Tests of the extended R-matrix theory of nuclear reactions

Abstract

The extended R-matrix theory of nuclear reactions is a generalization of the R-matrix formalism that makes it possible to calculate the collision matrix from the compound nucleus eignestates provided by any nuclear structure calculation. In addition, optical potentials for each channel may be used to represent the nonresonant part of the collision matrix. To test the extended R-matrix formalism (ERF) it was applied to simple, soluble, two channel, S-wave scattering models. The ERF was found to be superior to the standard R-matrix formalism (SRF). Like the SRF, the ERF results are very sensitive to the choice of the channel radius parameters. In addition the ERF is plagued by the formalism (XF) completely eliminates the dependence on the matching radius. The XF is found to give fairly good results in our model calculations and reduces the false resonance difficulty. However, the XF has the drawback of being sensitive to a set of boundary condition parameters whose values will be somewhat ambiguous in practical calculations. This shortcoming is eliminated in the modified X-matrix formalism (MXF) which is found to give excellent results for our two channel model and shows no false resonances. We conclude that the MXF is the version of choice among the various versions of the ERF.