The Scattering of Slow Neutrons by Molecular Gases

It has been shown by Fermi that the cross section for the scattering of slow neutrons by protons is four times greater for protons strongly bound to an infinite mass than it is for free protons initially at rest. A simple generalization of this factor of four can be given for the scattering of neutrons by molecular gases if the neutron energy is great as compared to the energy differences of the rotational levels of the scattering molecule but small compared to the quanta of molecular vibration. In this case, the proton may be replaced by a freely moving hypothetical mass point whose mass is a tensor depending on the mass and structure of the molecule. On this basis the total cross section for the scattering of slow neutrons by ${\mathrm{H}}_2$ and by C${\mathrm{H}}_4$, N${\mathrm{H}}_3$ and ${\mathrm{H}}_2$O at low temperatures has been calculated as a function of the ratio of the neutron energy to the thermal energy of the scattering gas. The possibility of applying the theory to a determination of the neutron-proton scattering cross section is discussed.