Rotational excitation of molecules by slow neutrons. II

Abstract

The contribution of the spin-orbit interaction to the rotationally inelastic scattering of neutrons from a closed-shell diatomic molecule is studied. For small momentum transfer and $\ensuremath{\Delta}J=\ifmmode\pm\else\textpm\fi{}1$ rotational transitions, the first Born-approximation amplitude depends approximately on the factor $\ensuremath{\Delta}\ensuremath{\omega}D{q}^{\ensuremath{-}1}$ (in atomic units), where $\ensuremath{\Delta}\ensuremath{\omega}$ is the energy transferred, $D$ is the permanent dipole moment of the target, and $q$ is the momentum transferred. The dependence on $\ensuremath{\Delta}\ensuremath{\omega}D$ is the same as that of the coefficient of absorption of long-wavelength radiation, and the dependence on ${q}^{\ensuremath{-}1}$ is characteristic of particle scattering in a dipole potential. Essentially $\ensuremath{\Delta}J=\ifmmode\pm\else\textpm\fi{}1$ cross sections are enhanced because rotational energy transfer can occur over appreciable target-neutron distances. Thus the tiny rotational transition strength $\ensuremath{\Delta}\ensuremath{\omega}D$ is weighted by the large factor ${q}^{\ensuremath{-}1}$. This means that a classical average of the cross section over molecular orientations cannot describe the physical process. The importance of this result to the theory of neutron-optical activity is discussed.