On the Temperature Dependence of the Thermal Neutron Flux Kernel

The thermal neutron flux kernel for a point fission source in a hydrogenous medium is obtained analytically by representing the epithermal slowing down source in a convenient functional form. Normalization is achieved by invoking an appropriate conservation condition. The temperature dependence is then assessed from experimentally determined variation in the diffusion length and appropriate variation in the fitting parameters for the slowing down source. It is concluded that the kernel for water is rather insensitive to change in the diffusion length, and in fact, the r²-flux varies to a good approximation as f(ρr), ρ being the temperature-dependent specific gravity.