Inferring the Distribution of Atomic Kinetic Energies from Neutron-Scattering Experiments

It is shown that the scattering of neutrons at large momentum transfers can provide information on the detailed shape of the distribution of atomic kinetic energies. An expansion of the kinetic-energy distribution function $n\left(E\right)\mathrm{}$ leads to a corresponding expansion of the large -$k$ limit of the scattering function $S(\overrightarrow{\mathrm{k}}, \omega )$. Deviations of the latter from a Gaussian shape reflect deviations of $n\left(E\right)\mathrm{}$ from a Maxwellian. Corrections for finite $k$ are also derived. An application to the scattering data of Harling for liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ leads to estimates of the condensate fraction and average kinetic energy for liquid temperatures in the range 1.27 to 4.2 °K.