Photoelectron angular distributions for the outer shell of the alkali-metal atoms

Abstract

Dirac-Fock calculations of the photoionization of the outer $\mathrm{ns}$ electrons in Na, K, Rb, and Cs have been performed. The resulting photoelectron angular distribution asymmetry parameters $\ensuremath{\beta}$ show strong variations with energy, in contrast to the nonrelativistic prediction of $\ensuremath{\beta}=2$, independent of energy, for $s$ electrons. This deviation is due to the spin-orbit interaction of the continuum electron which gives rise to two final states $\ensuremath{\epsilon}{p}_{\frac{1}{2}}$ and $\ensuremath{\epsilon}{p}_{\frac{3}{2}}$, in place of the single $\ensuremath{\epsilon}p$ nonrelativistically. The transitions to the $\ensuremath{\epsilon}{p}_{\frac{1}{2}}$ and $\ensuremath{\epsilon}{p}_{\frac{3}{2}}$ have matrix elements and phase shifts which differ and interfere, thereby resulting in an energy-dependent $\ensuremath{\beta}$. The effects are particularly dramatic between the Cooper minima in the two channels, and they persist even for $Z$ as low as that for Na.