K-matrix analysis of resonance nuclear reactions

Abstract

A simple parametrization of nuclear reaction cross sections in terms of resonance parameters is obtained from the expansion of a modified scrK matrix. The latter is defined in such a way that it has no other singularity in the complex energy plane than its poles. When expanded in terms of these poles, it can be used to analyze and parametrize low-energy data on resonance reactions. The pole energies ${\mathit{E}}_{\lambda }$ are the resonance energies without shift (except when there is a nearby threshold of a closed neutron channel), and the residues are the products of reduced width amplitudes ${\mathit{g}}_{\mathit{c}\lambda }$. These two sets of parameters (${\mathit{E}}_{\lambda }$,${\mathit{g}}_{\mathit{c}\lambda }$) are independent of the channel radii and no boundary condition constants are involved in their definitions. Also, few-level approximations of the expanded scrK matrix retain the unitarity of the S matrix. These properties add more reliability to the extrapolation of data to lower energies, as often necessary for reactions of astrophysical interest.