Dispersion of Phonons in LiquidHe4

Abstract

The long-wavelength dispersion of the phonon spectrum in liquid ${\mathrm{He}}^4$ can be computed from first principles. Part of the dispersion coefficient enters through the Feynman spectrum ${\epsilon }_0\mathrm{}\left(k\right)\mathrm{}$, and the other part enters through corrections to ${\epsilon }_0\mathrm{}\left(k\right)\mathrm{}$. The latter has been investigated by Jackson, Feenberg, and Lee using a perturbation expansion in the free-phonon basis. We define here a more plausible ordering scheme for the expansion and carry out the computation to second order.