Temperature dependence of spatial correlations in liquidHe4and the Bose-Einstein condensation

Abstract

The basis of the equation ${[1-n_0(T_1\left)\right]}^2=\frac{\left[g\right(r, T_1)-1]}{\left[g\right(r, T_2)-1]}$ is critically examined. Here $T_1<~T_{\lambda }$ and $T_2\gtrsim T_{\lambda }$. This equation, which relates the condensate fraction $n_0\mathrm{}\left(T\right)\mathrm{}$ to the radial distribution function $g(r, T)$, was proposed by F. W. Cummings, G. J. Hyland, and G. Rowland [Phys. Konden. Mater. 12, 90 (1970)]. It is shown to be based on two assumptions. It cannot be derived from the Frohlich decomposition of the two-particle density matrix.