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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.
Physical Review D – American Physical Society (APS)
Published: Aug 1, 1986
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