Rare-Gas-InducedgJShifts in the Ground States of Alkali Atoms

Based on the formal similarity between perturbations governing gyromagnetic ratio shifting and spin relaxation of alkali atoms in collisions with rare-gas atoms, a relatively direct semiempirical estimate of the $g_j$ shift as a function of buffer-gas density can be achieved. The expression $\frac{\Delta g_J}{g_J}=-{\left(\frac{4}{3\pi }\right)}^{\frac{1}{2}}n{{\sigma }_{\mathrm{dis}}}^{\frac{1}{2}}{\sigma }_{\mathrm{kin}}$ is obtained for the fractional shift in $g_J$, where $n$ is the rare-gas number density, ${\sigma }_{\mathrm{kin}}$ the alkali-rare-gas kinetic cross section, and ${\sigma }_{\mathrm{dis}}$ the cross section for alkali spin disorientation. With this relationship, we predict a fractional $g_J$ shift for Rb by He equal to -5. 3 × ${10}^{-11\mathrm{}}$ ${\mathrm{Torr}}^{-1\mathrm{}}$, as compared with a recent value, -(5±3) × ${10}^{-11\mathrm{}}$ ${\mathrm{Torr}}^{-1\mathrm{}}$, obtained through measurement by Hayne, Robinson, and their co-workers.