Electron Impact Excitation of the Rare Gases

Abstract

We utilize the analytic atomic independent-particle model (IPM) of Green, Sellin, and Zachor as a basis for calculating generalized oscillator strengths for the single-particle excitations of Ne, Ar, Kr, and Xe. First, we establish averages of the experimental energy levels to arrive at single-particle states. We then adjust the two parameters so that the IPM potentials accurately characterize these excited-state energies. Using the wave functions associated with these potentials and the Born approximation, we calculate the generalized oscillator strengths for excitations to $p^5\mathrm{ns}$ states. A very complex nodal structure is apparent at large values of momentum transfer and a rapid decline in magnitude occurs after the second node. We may accurately characterize the results up to the second node with a convenient analytic form which leads to analytic total excitation cross sections. We use available optical oscillator strengths to normalize our results. The systematics and regularities of the parameters for various Rydberg series are discussed and approximate scaling laws are given.