The time-dependent moments equations derived from the linearized Boltzmann equation are solved for the case of an infinite nonabsorbing medium of hard spheres. The distribution function at zero time is chosen to be Maxwellian at origin and zero elsewhere. The solutions can be applied to neutron diffusion in monatomic hydrogen and to the motion of atoms in a dilute monatomic gas. In the latter case, the solutions give the spatial moments of Van Hove's self-correlation function Gs(,t). Non-Gaussian corrections to Gs(, t) are studied. It is found that these corrections are very sensitive to the type of anisotropy of the scattering kernel. Various approximations (including synthetic kernel) of the exact kernel for a hard sphere gas are considered. The non-Gaussian corrections obtained from approximate kernels are compared with those obtained from the exact kernel. In particular, a recently published kinetic model calculation, using a separable isotropic kernel with l/v scattering cross section, overestimates the non-Gaussian corrections by a factor of almost 4.