Conversion between the formal and observed parameters in $R$-matrix theory

TL;DR

This paper introduces a method to convert formal parameters to observed parameters in R-matrix theory, improving calculations of nuclear reaction S-factors, especially for low-energy $^{12}$C($ ext{α}$,$ ext{γ}_0$)$^{16}$O, and demonstrates its application to interference effects.

Contribution

It presents a new conversion technique between formal and observed parameters in R-matrix theory that is independent of boundary conditions and refines low-energy S-factor calculations.

Findings

Reduced the $E$1 $S$-factor at 300 keV compared to previous evaluations.

Applied the method to study interference between 1$^-$ states in $^{16}$O.

Demonstrated the method's independence from boundary conditions in S-matrix calculations.

Abstract

The conversion between the formal and observed parameters is obtained from the phase equivalence between the $R$-matrix and Breit-Wigner formula, and it is applied to a study of the low-energy $E$1 $S$-factor of $^{12}$C($\alpha$,$\gamma_0$)$^{16}$O. As an example, weak interference between 1$^-$ states in $^{16}$O is discussed. As well as the ordinary $R$-matrix method, the present method calculates the $S$-matrix and cross sections, independent of the boundary condition. Therefore, the $E$1 $S$-factor at $E_{c.m.} = 300$ keV is found to be reduced from the current evaluation.