Time-Dependent Neutron Thermalization for a Bare Multiplying Medium

A perturbation theory solution is given for the time-dependent, exp(— λt), neutron thermalization problem for a bare homogeneous multiplying medium. The model is based on diffusion theory with the heavy gas scattering kernel assuming 1/υ cross sections with a constant D/(ξσυ). The fission spectrum is assumed to be a delta function at the mean fission energy, ^∈f . The fundamental eigenfunction and eigenvalue are expressed in terms of infinite sums involving the Laguerre polynomials at ^∈f . The sums were evaluated analytically and numerical results are given.