Calculation of neutron slowing down spectrum in water using green's function

Abstract

A method is presented which provides an analytical solution to the steady state, energy dependent neutron transport equation for the Hydrogen mixture case with isotropic elastic and inelastic scattering. The main characteristics of the method are the use of Green's function and diffusion approximation. A difference form of the Boltzman equation is derived as the final expression for machine computation.

Neutron slowing down spectrum is calculated from ³T(d, n)⁴He source put at the centre of a cubical block of water. A comparison is made with the slowing down spectrum calculated from ²⁴¹Am-⁹Be source. The effects of using different models for inelastic scattering by oxygen atom in water molecule on the slowing down spectrum are also investigated. Some thermal group cross-sections are developed and thermal spectrum in water is calculated for stationary nuclei and is compared with experiments; with good agreement obtained between them within the approximations made in the calculations and the difficulties involved in measuring the thermal spectrum in water.