Structure of the static pair-correlation function in superfluidHe4

Abstract

In 1970, Hyland, Rowlands, and Cummings suggested that one could obtain the condensate fraction $n_0\mathrm{}\left(T\right)\mathrm{}$ from careful measurements of the static pair-correlation function $g(r, T)$ in the superfluid and normal phases of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. Their arguments are critically analyzed by going back to the general structure of $S\left(Q\right)\mathrm{}$ and $S(Q, \omega )$ predicted by the field-theoretic analysis of a Bose-condensed liquid. It is shown that at low temperatures, the single-particle correlation functions, which Hyland et al. argue are negligible, in fact make a major contribution to $g(r, T)$ in the region $r\gtrsim 4$ Å.