Application of the Pseudopotential Method to Atomic Scattering

Abstract

The empirical pseudopotential method is discussed and applied to a calculation of the spin-exchange cross section in collisions of Na and Cs atoms. The difference between potential energy curves for the lowest singlet and triplet states of the Na-Cs system is calculated by the Heitler-London method, using a Hamiltonian in which the effects of tightly bound electrons are replaced by a pseudopotential. Wave functions for the free atoms are found by numerical integration using the pseudopotential, and agree well with the exact valence-electron functions at large distances. The scattering phase shifts are calculated in the WKB approximation, and the cross section computed from them is averaged over a Boltzmann distribution of relative velocities. At a temperature of 500°K, the averaged reduced spin-exchange cross section is 1.5 × 1.5×${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$.