Coulomb crystals in the harmonic lattice approximation
The dynamic structure factor &Stilde;(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, similarPlanck's over 2piomega(p), where omega(p) is the ion plasma frequency) and quantum (T<<Planck's over 2piomega(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, similarr/a less, similar7, where a is the ion-sphere radius. The HL Coulomb energy is calculated for classical and quantum bcc 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.
Baiko
DA
Ioffe Physical-Technical Institute, 194021 St. Petersburg, Russia.
Yakovlev
DG
De Witt HE
Slattery
WL