A New Variational Method for the Pulsed-Neutron Problem

A new variational method has been developed to study the pulsed-neutron problem in crystalline moderators, which permits one to take explicit account of the discontinuities in the values of transport cross section of crystalline moderators at Bragg energies. For the trial function, we take the exact solution of the eigenvalue equation for some suitably chosen large value of buckling, say . It is shown by considering the case of beryllium that the present method, quite simply and accurately, gives the values of the fundamental mode decay constant and the corresponding eigenfunction in a sufficiently large range of buckling without having to solve the eigenvalue equation for each buckling separately. The results are discussed for two different values of —0.04 and 0.06 cm⁻².