Temperature-Dependent Intermediate Neutron Resonance Integrals

The Intermediate Resonance (IR) formulation of resonance absorption is extended to the temperature-dependent case by obtaining an explicit expression for the IR parameters as a function of temperature. Use is made of the tabulated J functions. The resonance integral is given in terms of a temperature-dependent J function as a function of a temperature-dependent IR parameter and represents the complete generalization of the IR formulation to the temperature-dependent case. The temperature-dependent solutions obtained are similar in analytic form to the zero-temperature solutions and they reduce to the latter in the limit of zero temperature. They also yield the correct narrow or wide resonance limits for all temperatures. The formulation using temperature-dependent IR parameters not only gives accurate temperature-dependent resonance integrals, but also gives reasonably accurate Doppler coefficients.