Number and Density of Bound States in Ion–Atom Systems

Abstract

Gross features of bound states are studied for a model of ion–atom systems. The model potential is taken to be of the form $r^{\text{−4}}$ with a hard core. With the aid of an extensive tabulation, the number of bound states for a given rotational quantum number can be estimated quickly from the dipole polarizability of the atom, the reduced mass, and the hard‐core radius. The energy density of bound states near zero energy is treated approximately by the WKB method. The effect of additional interactions—i.e., departures from the hard‐core potential—is also discussed. The results are applicable to analyses of molecular–ion spectra and are relevant to ion–atom scattering at low energies.