Overlap integral between two electron clouds at different sites.

Abstract

The overlap integral between many-electron wave functions perturbed by local contact potentials at different sites is calculated with use of the determinantal method developed for the soft-x-ray problem. The expression for the exponent ${K}_{0}$ in the orthogonality theorem is derived as a function of the phase shift ${\ensuremath{\delta}}_{0}$ and the distance a between impurities and is found to behave differently from the result given by Yamada et al. [Prog. Theor. Phys. 70, 73 (1983)] when ${\ensuremath{\delta}}_{0}$ exceeds \ensuremath{\pi}/2. This implies that ${K}_{0}$ is discontinuous at a=\ensuremath{\infty} for such ${\ensuremath{\delta}}_{0}$, and that 2${K}_{0}$ will never be larger than 1/2 for any value of ${\ensuremath{\delta}}_{0}$.