S(Q,ω) for Liquid ⁴He: What More do We Need to Know?

Abstract

Since I completed my review article¹ on the temperature dependence of the dynamic structure factor S(Q,ω) of liquid ⁴He for the proceedings of the Hiroshima Symposium, there have been two very important developments: Stirling and Glyde² have provided us with a much more complete set of results for the temperature dependence of S(Q,ω) at low Q (0.4 Å⁻¹), and Glyde and Griffins have proposed a new and very appealing interpretation of S(Q,ω) covering the whole range of wave vectors Q and frequencies ω = 2πv for both the superfluid and normal phases of liquid ⁴He. In the Glyde-Griffin (GG) picture, the main peaks in S(Q,ω) at low Q (≲ 0.7 Å⁻¹, phonon region), which have been known⁴ since 1965 to change relatively little on passing through the superfluid transition temperature, T_λ, correspond to collective zero-sound (ZS) modes as first suggested by Pines.s In contrast, the sharp peaks in S(Q,ω) at larger Q (≳0.8 Å⁻¹), which have been known^6,7 since 1978 to be present only below T_λ, correspond to single-particle (SP) excitations. A very schematic representation⁸ of the GG interpretation is shown in Fig. 1. The shaded regions are simply meant to indicate that the SP modes may disappear at low Q while the ZS modes are expected to disappear at high Q. Hybridization between the ZS and SP modes, which GG propose is responsible for the existence of a smooth continuous dispersion relation for the single excitations, might cause the shaded region to actually be pushed away from the solid curve.