Theory of neutron scattering from liquid and solid hydrogen

The inelastic spectrum of cold neutrons scattered incoherently from condensed hydrogen shows a quasi-elastic peak and an ortho-para conversion peak. A theory is developed to calculate the broadening of these peaks due to the hindering of the rotation of ortho-hydrogen molecules by anisotropic inter-molecular interactions. The quadrupole-quadrupole, van der Waals and valence interactions are taken between pairs of molecules and contributions to the broadening up to the first power of the ortho concentration c are discussed. The quadrupole-quadrupole term is seen to be dominant, broadening the ortho-para peak in agreement with experiment but contributing a width to the quasi-elastic peak which is less than the resolution broadening. The theory is extended to the analogous incoherent scattering peaks in deuterium with similar results.