Comments on the shell model for lattice vibrations

Abstract

Abstract The nature of the effective core–core interactions that arise via core-shell and shell–shell interactions is discussed. The core–shell interactions give rise to electric dipole moments whose sum is zero leading to an effective interaction at large distances of quadrupole–quadrupole type varying asymptotically as 1/R5. The shell model is also shown to give rise to forces of nonelectrostatic type whose force constants have the asymptotic form R−1exp (— αR) of the Yukawa meson theory of nuclear forces. Although the range is comparable to the lattice constant, in fact, many sets of neighbors make a significant contribution. The need for imposing rotational invariance on the force constants is emphasized, as is the need for reducing the Lorentz local field in materials with unlocalized electronic charge. A treatment for lattice vibrations in metals is proposed that (in contrast to de Launay's method) preserves periodicity in reciprocal space and accounts for the energy of compression of the electron gas.