On the treatment of neutron scattering in the resonance range

An improved double-differential resonance-dependent scattering kernel is presented and its impact on criticality, Doppler Effect, absorption, and inventory of heavy isotopes for a typical unit cell is confirmed again to be significant. The influence of solid state effects is investigated. The way the resonant crystal lattice model based on a 4-point correlation function differs from the free gas scattering kernel is discussed and the differences are shown to be small. In deterministic calculations of the neutron slowing down spectrum in the resonance range a particularly simple approx- imation is usually made for the secondary energy distribution of scattered neutrons (the transfer kernel). This treats the scattering as uniform over the range αE → E where α = ((A − 1)/(A + 1)) 2 and A is the mass-ratio between the target and the neutron. It ignores the effects of the thermal motion and the associated up-scattering effects. In some Monte Carlo calculations the above 0degree K, asymptotic kernel is ex- tended for certain resonances, as a function of the temperature, and includes the effects of thermal motion on the scattering distributions in the resonance range. Yet this approach uses a form of secondary distribution which applies only to a scattering cross-section which is constant in energy. In this study we discuss an improvement of this approx- imate scattering kernel to include the effect of resonances and temperatures on the scattering kernel, and also discuss the impact of the solid state effects on the kernel. This is done by analysing the quantum crystal lattice formalism for resonant scattering by a bound nucleus developed by Word and Trammell. The results of former studies are discussed and new solution methods in the limit of the short time approximation are presented and compared with the free gas energy dependent scattering kernel. The applicability of the new resonant scattering kernel is also discussed relative to experiment, which might assess how well it predicts the secondary distribution. Since transmission and capture experiments do not focus on this important aspect, a new dedicated experiments is suggested to evaluate directly the predicted angular distribution of the model.