Neutron wave propagation in finite assemblies of graphite

Abstract

Neutron-wave propagation in graphite assemblies of finite transverse dimensions has been studied in the diffusion theory approximation using multigroup (30 groups) approach and energy dependent boundary conditions. Frequency dependence of the thirty eigenvalues is discussed. It is shown that the critical frequency $\text{f}{}^{\mathrm{\ast }}$ depends upon transverse size. For infinite transverse size ${}^{\mathrm{\ast }}$ is nearly equal to 130 Hz whereas for some critical transverse dimensions (in the present case it lies between 80 × 80 cm² and 70 × 70 cm²) ^∗ becomes zero. The existence of a pseudo-discrete mode in the continuum is discussed. Strong interference between the cold neutron density and the ’epicold‘ neutron density is predicted at some specific distance from the source. The position and intensity of interference is found to depend upon the frequency of the wave, the transverse size of the assembly, the energy spectrum of the source neutrons and the temperature of moderator. Neutron wave propagation in finite assemblies of graphite at 200°K and 150°K is also discussed.