Theory of the atomic interactions in (s,p)-bonded metals

Abstract

The authors carry out an analytic investigation of the form of the interatomic potential Phi (R) for (s,p)-bonded metals. They use a simple Ashcroft pseudopotential concentrating both on the shape of short-range screened repulsion and on the form of the Friedel oscillations. In particular, they consider their combined roles around the nearest-neighbour distance. The interaction in q space is fitted by simple but specially chosen functions to include correctly the important physical effects. The short-range repulsion has roughly the form of a simple exponential screening with a screening radius determined by the compressibility sum rule. However, this approximation is not adequate for most purposes, the real interaction cutting off much more sharply with a small overshoot, determined by momentum transfers up to about k_F. The authors' form includes the logarithmic singularity in the susceptibility chi (q), at 2k_F precisely, giving the Friedel oscillations over the wide range of distances including various phase-shift effects. This now explains physically all the features found previously in the numerically computed interactions for different pseudopotentials, electron densities and local field corrections.