Orientation averaged angular distributions of photo-electrons from free Na clusters

We explore, from a theoretical perspective, photo-electron angular distributions (PAD) of small Na clusters using the time-dependent local-density approximation (TDLDA). We assume an isotropic ensemble of free clusters and develop, for the case of one-photon emission, analytical formulae for the orientation averaged PAD which require only six TDLDA calculations in properly chosen reference frames. All information in the averaged PAD is contained in one anisotropy parameter. This parameter varies little with system size, but is crucially influenced by the detailed ionic structure.