Interpolation formula of thermal neutron scattering law in temperature interval

A very useful formula for interpolating the thermal neutron scattering law in temperature intervals is derived by separating the scattering law into two factors, strongly and weakly dependent on temperature. The strong temperature dependence of the scattering law is characterized by Debye-Waller factors, which are found to increase almost linearly with temperature for most moderators. The Debye-Waller factor is approximated by a linear function of temperature with the proportional constant determined so as to give the exact scattering laws at the boundaries of the temperature interval. Our formula is applied to two typical moderators (graphite and light water) to demonstrate its effectiveness and accuracy. It is shown that interpolated values of the scattering law are accurate within experimental errors in the practical range of momentum and energy transfers of neutrons.