Static Structure Factor and Static Response Function of Superfluid Helium 4: a Comparative Analysis

Abstract

Extensive neutron scattering data on liquid helium 4 are available, and have been analyzed to give a number of physical quantities, e.g. static structure factor S(q), excitation energy, and roton linewidth. X-rays also give access to S(q). However, a comprehensive comparison between experimental data and theoretical results, including their dependence on pressure, is still lacking. The static response function χ(q) has been particularly overlooked, despite its fundamental role in theories of inhomogeneous helium. We present here a critical review about the strength of the main peaks of S(q) and χ(q). We include in the comparison the analysis of unpublished neutron data and new Monte-Carlo calculations of χ(q). We find a significant discrepancy between experiments, and suggest corrections which account for some of the differences. We give recommendations for the best values to use for S(q) and χ(q).

Transport and Phonon Damping in $$^{4}$$He

“…The experimental results have been analyzed using the polynomial expression (12) to determine the dispersion coefficient γ for several 4 He densities. The speed of sound c determined by the fit agrees well with the well-known values measured by ultrasonic or thermodynamic techniques [28,29], as can be seen in the extrapolations to k = 0 in Fig. 4.…”

Ab initiolow-energy dynamics of superfluid and solidH4e

“…The position of such multiphonon maximum (see Fig.2c) is in qualitative agreement with experiments 25 : as we show in Appendix B, within the present implementation of GIFT there is no possibility to recover the detailed shape of the spectral function like the multiphonon substructures given by high resolution measurements 27 of S(q, ω). In the lower panel of Fig.5 we show the static density response function χ(q) obtained evaluating the ω −1 from S GIF T (q, ω); the agreement with experiments is impressive, also near freezing 28 . The calculation of the excitation spectrum ε(q) in superfluid 4 He via QMC was addressed for instance in Ref.…”

Ultra cold neutron production by multiphonon processes in superfluid helium under pressure

“…This higher value from Gibbs [18] (there called Z(Q)) is affirmed in a comparative analysis in Ref. [17]. A different approach by Yoshiki [24], calculating the total cross section for UCN production from single phonon excitations in a beryllium coated converter, gives a slightly larger value.…”

“…where E * = 2 q * 2 /2m n , and the Jacobian factor (7) relative factor 1 0.41 Table 1 Factors relevant for single phonon production rate deduced from Ref. [16,17,18]. An increase in flux of a factor ∼ 2.5, going from 8.9Å to 8.3Å is necessary to compensate for the loss in intensity.…”