Models of the Atomic Nucleus

Models of the Atomic Nucleus Second Edition Norman D. Cook Models of the Atomic Nucleus Unification Through a Lattice of Nucleons Second Edition 123 Prof. Norman D. Cook Kansai University Dept. Informatics 569 Takatsuki, Osaka Japan [email protected] Additional material to this book can be downloaded from http://extras.springer.com. ISBN 978-3-642-14736-4 e-ISBN 978-3-642-14737-1 DOI 10.1007/978-3-642-14737-1 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010936431 © Springer-Verlag Berlin Heidelberg 2006, 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Preface to the Second Edition Already by the 1970s, some theorists had declared that nuclear structure physics was a “closed chapter” in science, but since then it has repeatedly been found necessary to re-open this closed chapter to address old problems and to explain new phenomena. The present volume shows why a declaration that there is nothing more to learn about nuclear structure is premature – and outlines the path toward unification of the diverse models still in use by nuclear theorists. In preparing the Second Edition of Models of the Atomic Nucleus I have expanded on two topics mentioned only briefly in the First Edition. One is a more extensive discussion of the foundations of the independent-particle model, as established by Eugene Wigner in 1937. Despite first appearances, that discussion is not primar- ily historical, but rather is an explanation of Wigner’s early discovery of the lattice symmetries of the nucleus. For historical reasons, the geometry of the lattice was not emphasized in the 1930s and 1940s, but the symmetries inherent to the fcc lattice led directly to the establishment of the independent-particle model as the central paradigm of nuclear theory – and eventually to the shell model and its modern vari- ants. As discussed in Chap. 10, the coordinate-space geometry of the lattice, as distinct from an abstract “quantum space” interpretation, has clear implications for nuclear structure theory – and is indeed the motivation for writing this monograph. The bottom-line is that the lattice symmetries are truly at the heart of conventional nuclear physics – originally stated in Wigner’s work from 1937, developed by Friedrich Everling in the 1950s and Klaus Lezuo in the 1970s – and permeating every aspect of nuclear theory since then. In other words, I argue that it is incorrect to consider the fcc lattice as yet-another nuclear model with only limited applica- tions, or as an unorthodox “alternative” view. Rather, the lattice is a strong candidate for unifying the many previous and seemingly-contradictory models of nuclear theory employed since the 1950s. And it is strong because it is built, from the ground up, on Wigner’s description of the quantum mechanics of the nucleus. To state the argument more explicitly, the symmetries of the fcc lattice are identi- cal to those of the independent-particle model and the independent-particle model is orthodox nuclear theory. Following Wigner’s lead, it is easy to show that the conventional description of the energy states of nucleons has a straightforward geometry in v vi Preface to the Second Edition the form of a specific 3D lattice. In this regard, the unification of nuclear structure theory through the fcc lattice model is not as revolutionary as it may first appear to be. Unfortunately, the unarticulated “picture” in the back of the mind of nearly every nuclear physicist alive today is one of protons and neutrons buzzing around inside of the tiny nuclear volume – not unlike the random movements of electrons in over- lapping electron orbitals (“Zitterbewegung”). The idea that the shells and subshells of the nucleus have a geometrical basis quite unlike electron clouds is therefore seen as “counter-intuitive.” For this reason, much of the following text is devoted to showing why, on the contrary, a gaseous-phase picture of the nucleus should be considered counter-intuitive, and how a lattice model can reproduce the exact same sequence and occupancy of nucleons found in the independent-particle model on a geometrical basis. The second major change in the Second Edition is a more detailed examination of the predictions of the lattice with regard to fission. This includes an introduction to the nuclear structure aspects of so-called low-energy nuclear reactions (LENR), also known as condensed-matter nuclear science (CMNS) and chemically-assisted nuclear reactions (CANR). This branch of nuclear physics is the progeny of the controversial “cold fusion” phenomena, first reported in 1989, but now widely understood to have a solid empirical foundation. I do not delve into the history and politics of cold fusion – both of which have been discussed in detail by others, but have concentrated on the experimental results that have provided indication of the fission of Palladium in certain types of high-pressure electrolysis experiments. Many of the experimental and theoretical issues concerning the induction of LENR are still unresolved, but the so-called transmutation results are among the most unambiguous empirical findings indicative of nuclear effects in “tabletop” experimental set-ups. The Second Edition discusses both the experimental findings and their simulation using the fcc lattice model. Similar to the theoretical results obtained from the lattice model in explaining the fission of Uranium, predictions concerning the fission fragments from Palladium are concrete indication that the geometry of the nuclear lattice can be used to explain experimental data that the other nuclear structure models cannot. My hope is therefore that any nuclear physicist with lingering doubts about the “finality” and “completeness” of conventional nuclear structure theory will examine the two fission sections, and give some thought to the lattice “reconstruction” of nuclear theory that led to Wigner’s Nobel Prize in 1963. The bottom-line is that – despite the conceptual difficulties of quantum mechanics in general, nuclear structure itself is surprisingly straight-forward when viewed within the framework of a lattice of nucleons – and comprehensible on its own terms without invoking any of the various controversial quantum mechanical tricks of time-reversal, partial charge or the selective allowance of the impossible under the uncertainty flag. My main argument, in other words, is that nuclear structure can be understood on a geometrical basis that the traditional textbooks simply do not convey. Although both the lattice and the conventional independent-particle model description of nucleon states are based fundamentally on the Schrödinger wave-equation, it is Preface to the Second Edition vii only through the lattice that the geometrical symmetries become self-evident. Solid geometry is itself perhaps not “easy,” but the Nuclear Visualization Software allows for the 3D manipulation of specific nuclei and the visualization of their various quantum mechanical properties within the framework of the lattice model, or any of the other models of nuclear structure theory. The first Edition of this book was completed during a Sabbatical Leave of Absence from Kansai University (September 2004 to September 2005). Finally, I would like to thank Valerio Dallacasa, Paolo Palazzi, Friedrich Everling, Tracey Runciman, Paolo DiSia and Dennis Letts for their time and effort in contributing to the Second Edition. Osaka, November 2010 Norman D. Cook Preface to the First Edition Models of the Atomic Nucleus is a largely non-technical introduction to nuclear theory – an attempt to explain one of the most important objects in natural science in a way that makes nuclear physics as comprehensible as chemistry or cell biology. Unlike most other scientific fields, the popularization of nuclear physics has not gen- erally been successful because many fundamental issues remain controversial and, even after more than 70 years of study, a “unified theory” of nuclear structure has not yet been established. Nevertheless, despite some widely-acknowledged unfin- ished business, the theme developed in this book is that each of the many models in use in nuclear theory provides a partial perspective on the nucleus that can be integrated into a coherent whole within the framework of a lattice of nucleons. The proposed unification itself is not uncontroversial, but, at the very least, the lattice representation of nuclear structure illustrates how a complex physical object such as the nucleus can be understood as simultaneously exhibiting the properties of a gas, a liquid, a molecular cluster and a solid. The book is divided into three parts. Part I (Chaps. 1, 2, 3 and 4) introduces the main topics that must be addressed in any discussion of nuclear physics. My intention has been to present a brief, but even-handed summary of the basic models that have been devised to explain nuclear phenomena and to review the theoretical ideas that have occupied the minds of theorists for many decades. These chapters are historical and are intended to convey what the major insights and conceptual challenges of nuclear physics have been thus far.

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