TABLES OF COEFFICIENTS TO DETERMINE LONG-RANGE CONTRIBUTIONS TO LOW-ENERGY ELECTRON-ATOM SCATTERING

The difficulty in the extrapolation or interpolation in energy of the phase shifts deduced from electron-atom scattering data stems from the presence of an effective one-body long-range potential U(r). U(r) has its origin in the static and dynamic polarizabilities of the atom, assumed to have a spherically symmetric ground state, and gives rise to an unusual and rapidly varying energy dependence. The usual effective-range theory is inapplicable, but a modified effective-range theory (MERT) exists in which the effect of U(r) is taken into account exactly for arbitrarily strong (but specified) U(r). The applicability of MERT has previously been limited to U(r) sufficiently weak for the Born approximation to be adequate (because of the unavailability of numerical values for the long-range functions necessary for the analysis). We here tabulate these functions for the case in which U(r)→-12α1e2r4, where α1 is the atomic electric dipole polarizability. The functions have been tabulated in terms of dimensionless parameters over a range of values of angular momentum L, α1, and wave number k such that the entire elastic region for almost all atoms can be covered. The only interpolation necessary is that over k. A study of the e-H and e+H L=0 phase shifts provides an illustration of the application of the tables. © 1969 The American Physical Society.