Number of Bound States in Lennard-Jones Potentials

Abstract

Accurate approximation techniques are derived for evaluating WKBJ integrals for Lennard‐Jones potentials. These techniques allow one to evaluate the WKBJ integral at only two energy values: $\text{E\hspace{0.17em}=\hspace{0.17em}0}$ , which is the dissociation limit, and secondly, the energy at the height of the centrifugal barrier. These two special cases allow one to determine the number of bound and quasibound states of the Lennard‐Jones potential: Quasibound states have an energy greater than zero but less than the centrifugal barrier. A simple analytical formula is presented which estimates accurately the number of bound and quasibound states. Numerical results are presented for the interactions of alkali and noble‐gas atoms. The chemical equilibrium constant for molecule formation is also estimated for these systems.