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.
Categories: nucl-th nucl-ex