intellectual establishments were completely alienated from the capitalistic economic system represented by Britain and France. The fringe politicians began to embrace communism and fascism, and increa- singly blamed the Jewish (and other) minorities for the problems of the time. Communist and Fascist parties began to play an increasing role in the daily life of Hungarian citizens, with attendant chaos, brutality, and social disruption. The Teller family, Edward in particular, directly experienced the consequences of bizarre ideolo- gies, seized upon by opportunists and then impressed upon an unwitting public.

2. University Education in Germany: 1926–1933 While Teller himself knew that he was gifted in mathematics and physics, these skills were not a normal way to make a living in the

146 former Austro–Hungarian Empire. His father was unconvinced that Teller should continue his university education.1 After several consultations with relatives and after preliminary examina-tions by well-known professors, he was allowed to leave Hungary. It was 1926, he was 18, and he left Hungary for a university life in Germany. Attendance at a German university was natural because they were the most famous universities, he spoke German, the family had relatives there, and because anti-Semitism was becoming a serious issue in Hungary. He arrived in Karlsruhe, the city made famous by the German chemical industry, to begin his university education at the Karlsruhe Institute of Technology. He worked with several famous professors, first in Karlsruhe and later in Leipzig, Goettingen, Copenhagen, and London. Teller was the perfect student at the perfect time: arriving at the world’s center of scientific learning, and becoming an early participant in one of the greatest revolutions in human history. It was characterized by the discovery and the creation of mathematical descriptions of the underlying physical processes governing the dynamics of the universe. These were made possible by the recently created theories of quantum mechanics and relativity. He received his first university training at Karlsruhe with Professors Mark, Ewald, and Boehm, then to Leipzig where he met and worked with Heisenberg and obtained his Doctorate. He then moved to Göttingen for postdoctoral work with Eucken, Franck, and Born. Teller surely began to acquire an appreciation for the influence that singularly gifted individuals could make on students and on the societies around them. Because German universities were the international centers of modern science and science based industries in the 1920s and early ‘30s, gifted students were sent there from all over the world. Teller met and collaborated with virtually all of the soon-to-be great scientists of the world. They included Fermi, Szilard, Wigner, von Neumann, Gamow, Bethe, Franck, von Weizäcker, Landau, Placzek, von Karman, Goeppert–Mayer, Wheeler, Weisskopf, Law-rence, and many others. He continued to learn and began applying his talents to many of the unsolved chemical-physics and solid-state physics problems of the time. He and his colleagues resolved many of them using applications of quantum methodologies developed by the community around him and by Teller himself. He must have been 147 deeply impressed by how seemingly intractable problems could be explained using the relatively simple concepts of wave mechanics, careful physical observation, and a thorough grounding in the intellectual discipline needed to relate theory to experiment.

3. Copenhagen, Britain, and America: 1933–1941 Because of the take over of the German government by the Nazi party beginning in 1933, and the capitulation of the moderate parties to its excesses, it became important for Jewish citizens to leave the country. At the same time, it is worth remembering that Stalin was consolidating his power in Russia using similar techniques to those of Hitler. A distressing Soviet action led to an accusation of Lev Landau, Teller’s close friend, as an enemy of the state. Teller’s exit from Germany was greatly facilitated by the Rockefeller Foundation and the British based “Jewish Rescue Committee”, which enabled him to travel to Copenhagen where he met and was able to work with Neils Bohr and his group. After a year, he left for London in 1934. There he continued his work, meeting Hermann Jahn, and collaborating on one of his most important papers describing the Jahn–Teller process, in which the ground state configuration of a molecule or crystal is distorted to accommodate an even lower energy state. Finally in 1935 he received an invitation to travel to the United States and teach at George Washington University in Washington DC. This invitation to teach quantum mechanics was facilitated by his old friend George Gamow. While teaching in Washington, he had time to think and to meet many interesting people in other fields such those working at the National Bureau of Standards, at the Department of Agriculture, at the Carnegie Foundation. He noted and paid attention to surface physics problems, molecular physics, and terrestrial physics including magnetism and compression of solids — e.g. the earth’s iron core. In 1941, Teller went to Columbia University as a visiting professor, where he took on a very famous student, Arthur Kantrowitz. Kantrowitz finished his fluid physics work very rapidly, and went on to an illustrious career at Cornell University, then founding Avco Everett Laboratories, and then to Dartmouth where he

148 lives today.a In 1942, Teller left Chicago to be with Fermi at the Metallurgical Laboratory in Chicago, and then to the Los Alamos Laboratory 1943. In effect, Teller left George Washington University, became a visitor at Columbia, then joined the University of Chicago after the war, and in 1953 he joined the University of California. During this period he advised several very notable students, among them C.N. Yang, Marshall Rosenbluth, and Lincoln Wolfenstein.

4. Chicago and Los Alamos: 1942–1951 In 1942 Teller left New York to work with Fermi at the metallurgical laboratory at the University of Chicago, and then a year later left for Los Alamos. This period is well covered elsewhere, but it is clear that Teller’s contributions were important, especially his work with Bethe on shock waves, his knowledge of the compression of materials, and his basic understanding of fission and fusion. During this period he became very interested in the potential of fusion as a source of explosive energy and later, as a source of commercial energy. As time went on the technologies of mathematical and physical simulation improved with better computing, better measurement of physical parameters, and fusion assumed an increasing role in his intellectual endeavors. At the same time, the concerns of scientists associated with Los Alamos and their leaderships’ increasing reluctance to venture into new areas began to dominate both the policies of Washington and to prey upon Teller’s concerns. While it is difficult for this author to understand the politics, ethics, loyalties, and actions of his colleagues as well as those of the Soviet Union in those postwar years, Teller clearly believed that no matter what, fusion physics would have to be understood and would have to be dealt with. After the war, he returned to his professorship at the University of Chicago, and he began a very productive relationship with Professors Goeppert– Meyer, Fermi, and his famous students, e.g. C.N. Yang. During this period, he contributed a great deal to the Wigner committee on reactor design and safety. This and similar work further streng- thened his applied physics credentials. He also became increasingly certain that fission could provide abundant energy for the future. As a Arthur Kantrowitz died shortly prior to the publication of this volume. 149 time went on, he and others eventually worked out the physics of a fusion weapon. And, as it turned out, he also began to understand the complicated physics of fission–fusion interactive processes. Their understanding ultimately led to the most important defense technologies of the cold war. His concerns about understanding the basic physics of the important physical processes of fission and fusion ushered in the post atomic age. In addition his fears of Soviet domination were ever present. One must remember that he lost many members of his immediate family to both the homegrown Hungarian Fascists as well as to those in Germany. Then the terrible post war Soviet occupation visited even more hardships on his culture and family. His actions, as I view them today, were completely consistent with his drive to understand fundamental physical processes first, especially those that might enable a dictatorial adversary to gain a dominant world position.

5. The University of California and Livermore: 1952–1991 After several post war years dealing with Los Alamos management, and in addition worried that the American intellectual establishment believed in the appeasement of the Soviet Union, he believed that the leaders of the nuclear programs in the United States were exhibiting an incapacity to think about the future. He decided that he must return to take a leadership role in the U.S. nuclear programs by becoming an assistant director of the Los Alamos Laboratory in 1949. The first Russian atomic test hastened that decision. At Los Alamos he pursued nuclear work, helped develop improved computational systems, and worked to rebuild the staff of the laboratory. To find a way around the seemingly intractable problems at Los Alamos — logistic, ideological, and bureaucratic — he began discussions with Lawrence about considering a second nuclear Laboratory, and then about joining the physics department at the University of California Berkeley in 1953. Teller worked with Lawrence to construct the second laboratory at a government facility near the town of Livermore, California in 1952. He became its scientific director, then an associate director, and then director from 1958–1960. He built the Livermore laboratory as an applied-science institution, not a pure physics institution. His vast

150 experience in the applications of theoretical and computational physics to many problems usually enabled him and his colleagues to estimate the outcome before expensive experiments were conducted. At the same time, experiments almost always yielded surprises, which he insisted be understood, as soon as possible. As a member of the UC Berkeley department of physics, he encouraged many students to move to Livermore for their first jobs, where he continued to encourage teaching and the building of the institution. His effortless understanding of quantum mechanics due to his thorough internalization of the subject, made him a gifted graduate student teacher as well as a celebrity undergraduate teacher with his Physics 10 class, Physics for Non-Physicists. My wife Barbara, who was a student at UC Berkeley then, attended that class in 1962 and enjoyed it very much. Unwittingly, Dr. Teller enhanced our subsequent married relationship a great deal. During the 1950s in particular, the United States reexamined its views toward higher education and its support. This was a result of the astonishing number of applied-scientific inventions that helped win WWII. Yet more were needed to deal with the increasingly bitter cold war being waged with the Soviet Empire. In the early 1950s the U.S. government founded many new national laboratories to deal with defense problems, and enhanced the many existing ones left from WWII. These included such Laboratories as Livermore, Brookhaven, Argonne, Lincoln Laboratories, the Army Huntsville Laboratory, and many others. The effectiveness of highly educated, technical leaders working toward a common goal was not lost on the major corporations of America. They also began to hire experts in their companies’ fields of interest. To meet these manpower demands a great deal of money was dedicated to the support of gifted science and mathematics students by the government, companies and private foundations, policies that were strengthened with the Russian launch of Sputnik in 1957. I myself was finishing high school in Wisconsin at that time, and I recall observing Sputnik orbiting overhead and listening to its signal on an amateur radio. My parents were terrified that the Russians were ahead of us. This vast support for technology and the potential for obtaining interesting work after college, lead me into the field of

151

Fig. 2. Professor Teller in 1957 at the Lawrence Livermore Laboratory.

applied mathematics and engineering physics at the University of Wisconsin.2 Dr. Teller made many major contributions to the institutions that he served. In 1958, he led the academic committee at UC Berkeley to analyze and recommend the formation of the Space Sciences Center. Then, working with Fred de Hoffman, Hans Mark, and Tom Pigford, he helped form the department of Nuclear Engineering at UCB. Finally, working with UC Davis’ chcancellor and deans, he brought

152 the UC Davis, Department of Applied Science (DAS) campus into being on the Livermore site. These institutions played major roles in their specialty areas, and have graduated many notable leaders.

6. The Department of Applied Science, UC Davis at Livermore The Department of Applied Science was created because of his interests in young people who needed to be thoroughly educated to work in the new fields of nuclear energy, defense, and other applied science and engineering areas. In addition, specialty institutions such as Livermore needed many unusually gifted individuals. In the mid 1950s, Teller began considering the creation of a separate department of applied science. It would be located on the Livermore site itself. For a teaching facility to have university standing it needed to be part of one of the UC campuses and departments, and it had to be located on land owned (or leased) by said university itself. The challenges of setting up this facility were large, but the tremendous reservoir of Ph.D. level scientific and engineering talent at Livermore was remarkable. Much of the impetus came from LLNL staff who wished to teach their special skills to new employees who came from many walks of life. Both UC Davis and Livermore management, and Dr. Teller as leader spent a great of time ironing out the procedures. Teller became the chair of this department, DAS, and the first classes began in 1963. He enlisted many of his colleagues to teach including Montgomery Johnson, Al Kirschbaum, Mike May, Allen Kaufman, Harold Furth, Wilson Talley, Bernie Alder, John Kileen, Sid Fernbach, Richard Post, Chuck Leith, and many others. The department attracted students from many diverse backg- rounds. Types of students attracted included those wishing to work with computers or on nuclear problems, officers in the military who wished an advanced education, members of the Livermore Laboratory staff already employed as technicians or engineers who wished to upgrade their degree levels to the Ph.D. level. In addition, the on-site campus attracted many young professors wishing to teach and pursue advanced research, taking advantage of the special facilities on the Livermore site. This on-site college was very successful, graduating over 210 PhDs to date, and fulfilling a specific need for the education of unusually gifted people in unusual technical topics. 153

7. The Fannie and John Hertz Foundation One of the other co-creations of Prof. Teller is the Hertz Foundation. John Hertz emigrated from the Austro-Hungarian Empire in 1896, from eastern Czechoslovakia, now the separated state of Slovakia. By 1957 he had made several fortunes as an industrial leader in America by creating and expanding rental car and taxi-cab companies. He also was deeply committed to public service and he served under Roosevelt during WWII, directing the Office of War Transportation. John Hertz had no illusions about the fascists before the War or about the communists after the war. He was especially fearful of the Soviet Union and the intentions of its leaders as he watched them snuff out democratic governments in Eastern Europe. In 1957, he and his wife Fannie decided to transfer the assets of their family foundation to a new Fannie and John Hertz Foundation for Under- graduate Engineering Scholarships. Their intent was to induce young people to consider technical careers in national defense. Not surprisingly, they asked Prof. Teller to join them on the Foundation’s board of directors. By the early 1960s, Teller and other board members noted that the Foundation’s monies could be better spent supporting gifted technical leaders at the Ph.D. level. The transition to Ph.D. support occurred in 1963. Teller developed the methodologies for selection of Fellows and actually interviewed all of the first applicants. Shortly thereafter, Drs. Lowell Wood and Harry Sahlin began an evolved process by first holding first stage interviews, which were then followed by Dr. Teller’s final interviews. I was fortunate to have experienced and survived that in depth process. I enjoyed Hertz support while finishing my Ph.D. degree at Stanford in 1971 in laser spectroscopy. Hertz enabled me, and almost 1050 others, to finish a difficult but very satisfying thesis. I was then able to obtain productive employment, first at the Naval Research Laboratory, then at the Lawrence Livermore National Laboratory, and now at the Hertz Foundation. While the Hertz foundation started with an engineering and national defense emphasis, today it supports Ph.D. students in the applied physical, biological, and engineering sciences in all aspects of US society. The Fannie and John Hertz Foundation has spent more

154

Fig. 3 Professor Edward Teller celebrating the 40th anniversary of the Hertz Foundation’s graduate program in 2003. He is shown doing what he enjoyed most of all, talking with young scientists and engineers. than $120M directly supporting more than 1050 Fellows and it is still “going strong” (see www.hertzfoundation.org).

8. The Final Years: 1991–2003 The cold war and Prof. Teller’s “long wait” came to an end in 1991 with the fall of the Soviet Union. One of the main antagonists to the U.S. way of life and to Dr. Teller himself ceased to exist. He experien- ced a “Hero’s Welcome” in Hungary a few years later, but continued to voice his concerns regarding what he considered to be a deficit of courage and vigilance of its national leaders regarding national defense–feelings certainly exacerbated by the 9–11 attacks on the twin towers in New York City and the Pentagon. He also continued to work on unresolved questions in nuclear defense, on high tempera- ture superconductivity, and on many other topics. He spent a great deal of time on education, and he believed that the U.S. was wasting gifted students’ time using the outmoded, mass-production high- 155 school education system. He continued his efforts in education, and especially in teacher training. He supported the creation of the Edward Teller Education Center on the UCD-LLNL site for teacher training; he participated in Saturday science sessions, and in the Illinois gifted students programs by working with his daughter Wendy. He also wrote an entry level physics book “The Dark Secrets of Physics” with his daughter Wendy, and with Wilson Talley.3 According to Mort Weiss, one of Prof. Teller’s long time confidants, “ET would have taught kindergarten if asked”.

9. Conclusion Edward Teller was one of the scientific geniuses of the 20th century. He dedicated his life to the understanding of science and its influence on human kind. He was one of the great practitioners of Applied Science. His contributions were many. His detractors, those knowledgeable and otherwise were numerous and gave him enormous concern. I believe that it is worth placing into perspective the horrors of the middle 20th century that he directly experienced. Those events led to the deaths of more than 20 million human beings, including many members of his own family and many of his close friends. In addition, the remarkable new technologies appeared to favor despots and autocrats at the expense of “free” societies. These past and continuing world-shaping concerns have sorely tested the emotional balance of all thoughtful individuals, and not least those of Prof. Edward Teller.

Acknowledgments I would like to thank the many people listed below who helped me develop this lecture, and these notes. My own direct experiences with Teller’s worlds began with studies in applied mathematics, physics and engineering at the University of Wisconsin, under the tutelage of refugee professors from central Europe, such as Heinz Barschall, Wolfgang Wasow, and others. After Wisconsin, my wife and I spent a year living in Germany soaking up middle European language and history, and studying more physics and mathematics. Upon returning to Stanford for my Ph.D., I began working with Prof. Arthur Shawlow using lasers. I entered into my first Hertz interviews in 1968 with

156

Drs. Wood and Sahlin, and then with Prof. Teller. I received a Hertz Fellowship, and then employment first at NRL, and then at the Livermore Laboratory. During my career, I spoke with him on issues relating to lasers, inertial fusion, condensed matter physics, R&D management, education, DAS management, and the philosophical underpinnings of the Fannie and John Hertz Foundation, which I now have the privilege to direct. I had many personal conversations with Prof. Edward Teller over the years. For the talk and this note, I spoke with Hans Mark, Mike May, Arthur Kantrowitz, Chuck Leith, Wendy Teller, Richard Freeman, Wilson Talley, John Nuckolls, Lowell Wood, Don Correll, Richard Farnsworth, Charles Westbrook, and Mort Weiss. I also wish to acknowledge the assistance of Maxine Trost for archive services, Robin Roth for documents, and Barbara Nichols for research.

References 1. E. Teller, “Memoirs” w/ J. Shoolery, Perseus Publishing, Cambridge, MA, 2001. 2. J. Krige, “American Hegemony & the Postwar Reconstruction of Science in Europe”, MIT Press, 2006. 3. E. Teller, W. Teller and W. Talley, “Conversations on the Dark Secrets of Physics, ” Perseus Books, Cambridge, 2002. 157

MESSAGE TO THE NEXT GENERATION

EDWARD TELLER

April 3, 2000

In the whole history of physics, there have been three events that were most important because they were absurd and yet true. The first is that we are moving around at a great and variable speed in the universe much bigger than appears to our immediate perception. By much bigger, I mean more than a billion times a billion. The proposal was first made, to my knowledge, at the Greek Center of Knowledge in Alexandria two millennia ago by Aristarchus. It took nearly two thousand years until it was “proven” by Copernicus, advertised by Galileo and turned into a scientific fact by Newton. It has changed our outlook on the universe in a manner that is deep and thorough going, yet not deep enough. It is remarkable that there are only two other similarly absurd and magnificent changes both having been made in the early parts of the 20th century about the time I was born — or shortly after. These two topics are relativity and quantum mechanics. Relativity is absurd because it challenges the idea of time. Actually, it points out that we can’t talk about time independently of space: a concept far beyond our ability of immediate perception. The other development, quantum mechanics, disproves the mechanistic and predicable structure of our universe and concludes that about the future, we can only make probability statements and in a precise sense, never actual complete predictions. Indeed, a physicist of the 19th century, if he believed in God, should have maintained that God is now unemployed because he created the universe together with all its necessary future about which nothing 158 can be changed. Today, if you believe in God, you have more things for him to do than you can imagine. Some of these ideas acted upon me before I reached the age of 20 years. My curiosity, indeed, my absolute need to know, were awakened to the extent that I could not evade, and I joined the ranks of the wonderful physicists in Central Europe headed by Niels Bohr and followed by my teacher, Werner Heisenberg. My interest was the explicit explanation of the consequences of quantum mechanics in which, from case to case, I succeeded. Such a case, was, for instance, the controversy between Heisenberg and the young Russian, Landau. Landau had a somewhat abstract proof that electrons in the metal influenced the magnetic field. Heisenberg argued against it, together with Bohr, in a rather simple manner. And I found, surprisingly, that Heisenberg was wrong. More surprisingly, Heisenberg welcomed my ideas and gave me a fine dinner for explaining how a relatively few electrons at the boundaries of the metals can accomplish what the average electron inside the metal cannot. Another example was, years later, the explanation why a simple molecule, the organic molecule, benzene, has not one formula, one chemical formula, but two. The need for that had been evident for systematic reasons. Together with some collaborators, I was fortunate to find that the two formulae corresponded to two states of benzene: a ground state — a lower state, and a slightly excited state, which mixed in a manner unusual in chemistry but in our modern view, very explicitly defined. All this was hard work but more connected with pleasure than ever with exhaustion. And when I came to the United States, in the mid-1930s, I found plenty of interest in the new ideas and I hoped to be, what I always wanted to be, a professor forever. My hope was not fulfilled. A fellow Hungarian immigrant to the United States, Leo Szilard, disturbed my placid life and super-active work. He engaged me as chauffeur to take him to Einstein for the purpose that Einstein should write a letter to President Roosevelt asking for the practical application of enormous energies inside the atomic nucleus which itself fills less than a few thousandths of one percent of the linear dimensions of the practically invisible atoms. The letter was actually written by Szilard, read in my presence by 159

Einstein who signed it. This led to the atomic bomb and later to the hydrogen bomb. That kind of work was undertaken by American scientists with great reluctance. Looking back on the work, it turned out to be relatively simple. I was more easily convinced than most of my colleagues that the problems that presented themselves could be and should be solved. And this, in turn, gave now, in the second-third of the 20th century, to practical applications of very great importance. Having seen the horrible acts of Hitler getting closer and closer to my own family, I felt certain that knowledge leading to weapons cannot be neglected. And from there on, my main interest was with the applications that many others followed during the Second World War but not afterwards. It should be remembered by physicists and the general public alike that nuclear energy can be used in two forms. The more stable nuclei are of medium size. Uniting light nuclei or fusing them releases a lot of energy. Splitting-up the heaviest nucleus also gives energy due to the electrostatic repulsion between its parts. This second method, fission, was brought to a successful conclusion before the Second World War ended in Japan. Then, this actually led to the decisive bombing of Japan that cost many lives, but in ending the War, saved even more. To this day, I regret that the actual use of these explosives has not been preceded by a harmless demonstration. We would now look into the future with clearer eyes if we had a complete, unquestionable justification of everything that we actually have done. Unfortunately, the second half of the program, fusion energy, derived from bringing together the smallest kind of nuclei, the nuclei of the hydrogen remained uncompleted, and among “senior” physicists, even in my 30s, I was almost the only one who believed it should be done. The problems were not easy but not particularly difficult. My role has been that I knew that what could be done will be done and should be done particularly because the presence in the world of the menacing power of the Soviet Union. One personal note is that my good friend, Lev Landau, a devoted communist, whose ideas about metals I defended against Heisenberg’s proofs, was arrested in the Soviet Union as a capitalist spy. I claim to have a clearer knowledge what the Soviets meant to the world than most of 160 my American colleagues. That removed the hindrance that kept many of my friends from working on the same things as I and left me in many ways isolated. The result was the Cold War. And the one thing that I want people to remember about the Cold War is that it was unique. It was won by a weapon, the hydrogen bomb, and a second weapon, the initiatives of a second weapon- the defense initiatives, which most fortunately never had to be used. That weapons could make peace in the world – an incomplete peace to be sure – this is important when compared to the horrors of the First and Second World Wars. Strength in the hands of those who were reluctant to use weapons did mean peace. This is the new thing that should be remembered by present and future generations. Indeed, all this work had a positive outcome as far as the immediate effects on history were going. They had an unfortunate negative outcome in that they introduced thorough-going secrecy in relation to all these new discoveries. Such secrecy has now been practiced very vigorously for half a century. It did not prevent at least half of the world population to be, indirectly through their governments, in the knowledge and potential possession of these weapons. We could have and should have learned that secrecy, apart from being opposite to all scientific traditions, is also ineffective. We should learn the way to live in a thoroughly new world. And why and how is the world new? It is new because it has become small. Our actions should be, today, influenced by actions all over the world because weapons from practically anywhere can reach us with the help of the new technological accomplishments. What holds for machines holds at least equally for ideas. Publications are reached instantaneously — by everybody in the world. The world now is interconnected and the United States, with its tradition of centuries of isolation by the oceans, have lost that isolation. It is an absolute necessity that we learn to live in a world in which we are no longer alone and no longer protected against actions of violence any more than was Poland against the actions of Hitler. So far, the power of the United States with the firm intention of keeping peace has prevailed. This power of knowledge is, however, endangered by a very simple, very general and very terrible fact. People throughout the world becoming aware of the potential, 161 including also the evil potential inherent in new discoveries, are trying to limit knowledge. If I learned something in my existence of almost a century, it is this: Ignorance, though very general among humans, is the opposite of virtue. Virtue based on ignorance is ineffective and no good. We must share knowledge, at least knowledge about simple principles. Detailed plans and executions might be kept secret. But knowledge in general must be developed to its potential limits. And, in fact, these limits seem not to exist. They appear to recede into further parts of the unknown as more attention is paid to what used to be the limits of knowledge. And here are two joint problems: Knowledge and cooperation. Both are needed. They must be reconciled. How to do it? In the end, in detail, I don’t know. But I recommend to the attention of every young person the need to think in terms of the whole world: the need for cooperation and the probable answer that cooperation which, on a really big scale, never existed will not be brought about in a rapid decision. It must come gradually, and we must start small. I want to end with a very simple example. We are today afraid that our energy consumption will lead to a warming of the world to an uncomfortable extent. All kinds of radical proposals are made to prevent that. I claim that the first thing to do is to know, to predict what is going to happen in the distant future as well as particularly in the near future. Before we can take very seriously what will happen in half a century, we must be able to predict weather at least a couple of weeks ahead. And the magnificent progress in computers makes it possible to do this if only one difficult condition is fulfilled, if only we knew today how the world and its surrounding atmosphere behaves in regard to weather in every square mile. And such general knowledge could be obtained and would be very valuable in planning the immediate future of harvests, of the flight of airplanes, of the amelioration of worldwide weather catastrophes. Here is a topic where cooperation would pay and would be most important, not because of its immediate profits, but because of the experience it would give all of us how cooperation helps. Here is, therefore, the message to the next generation. Prepare for the strange state of one world, and in my ideas, one world does not mean uniformity. One world means permissiveness of 162 all kinds of things in this one world, as long as the world has no ______in it,a as long as differences are there, not for the sake of hatred, but for the sake of active and useful cooperation. This is what my life has been dedicated to and this is what is going to be described in this book.b

aIn the dictated manuscript, Teller’s words weren’t clear at this point. My memory (SBL) is that he said something like ``…as long the world has no coerced uniformity in it…” bThe book alluded to here is a still to be completed volume reprinting his papers with commentaries.