Determination of Asymptotic Normalization Coefficients by Analytic Continuation of the $${R}$$-Matrix

Abstract

Abstract The method of finding the values of asymptotic normalization coefficients (ANC) is proposed based on the analytic continuation of the $$R$$-matrix that describes the elastic nuclear scattering into the unphysical region of the negative energy of collision ($$E<0$$). The formula is derived, expressing the partial-wave scattering amplitude through the $$R$$-matrix and modified Coulomb functions. This formula allows, when continuing the amplitude to the region $$E<0$$, to overcome difficulties associated with irregular behavior of the scattering amplitude near $$E=0$$ if the Coulomb interaction is present. The proposed method is used to determine the ANC for the channel $${}^{16}\textrm{O}\to\alpha+{}^{12}$$C.