Astrophysical ${}^{15}\mathrm{N}(n,\gamma ){}^{16}\mathrm{N}$ reaction rate from precision measurement of the ${}^{15}\mathrm{N}(d,p){}^{16}\mathrm{N}$ angular distributions

Background: Asymptotic giant branch stars are one of the possible sites of fluorine production as confirmed by astronomical observation. The ${}^{15}\mathrm{N}(n,\gamma ){}^{16}\mathrm{N}$ reaction competes with ${}^{15}\mathrm{N}(\alpha ,\gamma ){}^{19}\mathrm{F}$ on the reaction chain and thus influences the production of the only stable fluorine isotope ${}^{19}\mathrm{F}$. The ${}^{15}\mathrm{N}(n,\gamma ){}^{16}\mathrm{N}$ reaction rate at low temperatures of astrophysical interest depends on the neutron spectroscopic factors of the four low-lying states in ${}^{16}\mathrm{N}$.

Purpose: The ${}^{16}\mathrm{N}$ neutron spectroscopic factors from two previous measurements of $(d,p)$ reaction differ by a factor of $\approx 2$. This work was intended to investigate these spectroscopic factors via a precision measurement of the ${}^{15}\mathrm{N}(d,p){}^{16}\mathrm{N}$ angular distributions using a Q3D magnetic spectrograph.

Methods: The high resolution of the Q3D magnetic spectrograph led to clear separation of these four closely spaced states. The neutron spectroscopic factors were extracted from the present angular distributions with the distorted wave Born approximation and adiabatic distorted wave approximation methods.

Results: The neutron spectroscopic factors of the ${}^{16}\mathrm{N}$ ground, 0.120, 0.298, and 0.397 MeV states were extracted to be $1.32\pm 0.12, 1.33\pm 0.18, 1.10\pm 0.10$, and $1.30\pm 0.14$, respectively. The new results support the conclusion that these four states in ${}^{16}\mathrm{N}$ are all good single-particle levels. The cross section and reaction rate of ${}^{15}\mathrm{N}(n,\gamma ){}^{16}\mathrm{N}$ were calculated based on the present spectroscopic factors.

Conclusions: The present work provides a precision measurement of the spectroscopic factors of the ${}^{16}\mathrm{N}$ states and the resulting ${}^{15}\mathrm{N}(n,\gamma ){}^{16}\mathrm{N}$ reaction rate. The present higher reaction rate of the ${}^{15}\mathrm{N}(n,\gamma ){}^{16}\mathrm{N}$ reaction suggests higher flow through ${}^{15}\mathrm{N}(n,\gamma ){}^{16}\mathrm{N}$ compared with previous expectation.

Figure 1

Focal-plane position of protons at ${\theta }_{\text{lab}}={36}^{\circ }$ from the present ${}^{15}\mathrm{N}(d,p){}^{16}\mathrm{N}$ measurement. The grey and red patterns dedicate the events from the ${}^{15}\mathrm{N}$ and ${}^{14}\mathrm{N}$ targets, respectively.

Figure 2

Angular distribution of the $d+{}^{15}\mathrm{N}$ elastic scattering at incident energy of 15 MeV. The black circles and solid blue curve denote the present experimental data and the theoretical calculation with the phenomenological potential [31], respectively.

Figure 3

Angular distributions of the ${}^{15}\mathrm{N}(d,p){}^{16}\mathrm{N}$ reaction leading to the ground and the first three excited states in ${}^{16}\mathrm{N}$. The black circles represent the present experimental data. The solid blue and dotted red curves represent the DWBA and ADWA calculations, respectively.

Figure 4

Comparison of the present neutron spectroscopic factors of the ground and first three excited states in ${}^{16}\mathrm{N}$ with the previous values from charge symmetry method [38, 39, 40] and transfer reaction method [24, 25, 26]. The blue lines represent the oxbash shell-model predictions [23]. The ground-state spectroscopic factor by Fujita et al. [39] was scaled by 4. Two values labeled by Bardayan(2008) correspond to the ones from Methods 1 and 2 in Table 2.

Figure 5

Calculated cross sections of ${}^{15}\mathrm{N}(n,\gamma ){}^{16}\mathrm{N}$ direct capture populating the four low-lying states in ${}^{16}\mathrm{N}$. The solid black curve represents the total cross section of each states. The dashed red and dotted blue curves represent the contribution of incoming $p$ and $f$ waves, respectively.

Figure 6

Astrophysical reaction rate of ${}^{15}\mathrm{N}(n,\gamma ){}^{16}\mathrm{N}$. The solid black, dashed red, and dotted blue curves represent total, direct, and resonant capture rates, respectively.

Figure 7

Comparison of ${}^{15}\mathrm{N}(n,\gamma ){}^{16}\mathrm{N}$ astrophysical reaction rate results (a) in the range of $0.05<T_9<3$, and (b) at $T_9=0.1$. The black, grey, green, red, blue, and orange patterns represent the present, Rauscher et al. [22], Merssner et al. [23], Bardayan et al. [25], Guo et al. [26], and Neelam et al. [27] results, respectively.