Kinetic energy and condensate fraction of superfluidHe4

A new method for the experimental determination of the condensate fraction, $n_0$, of superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ is presented. This method, which depends on the temperature variation of the average kinetic energy per atom, is applied to available neutron and x-ray data and yields values of $n_0$ that are consistent with those obtained from two previous methods. An analysis of the $n_0$ results from all methods gives the value $n_0=(13.3\mathrm{}\pm 1.2)\%$ at $T=0\mathrm{}$. This value is in excellent agreement with the value obtained recently by Campbell from the observed surface tension but is slightly higher than most theoretical estimates. The temperature variation of $n_0$ near the $\lambda$ point, $T_{\lambda }=2.17\mathrm{}$ K, is consistent with the expected form $n_0\simeq {(T_{\lambda }-T)}^{2\beta }$ and the critical exponent is estimated to be $2\beta =0.5\mathrm{}\pm 0.2$.