Excited-State Mixing in the Optical Pumping of Alkali-Metal Vapors

The effect of excited-state mixing on the optical pumping of alkali-metal vapors is considered for the case where the energy separation between the ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ first excited states is relatively large, allowing the isolation of mixing effects within a particular $J$ level. Two models for the mixing process are proposed, one a random reorientation of the total electronic angular momentum J, and the other a reorientation of J subject to the selection rule $\Delta m_J=0, \pm 2$. The probabilities for mixing transitions among $J$-state sublevels have been calculated for an alkali atom of nuclear spin $\frac{3}{2}$, and can be used to calculate the optical-pumping transition probabilities for a vapor subject to any degree of excited-state mixing. Several possible experiments suggested by these calculations are discussed.