Phonon dispersion in He II at long wavelengths and low temperatures

Abstract

Phonon dispersion in liquid He II at long wavelengths and low temperatures is calculated using a generalized polarization potential approach and shown to yield results in good agreement with both superthermal phonon propagation and neutron scattering experiments at pressures up to 24 bar. It is shown that the long-wavelength dispersion relation is of the form ω _q =s ₀ q(1+ω₂ q ²+ω₃ q ³+...) suggested by Feenberg and by Kemoklidze and Pitaevskii, but that the validity of such an expansion is restricted to wave vectorsq≲0.1Å ⁻¹. For larger values ofq, one can force a polynomial fit, containing only odd powers ofq, to the dispersion curve and other parameters of interest, but the number of terms which must be kept is so large as to render such an approach unwieldy.