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 ¹⁶O→α+¹² C.