The Scattering of Slow Neutrons by Ortho- and Paradeuterium

Information relating to the spin dependence of the neutron-deuteron interaction can be obtained from slow neutron scattering experiments in ortho- and paradeuterium. Theoretical formulae have been derived for the cross sections of the various transitions among the molecular rotational levels, which involve the scattering amplitudes $a_{\frac{3}{2}}$ and $a_{\frac{1}{2}}$ for the two spin states of the neutron-deuteron system. In particular, numerical results are given for the first few transitions originating from the ground levels of the ortho- and para-systems with neutron energies not exceeding 0.05 ev. The influence of the thermal motion of the molecule is described, and explicit formulae are given for the important transitions occurring at small neutron energies, on the assumption that the $D_2$ is in gaseous form at low temperature. The ratio of the ortho- and para-cross sections, under these conditions, is examined in its dependence upon the ratio of the scattering amplitudes. If the scattering amplitudes are of the same sign, the cross-section ratio is never greater than 1.31 and attains this magnitude only for small values of $a_{\frac{3}{2}}$ relative to $a_{\frac{1}{2}}$. If, however, the amplitudes are of opposite sign, this ratio can be as large as 1.75 and always exceeds 1.11. This experiment measures only the magnitudes of the amplitude combinations ($2a_{\frac{3}{2}}+a_{\frac{1}{2}}$) and ($a_{\frac{3}{2}}-a_{\frac{1}{2}}$), but not their signs, and thus leaves a fourfold ambiguity in interpretation. The possibility is discussed of determining the sign of ($2a_{\frac{3}{2}}+a_{\frac{1}{2}}$) by scattering experiments in HD. It is pointed out that the sign of ($a_{\frac{3}{2}}-a_{\frac{1}{2}}$) cannot be fixed by any experiment in which the deuteron spin is unoriented in space. An alternative experimental method, involving the depolarization of neutrons, is mentioned.