EFFECTIVE EIGENMODE DESCRIPTION OF NORMAL AND SUPERFLUID HE-4

We determine the behavior of the phonon excitations in liquid He-4, co vering both the normal and superfluid phase, for a range of temperatur es T (1<T<4.2K), wave numbers q (0.1<q<2.2 Angstrom(-1)) and pressures p (0<p<25 bars), by means of a numerical fitting procedure based on t he effective eigenmode description of the density correlation function . We find that the q,p and T dependence of all inelastic neutron scatt ering data cona be well described by using only one adjustable paramet er, the damping rate of the momentum fluctuations. We establish that t here is a close similarity between classical liquids, normal fluid He- 4 and superfluid He-4. We observe, for all q-values, a marked change i n the damping rate of the momentum fluctuations as one passes through the superfluid-transition temperature T-lambda. For the roton excitati ons, this results in a heavily damped (overdamped at p=20 bars) mode i n the normal phase, in contrast to the propagating mode observed in th e superfluid phase. The change in damping rate is found to occur predo minantly in a small temperature region just below T-lambda, for all q- values. We don not find any evidence for the sudden appearance of the predicted ''renormalized single-particle'' excitations as one enters t he superfluid phase. We argue that the full dispersion curve of the ph onon-maxon-roton excitations can be understood for all temperature and pressures in terms of the damping rate of the momentum fluctuations, whereas the rapid changes in this damping rate near T-lambda can be vi ewed as a direct consequence of the Bose symmetry requirements on the He-4-wavefunction.