Single-particle kinetic energies of noble-gas solids and liquids: Xenon, krypton, and argon

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Abstract
Direct measurements have been made on the average single‐particle kinetic energies, 〈E k 〉, of a series of solid and liquid specimens of heavy noble gases near melting. To do this, the distributions of energy losses of incident eV neutrons,scattered at angles ranging from 87 to 136 deg, were analyzed on the assumptions that atoms in these specimens have a Gaussian momentum distribution n(p) and that for these experimental conditions the atoms scatter independently of one another. It is known that the solids, Ar, Kr, and Xe show considerable differences in such characteristics as (a) their respective ratios of triple point to Debye temperatures, (b) the extent of multibody force contributions to cohesion, and (c) phonon anharmonicity. Regardless, it is found for all three solids near their respective triple points that 〈E k 〉 is equal to the equipartition value (3/2)k T well within the various estimated experimental uncertainties of 3% to 7%. Moreover, liquid Kr near its triple point yields the same result, as does liquid Xe at temperature up to 1.8 times its triple point temperature. Because all these systems are expected to be classical at these temperatures, these results demonstrate applicability of this neutron recoil method to determine 〈E k 〉 even of heavy atoms in suitable cases where a value may not be known in advance.