Some Characteristics of the Thermal Neutron Scattering Probability

An explicit form for the function representing the probability that a neutron with velocity v′ shall be scattered into an element of volume in velocity space d³υ about v, by elastic collisions with atoms of arbitrary mass number A in a Maxwell-Boltzmann distribution characterized by a temperature T, is derived. Analytical representations of this probability are presented for scattering cross sections which are either independent of relative speed or exhibit a Gaussian dependence. The scattering probability resulting from the former assumption is examined in some detail, and then employed in a calculation of the mean energy change per collision.