R-Matrix theory with level-dependent boundary condition parameters

TL;DR

This paper introduces a new R-matrix formalism with level-dependent boundary conditions that aligns formal parameters with observed resonance energies and widths, improving the accuracy of nuclear scattering models.

Contribution

The paper develops a nonorthogonal basis R-matrix theory with level-dependent boundary conditions, matching formal parameters to observed values without additional adjustments.

Findings

Successfully applied to 12C+p elastic scattering data

Formal parameters for energies and widths match observed values

Provides a consistent framework for resonance analysis

Abstract

I present a new formalism of the R-matrix theory where the formal parameters for the resonance energies and widths are identical to the observed values. By allowing the boundary condition parameters to vary from level to level, the freedom required to adjust the formal parameters for the pole positions to the observed values is obtained. The basis of the resulting theory becomes nonorthogonal, and I describe the procedure to construct a consistent R-matrix theory with such a nonorthogonal basis. And by adjusting the normalization of the states that form the basis, the formal parameters for the reduced decay widths also become the same as those observed, leaving no formal parameters that are different from the observed ones. A demonstration of the developed theory to the elastic 12C+p scattering data is presented.