The ${}^{13}\mathrm{C}{(}^3\mathrm{He}{,d)}^{14}\mathrm{N}$ proton transfer reaction has been measured at an incident energy of 26.3 MeV. Angular distributions for proton transfer to the ground state and excited states at $2.313$ and 3.948 MeV in ${}^{14}\mathrm{N}$ are analyzed within the framework of the modified DWBA. Asymptotic normalization coefficients (ANC’s) defining the amplitude of the tails of the ${}^{14}\mathrm{N}$ bound-state wave functions in the ${}^{13}\mathrm{C}+p$ channel are extracted that are in excellent agreement with values found previously with the ${}^{13}\mathrm{C}{(}^{14}\mathrm{N}{,}^{13}\mathrm{C}{)}^{14}\mathrm{N}$ reaction. We conclude that $C_{p_{1/2}}^2=18.2\mathrm{}\left(9\right)\mathrm{}\hspace{0.5em}{\mathrm{fm}}^{-1}$ and $C_{p_{3/2}}^2=0.91\mathrm{}\left(14\right)\mathrm{}\hspace{0.5em}{\mathrm{fm}}^{-1}$ for the virtual decay ${}^{14}\mathrm{N}(\mathrm{g}.\mathrm{s}.\mathrm{}{)}^{13}\mathrm{C}+p.\mathrm{}$ These are necessary for the analysis of the ${}^{14}\mathrm{N}{(}^7\mathrm{Be}{,}^8\mathrm{B}{)}^{13}\mathrm{C}$ and ${}^{14}\mathrm{N}{(}^{11}\mathrm{C}{,}^{12}\mathrm{N}{)}^{13}\mathrm{C}$ reactions to extract the ANC’s for ${}^7\mathrm{Be}+p^8\mathrm{B}$ and ${}^{11}\mathrm{C}+p^{12}\mathrm{N},$ which determine the direct radiative capture cross sections ${}^7\mathrm{Be}(p,\gamma {)}^8\mathrm{B}$ and ${}^{11}\mathrm{C}(p,\gamma {)}^{12}\mathrm{N}$ at astrophysical energies.

• Received 10 March 2000

DOI:https://doi.org/10.1103/PhysRevC.62.024320