Intermediate Scattering Function in Slow Neutron Scattering

The conditions under which the so-called intermediate scattering function occurring in the theory of slow neutron scattering and in the theory of the Mössbauer effect can be written in the form $\exp [-{\kappa }^2\gamma \mathrm{}(t\left)\right]$ have been explicitly stated; the intermediate scattering function is then factorizable into two parts; the part referred to in the paper as the displacement part gives on Fourier transformation a real space-time function which, quite unambiguously, has the meaning usually attributed to the Van Hove $G_s(\mathrm{x}, t)$ function; the other part arises out of the nucleus recoiling against the neutron. It is shown that for systems in thermal equilibrium, the recoil part can be expressed in terms of the displacement part. This relation enables one to take care of the recoil part in case a classical approximation is made for the dynamics of the scattering system.