Effect of Nuclear Mass on the Bound-ElectrongFactor

Abstract

The effect of nuclear mass on the g factor of the bound electron has been determined by measuring G=gj(R)/gj{D) to a precision pf 3x 10" 11 using a pulsed double-mode hydrogen maser. The result, G = 1 + (7.22 ±0.03) x 10" 9 , is in excellent agreement with the theory of Grotch and Hegstrom.The past several years have witnessed lively theoretical and experimental activity on the question of the interaction of atomic hydrogen with a magnetic field. 1 The problem is important not only because of the intrinsic interest in understanding the nature of electromagnetic interactions of composite systems, but because it bears on the validity of the Zeeman theory of hydrogen which plays an important role in understanding the hydrogen fine structure.The magnetic moment of the bound electron provides the most sensitive test for the theory of hydrogenlike atoms in external fields. The following result has been derived by Grotch and Hegstrom 2 for the g factor of hydrogenic atoms in the IS state:where g e is the free-electron g factor and M is the nuclear mass. This result has been derived independently by Faustov 3 and Close and Osborn 4 using different calculational techniques. The leading correction term (Za) 2 /3, the well-known Breit correction, 5 has so far not been observed directly because of the technical problem of comparing free and bound electrons. Consequently, interest has centered on the mass-dependent terms which can be observed by measuring the isotope shift of the bound-electron g factor. For hydrogen and deuterium we have, with G=gj(H, lS)/gj(D, IS),

Measurements of theg J -factors of12C in the3 P 1 and3 P 2 states

“…For hydrogen [1][2][3], helium [4,5] and lithium [6,7] the experimental g-factors are in excellent agreement with the theoretically calculated ones. The experimental uncertainties are between 1 to 4.10-7 g,,, where g,.…”

“…Only for oxygen in the states 3P~. 2 and fluorine in the state 2P3/2 there is good agreement between theory and experiment within the experimental uncertainties of 10-6 ge" In the case of nitrogen in the state kS the 3,2 difference between experiment and theory has been reduced by a new ABMR-experiment [11] to 4.0 (2.5)-10-6 ge. For carbon the previous experimental values [9] for gs(3Pt,2) are not accurate enough to check the calculations of Merzyn [8] within a few ppm.…”

Hydrogenic systems, frequency standards and fundamental constants

“…For the bound electron, similar calculations, but with additional terms due to the nucleus, are required; in this case the calculations have reached an uncertainty of order one part in 10 10 [159]. Early experiments on bound state g-factors used highfield hydrogen masers [160]. A new experimental realization with the highest precision uses hydrogenic ions of 12 C 5+ [161] in a Penning trap.…”

Gyromagnetic factors of bound particles with arbitrary spin in quantum electrodynamics

“…Recently, the scope of the experimental investigation of hydrogenic ions was essentially enlarged [3,4]. The measured values of the g factors of an electron in hydrogen-like atoms are presented in Table 1 [5][6][7][8][9].…”