Tables of Coefficients to Determine the 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)→-1/2α₁e²r⁴, 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⁺HL=0 phase shifts provides an illustration of the application of the tables.