Collective effects in atoms via a schematic model

Linear response theory is used to investigate the collective excitation spectra of the outer shells of heavy atoms. A model, based on the approximate separability of particle-hole interaction matrix elements, is solved in closed form and found to be in semi-quantitative agreement with experiment for the vibrations of the 4d shell in Xenon. The separability of these matrix elements in the relevant energy region is shown to be due to a general property of wave functions of atomic potentials. A comparison is also made with full random phase approximation calculations for Xe. It is shown that the schematic model contains all the relevant features to describe the enhanced photo-absorption of this system in the far ultraviolet. The role of anf-wave resonance in the average atomic field is stressed in connection with this enhancement. Detailed agreement between the schematic model and experiment is less good than that obtained from the full random phase calculation, the differences arising due to an approximate treatment of exchange in the former calculation. The total dipole strength in the photo-electric region is approximately the same for both calculations however and in reasonable accord with experiment.