Phase Shifts of the Static Screened Coulomb Potential

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Abstract
Phase shifts and their weighted sums over angular momentum states have been obtained for the static screened Coulomb potential (SSCP). Results are given for both an attractive and a repulsive SSCP. A procedure is given for obtaining the phase shifts which uses direct numerical integration near the origin and the first- and second-order WKB approximation at larger distances. At high energy a simple asymptotic fit to the weighted phase-shift sums is obtained. The results are applied to the calculation of the second virial coefficient of plasmas that have no bound states and of those that do have bound states. Very good agreement with the Wigner-Kirkwood expansion is found for a Boltzmann gas interacting through a repulsive SSCP, except that at high temperature, in agreement with DeWitt, the Wigner-Kirkwood expansion is shown to diverge for the SSCP.