Two-Component Character of S(k, ω) in Superfluid ⁴He

Abstract

WOODS and SVENSSON[1] analyzed the experimental results of the dynamical sturucture factor, S(k,ω) for superfluid ⁴He at finite temperatures and proposed in 1978 that S(k,ω) is described as the sum of two components:

$${\text{S}}\left( {{\text{k,}}\omega } \right){\text{ = }}\bar{\rho }{{{\text{ }}}_{{\text{s}}}}{{{\text{S}}}_{{\text{s}}}}\left( {{\text{k,}}\omega } \right){\text{ + }}{{\bar{\rho }}_{{\text{n}}}}{{{\text{S}}}_{{\text{n}}}}\left( {{\text{k,}}\omega } \right),$$

(1)

where ${{\overline \rho }_{s}} = {{\rho }_{s}}/\rho {\text{ and }}{{\overline \rho }_{n}} = {{\rho }_{n}}/\rho$, and ρ , ρ _s and ρ_n denote total, superfluid and normal fluid density, respectively. Later one of us (K.YAMADA[2]) investigated the response functions in superfluid ⁴He on the basis of the two fluid dynamics and showed that the S(k,ω), in the small but collisionless region of wave vector, can be described as the sum of two components, supporting the analysis proposed by Woods and Svensson. However the above treatment is restricted in temperatures lower than 1K and cannot be compared with the experimental results, because the contributions of phonons are taken into account as thermal excitations but those of rotons are not considered.