Effect of nuclear spin correlations on the scattering of neutrons by molecules

Abstract

The scattering of slow neutrons by spherical-top molecules is discussed taking into account the correlations in nuclear spin caused by the presence of identical nuclei in the molecule. Matrix elements for the scattering are evaluted between different symmetrized states using group-theoretical methods. It is shown that coherent scattering can cause only those transitions which leave the symmetry of the total molecular wave function unchanged, while incoherent scattering can cause transitions between states of different symmetry. Explicit expressions for the cross section for scattering from methane are derived. These are different from those obtained by Michael recently in a treatment of the same problem. Formulas for the cross section for symmetric-top molecules are also derived. Numerical calculations have been performed for the scattering of 0.025-eV neutrons through a 10° scattering angle by methane gas at 10 and 300°K. It is found, contrary to Michael's observations, that at 10°K nuclear-spin correlations produce considerable differences in the scattering compared with the case where their effects are ignored. At 300°K, however, their effects are negligible. These findings are in accord with the predictions made earlier by Zemach and Glauber.