Theory of Resonance Absorption of Neutrons

A treatment of resonance absorption intermediate between the narrow (NR) and wide resonance MR) approximations is developed for hornogeneous systems. An arbitrary parameter, lambda , is introduced into the flux and two distinct approximations are employed to determine lambda as a function of the resonance parameters. One approximation is based upon a method of equating successive orders of approximation and the other is based upon a variational principle. Formulas are given, from which the resonance integral may be calculated. The parameter lambda character izes, in essence, the location between the NR and WR extremes, of the actual resonance. When lambda is set equal to 0 or 1, the first-order WR or NR integrals are obtained. Sample calculations are carried out for an intermediate case (the 192-ev resonance of U/sup 238/in a 1: 1 atomic mixture with hydrogen) using linear and nonlinear trial functions for both types of approximations. All results agree to within less than one per cent of 0.172 barns. In comparison, the usual extreme energy-loss assumptions yield results which differ by more than a factor of 2 (0.121 and 0.253 barns for the NR and WR approximations, respectively. (auth)