Relationships between the pair-correlation function, the superfluid fraction, and the condensate fraction in liquidHe4

It is shown that the Woods-Svensson decomposition of the dynamic structure factor $S(Q,\omega )$ into superfluid and normal-fluid components implies relationships between $S\left(Q\right)\mathrm{}$ and the superfluid fraction $n_s=\frac{{\rho }_s}{\rho }$ and between $g\left(r\right)\mathrm{}$ and $n_s$, which are very well borne out by experiment. Combining our new relationship between $g\left(r\right)\mathrm{}$ and $n_s$ with that between $g\left(r\right)\mathrm{}$ and the condensate fraction $n_0$ proposed by Hyland, Rowlands, and Cummings then gives an explicit relationship between $n_0$ and $n_s$ for all temperatures in the superfluid phase.