Coulomb crystals in the harmonic lattice approximation

The dynamic structure factor (S) over tilde(k,omega) and the two-particle d istribution function g(r,t) of ions in a Coulomb crystal are obtained in a closed analytic form using the harmonic lattice (HL) approximation which ta kes into account all processes of multiphonon excitation and absorption. Th e static radial two-particle distribution function g(r) is calculated for c lassical (T greater than or similar to (h) over bar omega(p), where omega(p ) is the ion plasma frequency) and quantum (T much less than (h) over bar o mega(p)) body-centered-cubic (bcc) crystals. The results for the classical crystal are in a very good agreement with extensive Monte Carlo (MC) calcul ations at 1.5 less than or similar to r/a less than or similar to 7, where a is the ion-sphere radius. The HL Coulomb energy is calculated for classic al and quantum bce and face-centered-cubic crystals, and anharmonic correct ions are discussed. The inelastic part of the HL static structure factor S "(k), averaged over orientations of wave vector k, is shown to contain pron ounced singularities at Bragg diffraction positions. The HL method can serv e as a useful tool complementary to MC and other numerical methods.