Higher multipole and retardation corrections to the dipole angular distributions of<i>L</i>-shell photoelectrons ejected by polarized photons

We calculate first-retardation and multipole corrections to the dipole angular distributions of L-shell photoelectrons ejected by polarized photons. The calculation is performed nonrelativistically in the framework of the independent-particle model. It leads to general expressions for the s and p subshell retardation correction in terms of radial matrix elements and relative phase shifts. In the 2s case the retardation effects may contribute as much as 10--30% to the angular distribution even close to threshold, especially for higher-Z elements. In the 2p case the retardation effects are small close to threshold but can contribute as much as 10--20% for relatively low final electron energies of 1--3 keV. We have also obtained simple semianalytical expressions for the retardation corrections, based on the assumption that for inner shells screening effects beyond normalizations and phase shifts can be treated perturbatively. The semianalytic formulas compare quite well with the results of numerical calculations for the 2s subshell; they are somewhat worse for 2p photoelectrons, especially for lower energies and lower Z. This is due to the fact that in the latter case larger distances become more important in the integrals determining radial matrix elements. In the 2s case the retardation effects result in forward or backward peaking of the angular distributions. For the 2p initial state and linearly polarized photons, they lead to deviations from dipole predictions for a uniform angular distribution of photoelectrons whose momenta are perpendicular to the direction of photon polarization.

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