Slow Neutron Scattering by Molecular Hydrogen and Deuterium

Abstract

The cross sections for neutrons scattering from ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ have been calculated taking into account the spin correlations, rotations, and vibrations of the molecules exactly, to the extent that the vibrations are harmonic and do not interact with the rotations. Free translations of the molecules are assumed, but this assumption is expected to be valid in the liquid, as well as the gas, for neutron energies above 0.007 eV, the Debye temperature for hydrogen. Numerical results are given for the total cross section for both orthohydrogen and parahydrogen gas at 20.4\ifmmode^\circ\else\textdegree\fi{}K which agree reasonably well with the limited experimental results available. Also, curves of the double differential cross section are shown for selected incident neutron energies and scattering angles. These latter curves show very clearly the various rotational and vibrational transitions. The formulas given here are applicable at all temperatures below the thermal excitation of the first vibrational level.