Calculations of Magnetic Moments for Three-Electron Atomic Systems

Abstract

The first fully correlated calculations of the magnetic moment in lithium are presented. Relative to the free-electron value, the Zeeman gJ factor for the ground state lithium gJ/g(e)-1 is calculated to a computational accuracy of 200 parts in 10(9), including relativistic and radiative corrections of orders alpha2, alpha2m/M, and alpha3. The isotope shifts in gJ are predicted precisely for various isotopes. The extensions to the first excited S state of lithium and the ground state of Be+ are made.

The g factor in a light two-body atomic system: a determination of fundamental constants to test QED

“…[37] because we have applied a more accurate theory from Ref. [38] and a more accurate value of the beryllium-9 mass [39]. We present two theoretical evaluation of experiment [6].…”

Weighted difference ofgfactors of light Li-like and H-like ions for an improved determination of the fine-structure constant

“…The first one is the NRQED method (used, e.g., in [33]) that accounts for the nonrelativistic electron-electron interactions to all orders in 1/Z, but ex-pands the QED and relativistic effects in powers of α and Zα. The second approach (used, e.g., in [24,[26][27][28]) accounts for the relativistic effects to all orders in Zα but employs perturbation expansions in α (QED effects) and in 1/Z (electronelectron interaction).…”

Accurate determination of Be magnetic moment

“…Since r ð2;1Þ is small, it does not need to be calculated accurately, we neglect the so called mass polarization P a>bp a Áp b in the first and the second term in Eq. (14), and neglect the third term completely. Thus the approximate form of the finite nuclear mass correction is…”

“…Considering the electron g-factor, it was calculated for 9Be þ with high numerical precision by Yan [14] g J g e À 1 ¼ À28:554814ð1Þ Â 10 À6 :…”