High-precision calculations of the Zeeman effect in the 23PJ, 21P1, 23S1, and 33PJ states of helium

Abstract

The g factors for the Zeeman effect, including relativistic corrections up to order ${\mathrm{\alpha }}^2$ a.u., are calculated to high precision for the 2${\mathrm{}}^3$ ${\mathit{P}}_{\mathit{J}}$, 2${\mathrm{}}^1$ ${\mathit{P}}_1$, 2${\mathrm{}}^3$ ${\mathit{S}}_1$, and 3${\mathrm{}}^3$ ${\mathit{P}}_{\mathit{J}}$ states of helium, using variational wave functions constructed from doubled Hylleraas-type basis sets. Our results clarify the present disagreements among the existing theoretical values for the g factors. The experimental values of the fine-structure splittings for the helium 3${\mathrm{}}^3$ ${\mathit{P}}_{\mathit{J}}$ states, measured by Yang et al. [Phys. Rev. A 32, 2249 (1985); 33, 1725 (1986)], are reanalyzed, using our improved g factors.