Interatomic Potential Model for Ion-Atom Systems Including a Charge-Exchange Contribution

Abstract

A model for the interatomic potential between alkali ions and rare-gas atoms accounting for repulsive and attractive exchange forces has been calculated. The attractive exchange contribution is estimated using Mulliken's charge-transfer theory. The repulsive potential is calculated using Firsov's theory of interacting Thomas-Fermi-Dirac atoms. Two models, $\phi \mathrm{}\left(R\right)=\frac{A}{R^n}-\frac{B}{R^4}-\frac{C}{R^6}$ (12-4-6 model), and $\phi \mathrm{}\left(R\right)=\frac{A}{R^n}-\frac{B}{R^4}-\frac{C}{R^6}+\Delta E^{\mathrm{CT}}$ (exchange model), were used to calculate the interatomic potential for all the alkali-ion-rare-gasatom combinations. A comparison shows that the charge-exchange contribution $\Delta E^{\mathrm{CT}}\approx -\frac{\left[\frac{2S^2}{(1+S^2)}\right]{\left(E_{A^{+}}\right)}^2}{(I_B+\frac{B}{R^4+\frac{C}{R^6}-E_{A^{+}}})},$ where $E_{A^{+}}$ is the electron affinity of the ion, $I_B$ is the ionization potential of the atom, $B$ and $C$ are the coefficients of the polarization interaction terms, and $S$ is the two-center overlap integral between the outer orbitals, enhances the long-range attraction and increases the well depth by about a factor of 5 over the 12-4-6 model. The predictions of the classical rainbow scattering angle for the ${\mathrm{Cs}}^{+}$/Ar case are compared for the two models. The difference in the two calculated rainbow angles strongly suggests that low-energy elastic-scattering angular distributions would be a valid test of the assumptions used in the charge-exchange model.