The low-energy bare-nucleus cross section for ${}^{15}\mathrm{N}$$(p,\alpha )$${}^{12}\mathrm{C}$ is extracted by means of the Trojan horse method applied to the ${}^2\mathrm{H}$(${}^{15}\mathrm{N}$,$\alpha$${}^{12}\mathrm{C}$)$n$ reaction at $E_{\mathrm{beam}}=60$ MeV. For the first time we applied the modified half-off-energy-shell resonant $R$-matrix method that takes into account off-energy-shell effects and initial- and final-state interactions. In particular it has been shown that inclusion of Coulomb ${}^{15}\mathrm{N}$$\text{−}d$ scattering and off-shell effects do not affect the determination of the astrophysical factor. Also the simple plane-wave approximation used in previous analyses is justified. The results extracted via the Trojan horse method are compared to direct data in the same energy region and show very good agreement in the energy interval 70–312 keV. These results confirm the extrapolations of the $S$ factor reported in literature.

• Received 6 March 2007

DOI:https://doi.org/10.1103/PhysRevC.76.065804