Effective Eigenmode Description of Normal and Superfluid 4He

Abstract

We determine the behavior of the phonon excitations in liquid 4He, covering both the normal and superfluid phase, for a range of temperatures T (1 < T < 4.2 K), wave numbers q (0.1 < q < 2.2 A−1) and pressures p (0 < p < 25 bars), by means of a numerical fitting procedure based on the effective eigenmode description of the density correlation function. We find that the q, p and T dependence of all inelastic neutron scattering data can be well described by using only one adjustable parameter, the damping rate of the momentum fluctuations. We establish that there is a close similarity between classical liquids, normal-fluid 4He and superfluid 4He. We observe, for all q-values, a marked change in the damping rate of the momentum fluctuations as one passes through the superfluid-transition temperature Tλ. For the roton excitations, this results in a heavily damped (overdamped at p = 20 bars) mode in the normal phase, in contrast to the propagating mode observed in the superfluid phase. The change in damping rate is found to occur predominantly in a small temperature region just below Tλ, for all q-values. We do not find any evidence for the sudden appearance of the predicted “renormalized single-particle” excitations as one enters the superfluid phase. We argue that the full dispersion curve of the phonon-maxon-roton excitations can be understood for all temperatures and pressures in terms of the damping rate of the momentum fluctuations, whereas the rapid changes in this damping rate near Tλ can be viewed as a direct consequence of the Bose symmetry requirements on the 4He-wavefunction.