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 O-16 -> alpha + C-12.