Multilevel Formula for the Fission Process

The dispersion theory formalism of Wigner and Eisenbud has been applied to the problem of interference between resonances in the slow-neutron fission cross section. The development presented here assumes that the process involves one neutron channel and a large number of channels for the capture process. Although the treatment, for simplicity, assumes that only one fission channel is open, the relevant expressions for the fission cross section are presented in such a form that the generalization to any number of fission channels is readily apparent. Although no restriction as to the number of levels is necessary, the results are of practical use only when the number of assumed fission channels is small. Multilevel expressions for the radiative capture and scattering cross sections are also presented for one fission channel. The radiative capture cross section in the absence of fission is given and shown to differ formally from a sum of single-level Breit-Wigner terms.