Integral and Angular Characteristics of Thermal Neutron Leakage Spectra

The energy-dependent Milne problem for thermal neutrons has been investigated with increased experimental accuracy and more advanced theory in the past several years. Based on previously reported calculations and experiments of the authors and others, certain aspects of the Milne problem for a non-absorbing medium are sufficiently understood that semi-empirical expressions can be given for the dependence of various quantities. This paper gives the development of such expressions. Furthermore, a variational-iterative method used by the authors and others to solve the Milne problem is described briefly, and a further improvement to earlier solutions is given. Simple semi-empirical expressions are given for the average energy of the angular-dependent leakage spectra (energy distribution of neutrons leaking from the moderator surface into the vacuum) which depend on the value of the second energy-exchange moment (M2) of the scattering kernel, and on the space-asymptotic solution. The change near the moderator surface in the average energy of the current can also be described by a simple expression involving M2. Since the space-asymptotic solutions are easy to obtain numerically, this provides a simple method for calculating approximately the average energies of the leakage spectra and current. The validity of the semi-empirical expressions is supported N by showing qualitatively through the transport equation that the dependence on M2 is to be expected. Calculations were made for realistic scattering kernels for H2O, benzene, Dowtherm A, and ZrH1,7, as well as for the free gas and Corngold separable scattering kernels. Agreement with the experimental results available (primarily for H2O ) is good. (author)