Criticality and Flux Calculations for Hydrogenous Assemblies

The calculation of critical parameters, neutron distributions, and adjoint functions for reflected reactors is discussed. A variational technique and a modification of the Wiener-Hopf method are described. The major application is made for the case of reactors moderated by hydrogen, in which case the slowing-down kernel must be introduced either as a numerical function or as a polynomial fit to such a function. For the case of the polynomial fit, explicit formulas for critical size, neutron distributions, and adjoint functions have been found by the Wiener-Hopf method. A comparison with experimental results for water-moderated reactors shows discrepancies consistent with the discrepancy known to exist between the measured and calculated neutron age in water.