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

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, φ(R)=ARⁿ-BR⁴-CR⁶ (12-4-6 model), and φ(R)=ARⁿ-BR⁴-CR⁶+ΔECT (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 ${Δ}{E}CT{≈}{-}{[{2{S}²}{(1+{S}²)}]{({E}_{{A}⁺})}²}{({I}B+{B}{{R}⁴+{C}{{R}⁶}{-}{E}_{{A}⁺}})},$ 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 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.