Space- and angle-dependent steady-state thermal-neutron spectra inside finite prisms of graphite

Calculated results are reported of steady-state space- and angle-dependent thermal-neutron spectra inside an infinite slab as well as inside finite prisms of graphite with transverse dimensions varying from 100 x 100 cm2 to 30 x 30 cm2 and different longitudinal dimensions (ranging from 100 to 180 cm). It is found that in the forward direction, due to streaming, cold neutrons pile up with distance. Neutron spectra in backward directions are depleted in sub-Bragg neutrons. At all distances from the source plane, the proportion of cold neutrons in the energy spectrum in the forward direction increases with decrease in transverse dimensions. The question of the existence of asymptotic conditions in these assemblies has been discussed in detail. It is shown that in the forward direction a true discrete mode does not exist even in an infinite slab 150 cm thick. However, pseudo-asymptotic conditions should exist beyond 30 cm in a prism of transverse dimensions nearly 100 x 100 cm2. The critical transverse dimensions for the existence of a pseudo-asymptotic mode lie somewhere between 100 x 100 cm2 and 70 x 70 cm2, in conformity with the observed results of DeJuren and Swanson and theoretical predictions of Ahmed et al