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

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.

Comments: 4 pages, 2 figures; to appear in JPS Conference Proceedings, 15th International Symposium on Origin of Matter and Evolution of Galaxies (OMEG15), Kyoto Japan, July 2-5, 2019