Comments on Long-Wavelength Excitations and Structure Functions in the Theory of LiquidHe4atT=0

Abstract

Polynomial approximations for the liquid structure function $S\left(k\right)\mathrm{}$ and the energy of an elementary excitation $\epsilon \mathrm{}\left(k\right)\mathrm{}$ are found to contain both odd and even powers of $k$ if the interatomic potential falls off asymptotically as $r^{-6\mathrm{}}$. The proof is given under conditions of low density and weak interaction and hence has only suggestive force in applications to the real superfluid.