㰀椀洀最 愀氀椀最渀㴀氀攀昀琀 戀漀爀搀攀爀㴀㈀ 猀爀挀㴀∀搀攀栀洀攀氀琀⸀最椀昀∀㸀
The phenomenal accuracies achieved for the spectroscopy of single charged particles suspended in Penning traps has prompted this study of the imperfect Penning trap. The principal result is a new prescription for the cyclotron frequency in terms of the observable eigenfrequencies of the imperfect trap. The new prescription is completely insensitive to a misalignment of the magnetic field direction with the axis of the Penning electrodes, and it is also insensitive to the most significant imperfections in the electrostatic potential. These systematic effects can therefore be completely circumvented in measurements of the anomalous magnetic moments of the electron and positron, and also in experiments on protons and heavier ions where the effects are much larger㰀⼀戀爀㸀㰀戀爀㸀倀攀渀渀椀渀最 琀爀愀瀀猀 栀愀瘀攀 氀漀渀最 戀攀攀渀 愀渀 椀洀瀀漀爀琀愀渀琀 琀漀漀氀 昀漀爀 栀椀最栀 瀀爀攀挀椀猀椀漀渀 洀攀愀猀甀爀攀洀攀渀琀猀 椀渀 瀀栀礀猀椀挀猀Ⰰ 猀甀挀栀 愀猀 琀栀攀 洀攀愀猀甀爀攀洀攀渀琀猀 漀昀 琀栀攀 最ⴀ昀愀挀琀漀爀 漀昀 琀栀攀 攀氀攀挀琀爀漀渀 愀渀搀 琀栀攀 瀀爀漀琀漀渀⼀攀氀攀挀琀爀漀渀 洀愀猀猀 爀愀琀椀漀⸀ 吀栀攀 椀搀攀愀氀 倀攀渀渀椀渀最 琀爀愀瀀 昀攀愀琀甀爀攀猀 愀 猀瀀愀琀椀愀氀氀礀 甀渀椀昀漀爀洀 洀愀最渀攀琀椀挀 昀椀攀氀搀 愀渀搀 愀渀 攀氀攀挀琀爀漀猀琀愀琀椀挀 焀甀愀搀爀甀瀀漀氀攀 瀀漀琀攀渀琀椀愀氀⸀ 䄀 挀栀愀爀最攀搀 瀀愀爀琀椀挀氀攀 洀漀瘀椀渀最 椀渀 猀甀挀栀 愀渀 椀搀攀愀氀 琀爀愀瀀 椀猀 愀 氀椀渀攀愀爀 猀礀猀琀攀洀 愀渀搀 琀栀甀猀 最攀渀攀爀愀琀攀猀 栀愀爀洀漀渀椀挀 漀猀挀椀氀氀愀琀椀漀渀猀⸀ 䤀琀 椀猀 琀栀攀 愀挀挀甀爀愀挀礀 漀昀 洀攀愀猀甀爀椀渀最 琀栀漀猀攀 栀愀爀洀漀渀椀挀 昀爀攀焀甀攀渀挀椀攀猀 琀栀愀琀 搀攀琀攀爀洀椀渀攀猀 琀栀攀 愀挀挀甀爀愀挀礀 漀昀 愀 洀攀愀猀甀爀攀洀攀渀琀⸀ 䄀 最爀攀愀琀 搀攀愀氀 栀愀猀 戀攀攀渀 搀漀渀攀 琀漀 洀椀渀椀洀椀稀攀 琀栀攀 渀漀渀氀椀渀攀愀爀椀琀礀 眀栀椀挀栀 愀爀椀猀攀猀 椀渀 琀栀攀 愀挀琀甀愀氀 挀漀渀猀琀爀甀挀琀椀漀渀 漀昀 愀 倀攀渀渀椀渀最 琀爀愀瀀⸀ 䤀渀 琀栀椀猀 搀椀猀猀攀爀琀愀琀椀漀渀Ⰰ 眀攀 椀渀瘀攀猀琀椀最愀琀攀 琀栀攀 瀀漀猀猀椀戀椀氀椀琀礀 漀昀 漀戀猀攀爀瘀椀渀最 挀栀愀漀猀 椀渀 愀 猀礀猀琀攀洀 漀昀 愀 搀爀椀瘀攀渀 猀椀渀最氀攀 挀栀愀爀最攀搀 瀀愀爀琀椀挀氀攀 洀漀瘀椀渀最 椀渀 愀 渀漀渀氀椀渀攀愀爀 倀攀渀渀椀渀最 琀爀愀瀀Ⰰ 椀渀 眀栀椀挀栀 琀栀攀 渀漀渀氀椀渀攀愀爀椀琀礀 椀猀 氀愀爀最攀 愀渀搀 渀漀琀 樀甀猀琀 愀 瀀攀爀琀甀爀戀愀琀椀漀渀 漀昀 琀栀攀 氀椀渀攀愀爀 倀攀渀渀椀渀最 琀爀愀瀀⸀ 伀甀爀 愀渀愀氀礀猀椀猀 猀栀漀眀猀 琀栀愀琀 倀攀渀渀椀渀最 琀爀愀瀀猀 洀愀礀 戀攀 甀猀攀搀 愀猀 愀 琀漀漀氀 琀漀 猀琀甀搀礀 琀栀攀 戀攀栀愀瘀椀漀爀 漀昀 愀 渀漀渀氀椀渀攀愀爀 猀礀猀琀攀洀⸀ 圀攀 昀椀爀猀琀 猀甀最最攀猀琀 愀 搀攀猀椀最渀 漀昀 愀 渀漀渀氀椀渀攀愀爀 倀攀渀渀椀渀最 琀爀愀瀀 椀渀 眀栀椀挀栀 琀栀攀 攀氀攀挀琀爀漀猀琀愀琀椀挀 瀀漀琀攀渀琀椀愀氀 眀漀甀氀搀 最爀攀愀琀氀礀 搀椀昀昀攀爀 昀爀漀洀 琀栀攀 焀甀愀搀爀甀瀀漀氀攀 瀀漀琀攀渀琀椀愀氀⸀ 䤀渀 瀀愀爀琀椀挀甀氀愀爀Ⰰ 漀甀爀 搀攀猀椀最渀 椀猀 琀漀 最攀渀攀爀愀琀攀 愀 猀琀爀漀渀最 渀漀渀氀椀渀攀愀爀 愀砀椀愀氀 瀀漀琀攀渀琀椀愀氀 ⴀⴀ琀栀攀 瀀漀琀攀渀琀椀愀氀 愀氀漀渀最 琀栀攀 洀愀最渀攀琀椀挀 昀椀攀氀搀 愀砀椀猀⸀ 圀攀 琀栀攀渀 搀椀猀挀甀猀猀 琀栀攀 洀漀琀椀漀渀 漀昀 愀 猀椀渀最氀攀 挀栀愀爀最攀搀 瀀愀爀琀椀挀氀攀 椀渀 琀栀椀猀 渀漀渀氀椀渀攀愀爀 愀砀椀愀氀 瀀漀琀攀渀琀椀愀氀⸀ 吀栀攀 爀攀猀甀氀琀愀渀琀 攀焀甀愀琀椀漀渀 漀昀 洀漀琀椀漀渀 椀猀 䐀甀昀昀椀渀最✀猀 攀焀甀愀琀椀漀渀 眀栀椀挀栀 瀀栀礀猀椀挀愀氀氀礀 搀攀猀挀爀椀戀攀猀 愀 搀愀洀瀀攀搀 渀漀渀氀椀渀攀愀爀 漀猀挀椀氀氀愀琀漀爀 搀爀椀瘀攀渀 戀礀 愀 瀀攀爀椀漀搀椀挀 昀漀爀挀攀⸀ 吀栀攀 搀礀渀愀洀椀挀愀氀 戀攀栀愀瘀椀漀爀 漀昀 琀栀椀猀 䐀甀昀昀椀渀最✀猀 攀焀甀愀琀椀漀渀 椀猀 猀琀甀搀椀攀搀 渀甀洀攀爀椀挀愀氀氀礀 戀礀 瘀愀爀礀椀渀最 琀栀攀 搀愀洀瀀椀渀最 愀渀搀 琀栀攀 搀爀椀瘀椀渀最 昀爀攀焀甀攀渀挀礀 瀀愀爀愀洀攀琀攀爀猀 愀猀 眀攀氀氀 愀猀 琀栀攀 愀洀瀀氀椀琀甀搀攀 瀀愀爀愀洀攀琀攀爀⸀ 圀攀 昀椀渀愀氀氀礀 搀椀猀挀甀猀猀 琀栀攀 瀀漀猀猀椀戀椀氀椀琀礀 漀昀 漀戀猀攀爀瘀椀渀最 挀栀愀漀猀 椀渀 猀甀挀栀 愀 渀漀渀氀椀渀攀愀爀 猀礀猀琀攀洀⸀ 匀漀洀攀 挀栀愀漀琀椀挀 爀攀最椀漀渀猀 椀渀 琀栀攀 瀀愀爀愀洀攀琀攀爀 猀瀀愀挀攀 愀爀攀 椀搀攀渀琀椀昀椀攀搀⸀
㰀椀洀最 愀氀椀最渀㴀爀椀最栀琀 戀漀爀搀攀爀㴀㈀ 眀椀搀琀栀㴀∀㈀ ∀ 栀攀椀最栀琀㴀∀㈀㔀 ∀ 猀爀挀㴀∀㈀⸀樀瀀最∀㸀
㰀⼀戀爀㸀㰀戀爀㸀
䴀礀 昀愀琀栀攀爀Ⰰ 䜀攀漀爀最Ⰰ 栀愀搀 猀琀甀搀椀攀搀 氀愀眀 愀琀 琀栀攀 唀渀椀瘀攀爀猀椀琀琀 䈀攀爀氀椀渀 昀漀爀 猀漀洀攀 礀攀愀爀猀Ⰰ 愀渀搀 椀渀 琀栀攀 昀椀爀猀琀 圀漀爀氀搀 圀愀爀 栀愀搀 戀攀攀渀 愀渀 愀爀琀椀氀氀攀爀礀 漀昀昀椀挀攀爀⸀ 䠀攀 眀愀猀 漀昀 愀 瀀栀椀氀漀猀漀瀀栀椀挀愀氀 戀攀渀搀 漀昀 洀椀渀搀 愀渀搀 愀 洀愀渀 漀昀 椀渀搀攀瀀攀渀搀攀渀琀 漀瀀椀渀椀漀渀猀⸀ 䤀渀 琀栀攀 搀攀瀀琀栀 漀昀 琀栀攀 搀攀瀀爀攀猀猀椀漀渀 栀攀 樀甀猀琀 洀愀渀愀最攀搀 琀漀 洀愀欀攀 愀 氀椀瘀椀渀最 椀渀 爀攀愀氀 攀猀琀愀琀攀⸀ 圀栀攀渀 琀栀攀 昀愀洀椀氀礀 昀漀爀琀甀渀攀猀 栀愀搀 猀栀爀甀渀欀 琀漀 漀眀渀攀爀猀栀椀瀀 漀昀 愀 栀攀愀瘀椀氀礀 洀漀爀琀最愀最攀搀 愀瀀愀爀琀洀攀渀琀 戀甀椀氀搀椀渀最 氀漀挀愀琀攀搀 椀渀 愀渀 漀瘀攀爀眀栀攀氀洀椀渀最氀礀 䌀漀洀洀甀渀椀猀琀 瀀愀爀琀 漀昀 䈀攀爀氀椀渀Ⰰ
it seemed reasonable to move into one of the apartments ourselves as nobody paid any rent. Cannons were deployed on the streets on occasion and the class war had entered the class rooms. After a few bloody noses administered by a burly repeater, I shifted my interests from roaming the streets more towards playing with rudimentary radio receivers and noisy and smelly experiments in my mother's kitchen. In the spring of 1933 my mother, a very energetic lady, saw to it that, at the age of ten, I entered the Gymnasium zum Grauen Kloster, the oldest Latin school in Berlin, which counted Bismarck amongst its Alumni. This involved a stiff entrance examination and I was admitted on a scholarship. My father at that time expressed the opinion that I probably would be happier as a plumber. However, he apparently didn't quite believe this himself. Thus, in years before, he had bought me an erector set and books on the lives of famous inventors and Greek mythology, and when I was ill he had given me the encyclopedia to read. I supplemented the school curriculum with do-it-yourself radio projects until I had hardly any time left for my class work. Only tutoring from my father rescued me from disaster. Reading popular radio books deepened my interest in physics. While physics was taught at the Kloster only in the later grades, in the public library I read books with titles such as "Umsturz im Weltbild der Physik" and learned about the Balmer series and Bohr's energy levels of the hydrogen atom. My teachers at the Kloster were excellent, I remember in particular Dr. Richter, who taught Latin and Greek, and Dr. Splettstoesser, who taught biology and physics. Richter liked to expand on the classical works, which we were reading in class. I spent most of the ample breaks in related intense discussions with a group of classmates, Heppke, Hubner, Landau and Leiser while others engaged in boxing matches. Splettstoesser was a working scientist who spent Summers as a visitor with a marine biology institute on the Adriatic. I jumped a term and graduated in the spring of 1940.
Having received a notice from the draft board, I found it wise to volunteer for the anti-aircraft artillery and a motorized unit. I was not able to serve as a radio man but was assigned to a gun crew and never rose above the rank of senior private. Sent to relieve the German armies at Stalingrad, my battery was extremely lucky to escape the encirclement. A few months later I was even more lucky to be ordered back to Germany to study physics under an army program at the Universität Breslau in 1943. After one year of study, I was sent to the Western Front and captured in the Battle of the Bulge. I spent a year in an American prisoner of war camp in France and was released early in 1946. Supporting myself with the repair and barter of prewar radios, I took up my study of physics again at the Universität Göttingen. Here I attended lectures by Pohl, Richard Becker, Hans Kopfermann and Werner Heisenberg; Max v. Laue and Max Planck attended the physics colloquia. At the funeral of Planck I was chosen to be one of the pall bearers. At the university, I greatly enjoyed repeating the Frank-Hertz experiment, the Millikan oil drop, Zeemann effect, Hull's magnetron, Langmuir's plasma tube and other classic modern physics experiments in an excellent laboratory class run by Wolfgang Paul. In one of his Electricity & Magnetism classes Becker drew a dot on the blackboard and declared "Here is an electron..." Having heard in another class that the wave function of an electron at rest spreads out over all of space, and having read about ion trapping in radio tubes in my teens set me to wonder how one might realize Becker's localization feat in the laboratory. However, that had to wait a while. In 1948, in Kopfermann's Institute, which was heavily oriented towards hyperfine structure studies, I completed an experimental Diplom-Arbeit (master's thesis) on a Thomson mass spectrograph under Peter Brix. The results were published in "Die photographischen Wirkungen mittelschneller Protonen II," the first paper of which I was a (co)author. Soon thereafter, I began work on my doctoral thesis under Hubert Kruger in the same Institute. Well prepared by a series of excellent Institute seminars on the NMR work of Bloch and of Purcell, we were able to successfully compete with workers at Harvard University. In 1949 we discovered Nuclear Quadrupole Resonance and reported it in our paper "Kernquadrupolfrequenzen in festem Dichloraethylen." My doctoral thesis had the title "Kernquadrupolfrequenzen in kristallinen Jodverbindungen." This work led to an invitation to join Walter Gordy's well known microwave laboratory at Duke University as postdoctoral associate.㰀⼀栀㐀㸀㰀栀㐀㸀㰀⼀戀爀㸀㰀戀爀㸀
At Duke I had the pleasure of making the acquaintance of James Frank, Fritz London, Lothar Nordheim and Hertha Sponer. I advised Hugh Robinson, a graduate student of Gordy's in an NQR experiment, did my own research and also contributed some NMR expertise to an experiment by Bill Fairbank and Gordy on spin statistics in 3He/4He mixtures, gaining some very useful low temperature experience in this brief collaboration. Through Gordy's and Nordheim's good offices I was able to receive a visiting assistant professor appointment at the University of Washington with a charge to advise Edwin Uehling's students during his sabbatical and to do independent research. I had built my first electron impact tube during a brief interlude in 1955 in George Volkoffs laboratory at the University of British Columbia. Prior to that I had attempted a paramagnetic resonance experiment on free atoms in Gottingen and succeeded in doing so at Duke. During seminars at Göttingen on the magnetic resonance techniques of Rabi and of Kastler, it had occurred to me that because of the analogy between an atom and a radio dipole antenna, (a), alignment of the atom should show up in its optical absorption cross section, and (b), electron impact should produce aligned excited atoms. I put these two ideas to good use in 1956 in Seattle in an experiment entitled "Paramagnetic Resonance Reorientation of Atoms and Ions Aligned by Electron Impact." In this paper I first pointed out the usefulness of ion trapping for high resolution spectroscopy and mentioned the 1923 Kingdon trap as a suitable device. This work also brought me into close contact with spin exchange between electron and target atom, which gave me the idea for my 1958 experiment "Spin Resonance of Free Electrons Polarized by Exchange Collisions." However, first I had to learn how to produce polarized atoms, which could then transfer their orientation to trapped electrons. Falling back on buffer gas techniques developed in my 1955 Duke paper "Atomic Phosphorus Paramagnetic Resonance Experiment," I quickly demonstrated in my 1956 Seattle paper "Slow Spin Relaxation of Optically Polarized Sodium Atoms" how to efficiently produce and monitor a polarized atom cloud. Trapping the electrons in a neutralizing ion cloud slowly diffusing in the buffer gas, I was able to carry out the spin resonance experiment. My optical transmission monitoring scheme proved also very useful in the development of rubidium vapor magnetometers and frequency standards by Earl Bell and Arnold Bloom at Varian Associates, in which I acted as a consultant. The rubidium frequency standard is still the least expensive, smallest and most widely used commercial atomic frequency standard. The thesis "Experimental Upper Limit for the Permanent Electric Dipole Moment of Rb85 by Optical Pumping Techniques" of my first graduate student, Earl Ensberg, also made use of these novel optical pumping schemes and was finished in 1962. These early results were improved orders of magnitude by my doctoral student Philip Ekstrom in his 1971 thesis "Search for Differential Linear Stark Shift in Cs133 and Rb85 Using Atomic Light Modulation Oscillators."㰀⼀戀爀㸀㰀戀爀㸀