Spectroscopic factors for low-lying ${}^{16}\mathrm{N}$ levels and the astrophysical ${}^{15}\mathrm{N}$($n,\gamma$)${}^{16}\mathrm{N}$ reaction rate

Background: Fluorine is a key element for nucleosynthetic studies since it is extremely sensitive to the physical conditions within stars. The astrophysical site to produce fluorine is suggested to be asymptotic giant branch stars. In these stars the ${}^{15}\mathrm{N}$($n,\gamma$)${}^{16}\mathrm{N}$ reaction could affect the abundance of fluorine by competing with ${}^{15}\mathrm{N}$($\alpha ,\gamma$)${}^{19}\mathrm{F}$.

Purpose: The ${}^{15}\mathrm{N}$($n,\gamma$)${}^{16}\mathrm{N}$ reaction rate depends directly on the neutron spectroscopic factors of the low-lying states in ${}^{16}\mathrm{N}$. Shell model calculations and two previous measurements of the ($d,p$) reaction yielded the spectroscopic factors with a discrepancy by a factor of $\sim$2. The present work aims to explore these neutron spectroscopic factors through an independent transfer reaction and to determine the stellar rate of the ${}^{15}\mathrm{N}$($n,\gamma$)${}^{16}\mathrm{N}$ reaction.

Methods: The angular distributions of the ${}^{15}\mathrm{N}$(${}^7\mathrm{Li}$,${}^6\mathrm{Li}$)${}^{16}\mathrm{N}$ reaction populating the ground state and the first three excited states in ${}^{16}\mathrm{N}$ are measured using a Q3D magnetic spectrograph and are used to derive the spectroscopic factors of these states based on distorted wave Born approximation analysis.

Results: The spectroscopic factors of these four states are extracted to be 0.96 $\pm$ 0.09, 0.69 $\pm$ 0.09, 0.84 $\pm$ 0.08, and 0.65 $\pm$ 0.08, respectively. Based on the new spectroscopic factors we derive the ${}^{15}\mathrm{N}$($n,\gamma$)${}^{16}\mathrm{N}$ reaction rate.

Conclusions: The accuracy and precision of the spectroscopic factors are enhanced due to the first application of high-precision magnetic spectrograph for resolving the closely spaced ${}^{16}\mathrm{N}$ levels which cannot be achieved in most recent measurements. The present result demonstrates that two levels corresponding to neutron transfers to the 2$s_{1/2}$ orbit in ${}^{16}\mathrm{N}$ are not good single-particle levels although ${}^{15}\mathrm{N}$ is a closed neutron-shell nucleus. This finding is contrary to the shell model expectation. The present work also provides an independent examination to shed some light on the existing discrepancies in the spectroscopic factors and the ${}^{15}\mathrm{N}$($n,\gamma$)${}^{16}\mathrm{N}$ rate.

Figure 1

Focal-plane position spectrum of the ${}^6\mathrm{Li}$ events at ${\theta }_{\mathrm{lab}}$ = 10${}^{\circ }$ from the neutron-transfer reactions. The black solid and red dashed lines are the results from the enriched ${}^{15}\mathrm{N}$ target and natural ${}^{14}\mathrm{N}$ target, respectively. The break in the $x$ axis denotes the narrow gap between two separated detectors.

Figure 2

Angular distributions of the ${}^7\mathrm{Li}$ + ${}^{15}\mathrm{N}$ elastic scattering at incident energy of 44 MeV and ${}^6\mathrm{Li}$ + ${}^{15}\mathrm{N}$ elastic scattering at incident energy of 34.5 MeV. The black solid and red dashed curves represent the calculations using the fitted OMP parameters without and with a spin-orbit term, respectively.

Figure 3

Angular distributions of the ${}^{15}\mathrm{N}$(${}^7\mathrm{Li}$,${}^6\mathrm{Li}$)${}^{16}\mathrm{N}$ reaction leading to the ground and first three excited states in ${}^{16}\mathrm{N}$. The black solid and red dashed curves denote the DWBA calculations with the fitted OMP parameters without and with a spin-orbit term, respectively.

Figure 4

Present ${}^{15}\mathrm{N}$($n,\gamma$)${}^{16}\mathrm{N}$ rate for temperatures of 0.01–3 GK, and comparison of the present rate with the previous results by Fowler et al. [44], Rauscher et al. [45], Meissner et al. [18], and Bardayan et al. [19]. $T_9$ is the temperature in units of 1 GK. See text for details.