Angular distributions of photoelectrons from free Na clusters
We explore, from a theoretical perspective, photoelectron angular distributions (PADs) of the Na clusters Na{sub 8}, Na{sub 10}, Na{sub 12}, Na{sub 18}, Na{sub 3}{sup +}, Na{sub 11}{sup +}, Na{sub 13}{sup +}, and Na{sub 19}{sup +}. The basis of the description is the time-dependent local-density approximation (TDLDA), augmented by a self-interaction correction (SIC) to describe ionization properties correctly. The scheme is solved on a numerical grid in coordinate space with absorbing bounds. We assume for each cluster system an isotropic ensemble of free clusters and develop for the case of one-photon emission analytical formulas for computing the orientation-averaged PAD on the basis of a few TDLDA-SIC calculations for properly chosen reference orientations. It turns out that all the information in the averaged PAD is contained in one anisotropy parameter. We find that this parameter varies very little with system size, but as a whole is crucially influenced by the detailed ionic structure. We also make comparisons with direct orientation averaging and consider one example reaching outside the perturbative regime.