Asymptotic normalization coefficient (ANC) of the system 13O → 12N + p determined from a (12N,13O) proton transfer reaction

We report on the determination of the ANC for the system O → N + p. The study was carried out in relation to the radiative proton capture reaction N(p,γ)O for the role that it may play in the hot pp-chain nuclear burning processes possibly occurring in Population III stars [1]. As is generally the case with radiative proton capture reactions, due to the presence of large Coulomb barriers compared to small stellar kinetic energies, the reaction cross sections are in the order of picobarns, too small to be measured directly in the laboratory. Thus, they are studied by indirect methods. For our reaction of interest, we have applied the indirect ANC method [2] by using a (N,O) proton transfer reaction. Details of the experiment are presented elsewhere [3]. The basic of the ANC method is in the fact that the cross section for the radiative proton capture is completely determined by the Asymptotic Normalization Coefficient. This is equivalent with determining the amplitude of the tail of the overlap integral of the ground state wave function of O into the two-body channel N + p. The ANC of the radiative capture of interest is extracted from a peripheral proton transfer reaction in which one of the two reaction vertices is characterized by the same ANC, provided that the other ANC vertex of the transfer reaction is known. In our particular case, the transfer reaction was N(N,O)C. Basically, the ANC of interest is extracted by fitting the experimental angular distributions with calculated Distorted Wave Born Approximation (DWBA) cross sections. This is written in the conventional DWBA formalism as: