AstrophysicalSfactor for the radiative captureN12(p,γ)O13determined from theN14(N12,O13)C13proton transfer reaction

Abstract

The cross section of the radiative proton capture reaction on the drip line nucleus $^{12}\mathrm{N}$ was investigated using the asymptotic normalization coefficient (ANC) method. We have used the $^{14}\mathrm{N}(^{12}\mathrm{N},^{13}\mathrm{O})^{13}\mathrm{C}$ proton transfer reaction at 12 MeV/nucleon to extract the ANC for $^{13}\mathrm{O}\ensuremath{\rightarrow}^{12}\mathrm{N}+p$ and calculate from it the direct component of the astrophysical $S$ factor of the $^{12}\mathrm{N}(p,\ensuremath{\gamma})^{13}\mathrm{O}$ reaction. The optical potentials used and the distorted-wave Born approximation analysis of the proton transfer reaction are discussed. For the entrance channel, the optical potential was inferred from an elastic scattering measurement carried out at the same time as the transfer measurement. From the transfer, we determined the square of the ANC, ${C}_{{p}_{1/2}}^{2}(^{13}\mathrm{O}{}_{\mathrm{g}.\mathrm{s}.})=2.53\ifmmode\pm\else\textpm\fi{}0.30 {\mathrm{fm}}^{\ensuremath{-}1}$, and hence a value of $0.33(4) \mathrm{keV}$ b was obtained for the direct astrophysical $S$ factor at zero energy. Constructive interference at low energies between the direct and resonant captures leads to an enhancement of ${S}_{\mathrm{total}}(0)=0.42(6) \mathrm{keV}$ b. The $^{12}\mathrm{N}(p,\ensuremath{\gamma})^{13}\mathrm{O}$ reaction was investigated in relation to the evolution of hydrogen-rich massive Population III stars, for the role that it may play in the hot $\mathit{pp}$-chain nuclear burning processes, possibly occurring in such objects.