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• W2069962254 abstract "The magnetic moment of a free electron has been measured by observing both its low-energy spin and cyclotron resonances (at ${ensuremath{nu}}_{s}$=${ensuremath{omega}}_{s}$/2ensuremath{pi} and ${ensuremath{nu}}_{c}$=${ensuremath{omega}}_{c}$/2ensuremath{pi}, 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 ${ensuremath{nu}}_{z}$=${ensuremath{omega}}_{z}$/2ensuremath{pi} for the harmonically bound electron, to change in frequency by a small fixed amount ensuremath{delta} per unit change in magnetic quantum number.Spin flips are indirectly induced by a scheme which weakly drives the axial motion at the ${ensuremath{nu}}_{a}$=${ensuremath{omega}}_{a}$/2ensuremath{pi} spin-cyclotron difference frequency within the inhomogeneous magnetic field, thus yielding a measure of ${ensuremath{omega}}_{a}$ensuremath{equiv}${ensuremath{omega}}_{s}$-${ensuremath{omega}}_{c}$. The magnetic moment ${ensuremath{mu}}_{s}$ in terms of the Bohr magneton ${ensuremath{mu}}_{B}$ equals (1/2) the spin's g factor, which in turn is described by ${ensuremath{omega}}_{s}$ and ${ensuremath{omega}}_{c}$: g=2${ensuremath{mu}}_{s}$/${ensuremath{mu}}_{B}$=2${ensuremath{omega}}_{s}$/${ensuremath{omega}}_{c}$. In a Penning trap, however, these resonance frequencies are obtained from the observed cyclotron frequency at ${ensuremath{omega}}_{c}^{mathcal{'}}$=${ensuremath{omega}}_{c}$-${ensuremath{delta}}_{e}$ and the observed anomaly frequency at ${ensuremath{omega}}_{a}^{mathcal{'}}$=${ensuremath{omega}}_{s}$-${ensuremath{omega}}_{c}^{mathcal{'}}$, which are related by the small electric shift ${ensuremath{delta}}_{e}$ computed using the measured axial frequency and 2${ensuremath{delta}}_{e}$${ensuremath{omega}}_{c}^{mathcal{'}}$=${ensuremath{omega}}_{z}$${mathrm{}}^{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 ${ensuremath{omega}}_{c}$${<10}^{mathrm{ensuremath{-}}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 ${<10}^{mathrm{ensuremath{-}}11}$. 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." @default.
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• W2069962254 date "1986-08-01" @default.
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• W2069962254 title "Electron magnetic moment from geonium spectra: Early experiments and background concepts" @default.
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• W2069962254 doi "https://doi.org/10.1103/physrevd.34.722" @default.
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