Number and Density of Bound States in Ion–Atom Systems

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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−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.
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