Theory of neutron scattering from thermally excited quasiparticles in superfluidHe4

We present the first detailed theoretical study of the inelastic neutron scattering contribution $S^{\mathrm{th}}(\overrightarrow{\mathrm{Q}},\omega )$ from thermally excited quasiparticles in superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$, with emphasis on the low-$Q$ collisionless limit. In the temperature region where rotons are the dominant excitation, our results for $S^{\mathrm{th}}(\overrightarrow{\mathrm{Q}},\omega )$ scale with Landau's normal fluid density. We argue that $S^{\mathrm{th}}(\overrightarrow{\mathrm{Q}},\omega )$ is the origin of the broad temperature-dependent continuum which Woods and Svensson (1978) have observed at temperatures above about 1.7 K. Our specific model calculations of $S^{\mathrm{th}}(\overrightarrow{\mathrm{Q}},\omega )$ are based on evaluating the regular part of the longitudinal momentum current-current correlation function within the Bogoliubov approximation, but the experimental quasiparticle (roton) spectrum is used in our numerical calculations. Our expression satisfies the normal fluid $f$-sum rule in the long-wavelength collisionless limit and is in essential agreement with the general picture suggested by Pines and Nozières in 1964. Our present theory involves several approximations which probably limit its validity to $Q\lesssim 0.5$ ${\mathrm{\AA }}^{-1\mathrm{}}$. Some generalizations to deal with the larger values of $Q$ studied by Woods and Svensson are briefly discussed.