Scattering of Slow Neutrons byH2and CH4

Abstract

The mass tensor approximation, introduced by previous authors to calculate the scattering cross section of slow neutrons by molecules when the incident energy $E_0$ of the neutron is large compared with the average level spacing of the molecular rotations, is extended here to take into account the molecular vibrations. Calculations are made in the case of ${\mathrm{H}}_2$ and C${\mathrm{H}}_4$ at room temperature for neutron energies below the threshold of excitation of higher vibrational states. The agreement with experiment is very satisfactory in the expected range of validity of this theory. The cross section for higher $E_0$ is also treated in the case of ${\mathrm{H}}_2$, without taking into account, however, the thermal agitation of the scattering molecules: the asymptotic form of the total cross section for large values of $E_0$ is derived, and numerical calculations show that the asymptotic behavior is quickly reached.