Threshold law for electron-atom impact ionization: towards the inside contribution of the Coulomb-dipole theory

Abstract

The author has previously derived an ionization threshold law on the basis of the Coulomb-dipole theory, but including only the contribution from the outer (semi-asymptotic) region of configuration space to the relevant matrix element. Here the author initiates a study of the (overwhelmingly dominant) inside contribution. The main part of this paper is devoted to a detailed analysis of the asymptotic form to which the inside function must be attached. The author returns to an older approach of deriving the ionization yield by extrapolating excitation cross sections of excited states (N) (because the asymptotic form there is known to be dipole configurations of degenerate (l) states for each N excited by the incoming electron) into the continuum. Here the author concentrates on the dipole matrix from which the dipole configurations are obtained; it is derived analytically; its eigenfunctions and eigenvalues are evaluated numerically to very high N (for several of the lower partial waves L). A key parameter emerges, JC(N,L), which specifies the number of coherent, attractive, dipole states as a function of N and L.