An elgenvalue and eigenfunction study of time-dependent fast-neutron spectra in 232Th

The pulsed problem for fast neutrons in Th has been studied using the multigroup diffusion equation and eigenfunction expansion method. The time-dependent fast-neutron spectra have been obtained up to 8000 ns inside Th systems with buckling ranging from 0.0 to 0.015 cm⁻². The results have been obtained using the 27-group BARC data set. It has been shown that for a fast Th system, unlike a fast U system, all the time eigenvalues lie in the continuum and no discrete time eigenvalue exists. A fast Th system behaves more like a non-multiplying system. The spectra shift continuously to lower energies with increasing time. However, pseudo-asymptotic conditions are established in certain time intervals. The start of pseudo-equilibrium conditions and the duration for which they persist is seen to increase with decreasing buckling. The reason for the establishment of pseudo-equilibrium conditions has been discussed. The theoretical results for the instantaneous decay constant inside a 40 cm cube of Th have been compared with the experimental results of Moo et al. (1973). The present results are in good agreement with the above experimental results based on the ²³⁹Pu detector.