Determination of Asymptotic Normalization Coefficients by Analytic Continuation of Differential Cross Sections

Abstract A method is discussed for determining the asymptotic normalization coefficients (ANC) using the analytic continuation of experimental differential cross sections for nuclear transfer reactions to the pole point of the reaction amplitude with respect to the variable $$\cos\theta$$ , where $$\theta$$ is the scattering angle. Within the framework of this method, using experimental data on the differential cross section for the reaction $${}^{12}\textrm{C}(0^{+};0\textrm{ MeV})(d,p){}^{13}\textrm{C}(1/2^{+};3.09\textrm{ MeV})$$ the ANC for the channel $${}^{13}\textrm{C}(1/2^{+};3.09\textrm{ MeV})\to{}^{12}\textrm{C}(0^{+};0\textrm{ MeV})+n$$ was determined. When determining the ANC, the corrections caused by the Coulomb interaction in the initial, final and intermediate states of the reaction were taken into account. It is shown that these corrections significantly affect the extracted ANC value.

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