Determination of Asymptotic Normalization Coefficients by Analytic Continuation of the \({R}\)-Matrix

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.