Astrophysical $S$ factor for the radiative capture ${}^{12}\mathrm{N}(p,\gamma ){}^{13}\mathrm{O}$ determined from the ${}^{14}\mathrm{N}({}^{12}\mathrm{N},{}^{13}\mathrm{O}){}^{13}\mathrm{C}$ proton transfer reaction

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 ${}^{13}\mathrm{O}\to {}^{12}\mathrm{N}+p$ and calculate from it the direct component of the astrophysical $S$ factor of the ${}^{12}\mathrm{N}(p,\gamma ){}^{13}\mathrm{O}$ 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, $C_{p_{1/2}}^2({}^{13}\mathrm{O}{}_{\mathrm{g}.\mathrm{s}.})=2.53\pm 0.30\hspace{0.5em}{\mathrm{fm}}^{-1}$, and hence a value of $0.33(4)\hspace{0.5em}\mathrm{keV}$ 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 $S_{\mathrm{total}}(0)=0.42(6)\hspace{0.5em}\mathrm{keV}$ b. The ${}^{12}\mathrm{N}(p,\gamma ){}^{13}\mathrm{O}$ 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.

Figure 1

Particle identification plots $\Delta E$ vs $E$ residual for (a) telescope 1, covering the small angle region, and (b) telescope 3 at large angles.

Figure 2

Reconstructed $Q$ value for the ${}^{12}\mathrm{N}$ elastic scattering channel off the melamine target detected at small angles. The distribution around zero energy corresponds to elastic scattering on both ${}^{12}\mathrm{C}$ and ${}^{14}\mathrm{N}$ nuclei in the target. The small bump centered around −6 MeV (includes the kinematics shift) corresponds to the inelastic channel ${}^{12}\mathrm{N}\text{−}{}^{12}\mathrm{C}{}^{*}(2^{+})$, while the left-most distribution is the elastic scattering off ${}^1\mathrm{H}$ nuclei in the target.

Figure 3

Angular distribution for elastic scattering of ${}^{12}\mathrm{N}$ off ${}^{14}\mathrm{N}$ and ${}^{12}\mathrm{C}$ nuclei in the melamine target. The theoretical calculation (dotted curve) was filtered with the experimental conditions through a Monte Carlo simulation to obtain the dashed curve. The calculations were carried out with $N_V=0.37$, $N_W=1.0$, $t_V=1.2\hspace{0.5em}\mathrm{fm}$, $t_W=1.75$ fm. The red solid curve was calculated with $N_W=0.80$.

Figure 4

Comparison between experimental data and theoretical calculation that describes the scattering off ${}^{12}\mathrm{C}$ target (plotted in the laboratory frame as per Fig. 3 for comparison). Shown here in the blue dashed line is a double-folding potential calculation of the elastic channel. The green dotted line represents coupled-channel calculation of the inelastic scattering corresponding to the first excited $2^{+}$ state in ${}^{12}\mathrm{C}$, and the red solid line is the incoherent sum between these two scattering components. See text for details.

Figure 5

Reconstructed $Q$ value of the (${}^{12}\mathrm{N},{}^{13}\mathrm{O}$) proton transfer reaction employing the melamine target. The peak on the right-hand side corresponds to the transfer channel of interest, ${}^{14}\mathrm{N}({}^{12}\mathrm{N},{}^{13}\mathrm{O}){}^{13}\mathrm{C}$, whereas the other peak corresponds to the transfer channel ${}^{12}\mathrm{C}({}^{12}\mathrm{N},{}^{13}\mathrm{O}){}^{11}\mathrm{B}$.

Figure 6

Transfer reaction angular distribution for ${}^{14}\mathrm{N}({}^{12}\mathrm{N},{}^{13}\mathrm{O}){}^{13}\mathrm{C}$. The solid red curve is the fit with DWBA calculation.

Figure 7

Comparison between the spectroscopic factor $S_{p_{1/2}}$(full squares) and the $C_{p_{1/2}}^2$ (open squares) extracted for the ground state of ${}^{13}\mathrm{O}$ as a function of the single-particle ANC, $b_{p_{1/2}}$. See text for details.

Figure 8

Astrophysical $S$ factor of the ${}^{12}\mathrm{N}(p,\gamma ){}^{13}\mathrm{O}$ reaction as a function of the energy in the center-of-mass reference system. The dashed curve shows the direct capture component of the $S$ factor, while the dotted curve is the resonant component. The solid curve is the total astrophysical $S$ factor.

Figure 9

Total reaction rate of the radiative capture ${}^{12}\mathrm{N}(p,\gamma ){}^{13}\mathrm{O}$ determined by this work and plotted in comparison with the reaction rate corresponding to the direct capture only as evaluated in Ref. [3].

Figure 10

Temperature and density conditions at which the ${}^{12}\mathrm{N}(p,\gamma ){}^{13}\mathrm{O}$ reaction may play a role. Curve 1 represents the equilibrium line between the rates for ${}^{12}\mathrm{N}$ proton capture and ${}^{12}\mathrm{N}\beta$ decay. Curve 3 illustrates the same result as determined from Ref. [3]. Curve 2 shows the line of equal strength between the rate of the ${}^{12}\mathrm{N}$ radiative proton capture to ${}^{13}\mathrm{O}$ and the rate for the inverse process, ${}^{13}\mathrm{O}$ photodisintegration. See text for details.