Lattice vibrations and elastic constants of crystalline [formula omitted] and [formula omitted] near low-temperature melting

Abstract

The phonon dispersion curves and the elastic constants are evaluated for crystalline 4 He and 3 He near melting at low temperature in the deep quantal regime. The structures considered are the hexagonal close-packed and the body-centred and face-centred cubic ones for 4 He and the body-centred cubic one for 3 He . The calculations use a density functional approach to construct a field of effective force constants in the strongly anharmonic solid near melting from its Debye–Waller factor and from the linear density response function of the fluid phase at freezing. The results of the calculations are compared with the available experimental evidence: good agreement is generally found for transverse phonon frequencies and shear elastic constants, and phenomenological adjustments of the force-constant field are proposed for a quantitative description of the longitudinal modes. A relationship between the dispersion curves of phonons in crystalline 4 He and that of elementary collective excitations in superfluid 4 He is displayed and discussed in the light of current interpretations of atomic dynamics in the superfluid phase, with main emphasis on the region of the roton minimum.