Theory of Critical Screening Radius of Energy Levels of Hydrogen-Like Atoms in Plasmas

Abstract

The electronic states in the Debye-Hückel potential, −(Ze²⁄r)exp(−r⁄D), are investigated and the critical screening radius D=D_c(n,l) is given by the simple formulae
(Remark: Graphics omitted.),
where n and l denote the principal and azimuthal quantum numbers, respectively, and a=h²⁄me². By a comparison with the results of numerical calculations, it is ascertained that these formulae hold with sufficient accuracy. The method is to connect the quasi-classical solution of the Schrödinger equation with the solution for the pure Coulomb potential in the region where both approximations are valid.