Coulomb crystals in the harmonic lattice approximation

The dynamic structure factor (S) over tilde(k,omega) and the two-particle distribution function g(r,t) of ions in a Coulomb crystal are obtained in a closed analytic form using the harmonic lattice (HL) approximation which takes into account all processes of multiphonon excitation and absorption. The static radial two-particle distribution function g(r) is calculated for classical (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 omega(p)) body-centered-cubic (bcc) crystals. The results for the classical crystal are in a very good agreement with extensive Monte Carlo (MC) calculations 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 classical and quantum bce and face-centered-cubic crystals, and anharmonic corrections are discussed. The inelastic part of the HL static structure factor S "(k), averaged over orientations of wave vector k, is shown to contain pronounced singularities at Bragg diffraction positions. The HL method can serve as a useful tool complementary to MC and other numerical methods.