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 kF. The authors' form includes the logarithmic singularity in the susceptibility chi (q), at 2kF 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.