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Electron magnetic moment from geonium spectra: Early experiments and background concepts

Electron magnetic moment from geonium spectra: Early experiments and background concepts The magnetic moment of a free electron has been measured by observing both its low-energy spin and cyclotron resonances (at ν s = ω s /2π and ν c = ω c /2π, respectively) by means of a sensitive frequency-shift technique. Using radiation and tuned-circuit damping of a single electron, isolated in a special anharmonicity-compensated Penning trap, also cooled to 4 K, the electron’s motion is brought nearly to rest, thus preparing it in a cold quasipermanent state of the geonium ‘‘atom.’’ The magnetic-coupling scheme, described as a continuous Stern-Gerlach effect, is made possible through a weak Lawrence magnetic bottle which causes the very narrow axial resonance, at ν z = ω z /2π for the harmonically bound electron, to change in frequency by a small fixed amount δ per unit change in magnetic quantum number. Spin flips are indirectly induced by a scheme which weakly drives the axial motion at the ν a = ω a /2π spin-cyclotron difference frequency within the inhomogeneous magnetic field, thus yielding a measure of ω a ≡ ω s - ω c . The magnetic moment μ s in terms of the Bohr magneton μ B equals (1/2) the spin’s g factor, which in turn is described by ω s and ω c : g=2 μ s / μ B =2 ω s / ω c . In a Penning trap, however, these resonance frequencies are obtained from the observed cyclotron frequency at ω c ’ = ω c - δ e and the observed anomaly frequency at ω a ’ = ω s - ω c ’ , which are related by the small electric shift δ e computed using the measured axial frequency and 2 δ e ω c ’ = ω z 2 . This last expression, derived for a perfectly axially symmetric trap, happens to be practically invariant against small imperfections in the electric quadrupole field (error in ω c < 10 - 16 ). The magnetic-bottle-determined line shapes are analyzed and found to have sharp low-frequency edge features which correspond to the electron being temporarily at the trap center and at the bottom of the magnetic well. Relativistic shifts are considered and found to be < 10 - 11 . Our result at the time of submission, g/2=1.001 159 652 200 (40), is the most accurately determined parameter of any elementary charged particle which in addition can be directly compared with theory. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review D American Physical Society (APS)

Electron magnetic moment from geonium spectra: Early experiments and background concepts

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Publisher
American Physical Society (APS)
Copyright
Copyright © 1986 The American Physical Society
ISSN
1089-4918
DOI
10.1103/PhysRevD.34.722
Publisher site
See Article on Publisher Site

Abstract

The magnetic moment of a free electron has been measured by observing both its low-energy spin and cyclotron resonances (at ν s = ω s /2π and ν c = ω c /2π, respectively) by means of a sensitive frequency-shift technique. Using radiation and tuned-circuit damping of a single electron, isolated in a special anharmonicity-compensated Penning trap, also cooled to 4 K, the electron’s motion is brought nearly to rest, thus preparing it in a cold quasipermanent state of the geonium ‘‘atom.’’ The magnetic-coupling scheme, described as a continuous Stern-Gerlach effect, is made possible through a weak Lawrence magnetic bottle which causes the very narrow axial resonance, at ν z = ω z /2π for the harmonically bound electron, to change in frequency by a small fixed amount δ per unit change in magnetic quantum number. Spin flips are indirectly induced by a scheme which weakly drives the axial motion at the ν a = ω a /2π spin-cyclotron difference frequency within the inhomogeneous magnetic field, thus yielding a measure of ω a ≡ ω s - ω c . The magnetic moment μ s in terms of the Bohr magneton μ B equals (1/2) the spin’s g factor, which in turn is described by ω s and ω c : g=2 μ s / μ B =2 ω s / ω c . In a Penning trap, however, these resonance frequencies are obtained from the observed cyclotron frequency at ω c ’ = ω c - δ e and the observed anomaly frequency at ω a ’ = ω s - ω c ’ , which are related by the small electric shift δ e computed using the measured axial frequency and 2 δ e ω c ’ = ω z 2 . This last expression, derived for a perfectly axially symmetric trap, happens to be practically invariant against small imperfections in the electric quadrupole field (error in ω c < 10 - 16 ). The magnetic-bottle-determined line shapes are analyzed and found to have sharp low-frequency edge features which correspond to the electron being temporarily at the trap center and at the bottom of the magnetic well. Relativistic shifts are considered and found to be < 10 - 11 . Our result at the time of submission, g/2=1.001 159 652 200 (40), is the most accurately determined parameter of any elementary charged particle which in addition can be directly compared with theory.

Journal

Physical Review DAmerican Physical Society (APS)

Published: Aug 1, 1986

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