DISPERSION-LAWS OF COLLECTIVE EXCITATIONS IN CRYSTALLINE AND SUPERFLUID HE-4 RELATED VIA DENSITY-FUNCTIONAL THEORY

A simple relation is demonstrated between the phonon dispersion curves of crystalline He-4 in both the h.c.p. and the b.c.c. phase near melting and the dispersion law of elementary excitations in the superfluid phase near freezing. The collective dynamics as seen in neutron inelastic-scattering experiments from all these phases near coexistence reflects primarily the static density response function of the liquid and a suitably defined Debye-Waller factor. It is further pointed out that the curvature of the dispersion law at the roton minimum in the liquid is approximately related to the c(44) shear elastic constant of the b.c.c. phase.