FELIX BLOCH October 23, 1905-September 10, 1983
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A Beginner's Guide to Bloch Equation Simulations of Magnetic
A Beginner’s Guide to Bloch Equation Simulations of Magnetic Resonance Imaging Sequences ML Lauzon, PhD Depts of Radiology and Clinical Neurosciences, University of Calgary, Calgary, AB, Canada Seaman Family MR Research Centre, Calgary, AB, Canada [email protected] ABSTRACT Nuclear magnetic resonance (NMR) concepts are rooted in quantum mechanics, but MR imaging principles are well described and more easily grasped using classical ideas and formalisms such as Larmor precession and the phenomenological Bloch equations. Many textbooKs provide in-depth descriptions and derivations of the various concepts. Still, carrying out numerical Bloch equation simulations of the signal evolution can oftentimes supplement and enrich one’s understanding. And though it may appear intimidating at first, performing these simulations is within the realm of every imager. The primary objective herein is to provide novice MR users with the necessary and basic conceptual, algorithmic and computational tools to confidently write their own simulator. A brief background of the idealized MR imaging process, its concepts and the pulse sequence diagram are first provided. Thereafter, two regimes of Bloch equation simulations are presented, the first which has no radio frequency (RF) pulses, and the second in which RF pulses are applied. For the first regime, analytical solutions are given, whereas for the second regime, an overview of the computationally efficient, but often overlooked, Rodrigues’ rotation formula is given. Lastly, various simulation conditions of interest and example code snippets are given and discussed to help demonstrate how straightforward and easy performing MR simulations can be. INTRODUCTION Magnetic resonance (MR) imaging is one of the most versatile imaging modalities used clinically. -
Edward Mills Purcell (1912–1997)
ARTICLE-IN-A-BOX Edward Mills Purcell (1912–1997) Edward Purcell grew up in a small town in the state of Illinois, USA. The telephone equipment which his father worked with professionally was an early inspiration. His first degree was thus in electrical engineering, from Purdue University in 1933. But it was in this period that he realized his true calling – physics. After a year in Germany – almost mandatory then for a young American interested in physics! – he enrolled in Harvard for a physics degree. His thesis quickly led to working on the Harvard cyclotron, building a feedback system to keep the radio frequency tuned to the right value for maximum acceleration. The story of how the Manhattan project brought together many of the best physicists to build the atom bomb has been told many times. Not so well-known but equally fascinating is the story of radar, first in Britain and then in the US. The MIT radiation laboratory was charged with developing better and better radar for use against enemy aircraft, which meant going to shorter and shorter wavelengths and detecting progressively weaker signals. This seems to have been a crucial formative period in Purcell’s life. His coauthors on the magnetic resonance paper, Torrey and Pound, were both from this lab. I I Rabi, the physicist who won the 1944 Nobel Prize for measuring nuclear magnetic moments by resonance methods in molecular beams, was the head of the lab and a major influence on Purcell. Interestingly, Felix Bloch (see article on p.956 in this issue) was at the nearby Radio Research lab but it appears that the two did not interact much. -
4 Nuclear Magnetic Resonance
Chapter 4, page 1 4 Nuclear Magnetic Resonance Pieter Zeeman observed in 1896 the splitting of optical spectral lines in the field of an electromagnet. Since then, the splitting of energy levels proportional to an external magnetic field has been called the "Zeeman effect". The "Zeeman resonance effect" causes magnetic resonances which are classified under radio frequency spectroscopy (rf spectroscopy). In these resonances, the transitions between two branches of a single energy level split in an external magnetic field are measured in the megahertz and gigahertz range. In 1944, Jevgeni Konstantinovitch Savoiski discovered electron paramagnetic resonance. Shortly thereafter in 1945, nuclear magnetic resonance was demonstrated almost simultaneously in Boston by Edward Mills Purcell and in Stanford by Felix Bloch. Nuclear magnetic resonance was sometimes called nuclear induction or paramagnetic nuclear resonance. It is generally abbreviated to NMR. So as not to scare prospective patients in medicine, reference to the "nuclear" character of NMR is dropped and the magnetic resonance based imaging systems (scanner) found in hospitals are simply referred to as "magnetic resonance imaging" (MRI). 4.1 The Nuclear Resonance Effect Many atomic nuclei have spin, characterized by the nuclear spin quantum number I. The absolute value of the spin angular momentum is L =+h II(1). (4.01) The component in the direction of an applied field is Lz = Iz h ≡ m h. (4.02) The external field is usually defined along the z-direction. The magnetic quantum number is symbolized by Iz or m and can have 2I +1 values: Iz ≡ m = −I, −I+1, ..., I−1, I. -
I. I. Rabi Papers [Finding Aid]. Library of Congress. [PDF Rendered Tue Apr
I. I. Rabi Papers A Finding Aid to the Collection in the Library of Congress Manuscript Division, Library of Congress Washington, D.C. 1992 Revised 2010 March Contact information: http://hdl.loc.gov/loc.mss/mss.contact Additional search options available at: http://hdl.loc.gov/loc.mss/eadmss.ms998009 LC Online Catalog record: http://lccn.loc.gov/mm89076467 Prepared by Joseph Sullivan with the assistance of Kathleen A. Kelly and John R. Monagle Collection Summary Title: I. I. Rabi Papers Span Dates: 1899-1989 Bulk Dates: (bulk 1945-1968) ID No.: MSS76467 Creator: Rabi, I. I. (Isador Isaac), 1898- Extent: 41,500 items ; 105 cartons plus 1 oversize plus 4 classified ; 42 linear feet Language: Collection material in English Location: Manuscript Division, Library of Congress, Washington, D.C. Summary: Physicist and educator. The collection documents Rabi's research in physics, particularly in the fields of radar and nuclear energy, leading to the development of lasers, atomic clocks, and magnetic resonance imaging (MRI) and to his 1944 Nobel Prize in physics; his work as a consultant to the atomic bomb project at Los Alamos Scientific Laboratory and as an advisor on science policy to the United States government, the United Nations, and the North Atlantic Treaty Organization during and after World War II; and his studies, research, and professorships in physics chiefly at Columbia University and also at Massachusetts Institute of Technology. Selected Search Terms The following terms have been used to index the description of this collection in the Library's online catalog. They are grouped by name of person or organization, by subject or location, and by occupation and listed alphabetically therein. -
Appendix E Nobel Prizes in Nuclear Science
Nuclear Science—A Guide to the Nuclear Science Wall Chart ©2018 Contemporary Physics Education Project (CPEP) Appendix E Nobel Prizes in Nuclear Science Many Nobel Prizes have been awarded for nuclear research and instrumentation. The field has spun off: particle physics, nuclear astrophysics, nuclear power reactors, nuclear medicine, and nuclear weapons. Understanding how the nucleus works and applying that knowledge to technology has been one of the most significant accomplishments of twentieth century scientific research. Each prize was awarded for physics unless otherwise noted. Name(s) Discovery Year Henri Becquerel, Pierre Discovered spontaneous radioactivity 1903 Curie, and Marie Curie Ernest Rutherford Work on the disintegration of the elements and 1908 chemistry of radioactive elements (chem) Marie Curie Discovery of radium and polonium 1911 (chem) Frederick Soddy Work on chemistry of radioactive substances 1921 including the origin and nature of radioactive (chem) isotopes Francis Aston Discovery of isotopes in many non-radioactive 1922 elements, also enunciated the whole-number rule of (chem) atomic masses Charles Wilson Development of the cloud chamber for detecting 1927 charged particles Harold Urey Discovery of heavy hydrogen (deuterium) 1934 (chem) Frederic Joliot and Synthesis of several new radioactive elements 1935 Irene Joliot-Curie (chem) James Chadwick Discovery of the neutron 1935 Carl David Anderson Discovery of the positron 1936 Enrico Fermi New radioactive elements produced by neutron 1938 irradiation Ernest Lawrence -
Proton Remains Puzzling
Proton remains puzzling The 10th Circum-Pan-Pacific Symposium on High Energy Spin Physics Taipei, October 5-8, 2015 Haiyan Gao Duke University and Duke Kunshan University 1 Lepton scattering: powerful microscope! • Clean probe of hadron structure • Electron (lepton) vertex is well-known from QED • One-photon exchange dominates, higher-order exchange diagrams are suppressed (two-photon physics) • Vary the wave-length of the probe to view deeper inside 2 ' " 2 2 % dσ α E GE +τGM 2 θ 2 2 θ = $ cos + 2τGM sin ' 2 2 2 4 θ τ = −q / 4M dΩ 4E sin E # 1+τ 2 2 & 2 Virtual photon 4-momentum! q = k − k' = (q,ω) Q2 = −q2 1 k’ α = 137 2 k € What is inside the proton/neutron? 1933: Proton’s magneHc moment 1960: ElasHc e-p scaering Nobel Prize Nobel Prize In Physics 1943 In Physics 1961 Oo Stern Robert Hofstadter "for … and for his thereby achieved discoveries "for … and for his discovery of the magne;c concerning the structure of the nucleons" moment of the proton". g =2 Form factors Charge distributions 6 ! 1969: Deep inelasHc e-p scaering 1974: QCD AsymptoHc Freedom Nobel Prize in Physics 1990 Nobel Prize in Physics 2004 Jerome I. Friedman, Henry W. Kendall, Richard E. Taylor David J. Gross, H. David Politzer, Frank Wilczek "for their pioneering inves;ga;ons "for the discovery of asympto;c concerning deep inelas;c sca<ering of freedom in the theory of the strong electrons on protons …". 3 interacon". From J.W. Qiu Tremendous advances in electron scattering Unprecedented capabilities: • High Intensity • High Duty Factor • High Polarization • Parity -
Nobel Prize Physicists Meet at Lindau
From 28 June to 2 July 1971 the German island town of Lindau in Nobel Prize Physicists Lake Constance close to the Austrian and Swiss borders was host to a gathering of illustrious men of meet at Lindau science when, for the 21st time, Nobel Laureates held their reunion there. The success of the first Lindau reunion (1951) of Nobel Prize win ners in medicine had inspired the organizers to invite the chemists and W. S. Newman the physicists in turn in subsequent years. After the first three-year cycle the United Kingdom, and an audience the dates of historical events. These it was decided to let students and of more than 500 from 8 countries deviations in the radiocarbon time young scientists also attend the daily filled the elegant Stadttheater. scale are due to changes in incident meetings so they could encounter The programme consisted of a num cosmic radiation (producing the these eminent men on an informal ber of lectures in the mornings, two carbon isotopes) brought about by and personal level. For the Nobel social functions, a platform dis variations in the geomagnetic field. Laureates too the Lindau gatherings cussion, an informal reunion between Thus chemistry may reveal man soon became an agreeable occasion students and Nobel Laureates and, kind’s remote past whereas its long for making or renewing acquain on the last day, the traditional term future could well be shaped by tances with their contemporaries, un steamer excursion on Lake Cons the developments mentioned by trammelled by the formalities of the tance to the island of Mainau belong Mössbauer, viz. -
Its Selflessness,Friendliness, Statesmanship, Helped to Establish
Leonard I. Schiff died on January 19, 1971 in the midst of a full life, which was unusual for its selflessness, friendliness, statesmanship, and remarkable scientific productivity. He was a teacherand scholar of extraordinary breadth. In his memory and to affirm the high standards in lecturing and research that he so greatly helped to establish, it is most fitting to bring to Stanford a diverse group of outstanding physicists. The Physics Department is establishing a memorial fund, which will be used to support an annual Distinguished Lectureship for physicists of great distinction who will be invited to give a memorial lecture open to the public. Ii is hoped that sufficient funds will be raised to enable the Distinguished Lecturer on occasion to remain in the Department for an extensive stay so that he can interact with students and faculty. Contributions and pledges to the Leonard I. Schiff Memorial Fund should be mailed to the Departmentof Physics, Stanford University, California 94305. Felix Bloch David Ritson Marvin Chodorow Arthur Schawlow William Fairbank Melvin Schwartz Alexander Fetter Alan Schwettman Stanley Hanna Dirk Walecka Robert Hofstadter Stanley Wojcicki William Little Mason Yearian Walter Meyerhof A Distinguished Lectureship in memory of Leonard I. Schiff Professor of Physics Stanford University DistinguishedLectures in memory An invitation to attend the of Leonard I. Schiff: 1976DistinguishedLectures inmemoryof 1972 "HadronStructure and High Energy Collisions" LEONARD I. SCHIFF by Chen Ning Yang Professor of Physics Stanford University 1973 "The Approachto Thermal Equilibrium and Other Steady States" by Willis EugeneLamb, Jr. 1974 "The Evolution of a Nuclear Reaction" by Herman Feshbach 1975 "The World as Quarks, Leptons and Bosons" by Murray Gell-Mann Leonard I. -
Sidney D. Drell 1926–2016
Sidney D. Drell 1926–2016 A Biographical Memoir by Robert Jaffe and Raymond Jeanloz ©2018 National Academy of Sciences. Any opinions expressed in this memoir are those of the authors and do not necessarily reflect the views of the National Academy of Sciences. SIDNEY daVID DRELL September 13, 1926–December 21, 2016 Elected to the NAS, 1969 Sidney David Drell, professor emeritus at Stanford Univer- sity and senior fellow at the Hoover Institution, died shortly after his 90th birthday in Palo Alto, California. In a career spanning nearly 70 years, Sid—as he was universally known—achieved prominence as a theoretical physicist, public servant, and humanitarian. Sid contributed incisively to our understanding of the elec- tromagnetic properties of matter. He created the theory group at the Stanford Linear Accelerator Center (SLAC) and led it through the most creative period in elementary particle physics. The Drell-Yan mechanism is the process through which many particles of the Standard Model, including the famous Higgs boson, were discovered. By Robert Jaffe and Raymond Jeanloz Sid advised Presidents and Cabinet Members on matters ranging from nuclear weapons to intelligence, speaking truth to power but with keen insight for offering politically effective advice. His special friendships with Wolfgang (Pief) Panofsky, Andrei Sakharov, and George Shultz highlighted his work at the interface between science and human affairs. He advocated widely for the intellectual freedom of scientists and in his later years campaigned tirelessly to rid the world of nuclear weapons. Early life1 and work Sid Drell was born on September 13, 1926 in Atlantic City, New Jersey, on a small street between Oriental Avenue and Boardwalk—“among the places on the Monopoly board,” as he was fond of saying. -
Proton Radius Puzzle Intensified
Proton Charge Radius 7th Workshop on Hadron Physics in China and Opportunities Worldwide Kunshan, August 3-7, 2015 Haiyan Gao Duke University and Duke Kunshan University 1 QCD: still unsolved in non-perturbative region Gauge bosons: gluons (8) • 2004 Nobel prize for ``asympto5c freedom’’ • non-perturbave regime QCD ????? • One of the top 10 challenges for physics! • QCD: Important for discovering new physics beyond SM • Nucleon structure is one of the most ac5ve areas What is inside the proton/neutron? 1933: Proton’s magne+c moment 1960: Elas+c e-p scaering Nobel Prize Nobel Prize In Physics 1943 In Physics 1961 Oo Stern Robert Hofstadter "for … and for his thereby achieved discoveries "for … and for his discovery of the magne7c moment concerning the structure of the nucleons" of the proton". g =2 Form factors Charge distributions 6 ! 1969: Deep inelas+c e-p scaering 1974: QCD Asymptoc Freedom Nobel Prize in Physics 1990 Nobel Prize in Physics 2004 Jerome I. Friedman, Henry W. Kendall, Richard E. Taylor David J. Gross, H. David Politzer, Frank Wilczek "for their pioneering inves7ga7ons "for the discovery of asympto7c concerning deep inelas7c sca9ering of freedom in the theory of the strong electrons on protons …". interacon". 3 Lepton scattering: powerful microscope! • Clean probe of hadron structure • Electron (lepton) vertex is well-known from QED • Vary probe wave-length to view deeper inside 2 ' " 2 2 % dσ α E GE +τGM 2 θ 2 2 θ 2 2 = $ cos + 2τGM sin ' q / 4M 2 4 θ τ = − dΩ 4E sin E # 1+τ 2 2 & 2 Virtual photon 4-momentum! q = k − k' = (q,ω) Q2 = −q2 1 k’ α = 137 4 k € Unpolarized electron-nucleon scaOering (Rosenbluth Separa5on) • Elas+c e-p cross sec+on • At fixed Q2, fit dσ/dΩ vs. -
The Classical Bloch Equations
The classical Bloch equations Martin Frimmer and Lukas Novotny ETH Zurich,€ Photonics Laboratory, 8093 Zurich,€ Switzerland (www.photonics.ethz.ch) (Received 13 October 2013; accepted 7 May 2014) Coherent control of a quantum mechanical two-level system is at the heart of magnetic resonance imaging, quantum information processing, and quantum optics. Among the most prominent phenomena in quantum coherent control are Rabi oscillations, Ramsey fringes, and Hahn echoes. We demonstrate that these phenomena can be derived classically by use of a simple coupled- harmonic-oscillator model. The classical problem can be cast in a form that is formally equivalent to the quantum mechanical Bloch equations with the exception that the longitudinal and the transverse relaxation times (T1 and T2) are equal. The classical analysis is intuitive and well suited for familiarizing students with the basic concepts of quantum coherent control, while at the same time highlighting the fundamental differences between classical and quantum theories. VC 2014 American Association of Physics Teachers. [http://dx.doi.org/10.1119/1.4878621] I. INTRODUCTION offers students an intuitive entry into the field and prepares them with the basic concepts of quantum coherent control. The harmonic oscillator is arguably the most fundamental building block at the core of our understanding of both clas- sical and quantum physics. Interestingly, a host of phenom- II. THE MECHANICAL ATOM ena originally encountered in quantum mechanics and A. Equations of motion initially thought to be of purely quantum-mechanical nature have been successfully modelled using coupled classical har- Throughout this paper, we consider two oscillators, as monic oscillators. -
The Federal Government: a Nobel Profession
The Federal Government: A Nobel Profession A Report on Pathbreaking Nobel Laureates in Government 1901 - 2002 INTRODUCTION The Nobel Prize is synonymous with greatness. A list of Nobel Prize winners offers a quick register of the world’s best and brightest, whose accomplishments in literature, economics, medicine, science and peace have enriched the lives of millions. Over the past century, 270 Americans have received the Nobel Prize for innovation and ingenuity. Approximately one-fourth of these distinguished individuals are, or were, federal employees. Their Nobel contributions have resulted in the eradication of polio, the mapping of the human genome, the harnessing of atomic energy, the achievement of peace between nations, and advances in medicine that not only prolong our lives, but “This report should serve improve their quality. as an inspiration and a During Public Employees Recognition Week (May 4-10, 2003), in an effort to recognize and honor the reminder to us all of the ideas and accomplishments of federal workers past and present, the Partnership for Public Service offers innovation and nobility of this report highlighting 50 American Nobel laureates the work civil servants do whose award-winning achievements occurred while they served in government or whose public service every day and its far- work had an impact on their career achievements. They were honored for their contributions in the fields reaching impact.” of Physiology or Medicine, Economic Sciences, and Physics and Chemistry. Also included are five Americans whose work merited the Peace Prize. Despite this legacy of accomplishment, too few Americans see the federal government as an incubator for innovation and discovery.