Speaker
Description
We investigated the radiative proton capture on nitrogen isotopes $^{12}$N, $^{13}$N, and $^{14}$N [1 - 4] in the framework of the MPCM and obtained the reaction rates and their parametrizations. There are two stable nitrogen isotopes $^{14}$N and $^{15}$N, and among short-lived nitrogen isotopes, the longest-lived are $^{12}$N ($t_{1/2} = 11$ ms) and $^{13}$N ($t_{1/2} = 9.965$ min).
We compare the reaction rates to understand the relevance of each process at a given astrophysical temperature. The radiative proton $^{12}$N($p,\gamma)^{13}$O, $^{13}$N($p,\gamma)^{14}$O, $^{14}$N($p,\gamma)^{15}$O, and $^{15}$N($p,\gamma)^{16}$O processes have the same Coulomb barrier, so the reaction rates will differ only due to the different values of the $S(E)$ and reduced mass $\mu$ of interacting particles in the entrance channel. The reduced masses of the pairs $p^{12}$N, $p^{13}$N, $p^{14}$N, and $p^{15}$N are always less than the proton mass and are within the range $0.9294 \leq \mu $(amu) $\leq 0.9439$. Therefore, the impact of the reduced mass can be omitted, and the reaction rates depend entirely on the reaction $S$-factor [4].
The $p^{15}$N reaction is the fastest, and its rate dominates up to $T_9 \tilde{a} 0.175$. $^{14}$N($p,\gamma)^{15}$O is the slowest process up to $T_9 \tilde{a} 0.1$, and it controls the rate and time of nucleosynthesis cycles. The $p^{15}$N rate becomes dominant at temperature-explosive hydrogen burning scenarios in stars. Only in the temperature windows $0.18 \leq T_9 \leq 1.14$ and $0.66 \leq T_9 \leq 3$ the reaction $^{15}$N($p,\gamma)^{16}$O is slower than $^{13}$N($p,\gamma)^{14}$O and $^{14}$N($p,\gamma)^{15}$O reactions, respectively. Hence the $p^{15}$N reaction controls the rate and time of cycles of nucleosynthesis in these two temperature windows [4].
The $^{15}$N($p,\gamma)^{16}$O reaction rate shows a strong interference effect but minor sensitivity to the asymptotic constant.
The main difficulty in determining reliable reaction rates of $^{12}$N($p,\gamma)^{13}$O, $^{13}$N($p,\gamma)^{14}$O, $^{14}$N($p,\gamma)^{15}$O, $^{15}$N($p,\gamma)^{16}$O reactions for the CNO cycles is the uncertainty in the very low cross-sections at the Gamow range. Developments within the low-energy underground accelerator facility LUNA [5] and recent improvements in the detection setup [6] make taking direct measurements of nuclear reactions near the Gamow range feasible. This advantage has been demonstrated in the $^{14}$N($p,\gamma)^{15}$O reaction, which was successfully measured down to energies of 70 keV at LUNA [7].
References
1. S. B. Dubovichenko, et al. Nucl. Phys. A 1028, 122543 (2022).
2. S. B. Dubovichenko, et al. Phys. Rev. C 102, 045805 (2020).
3. S. Dubovichenko, et al. Int. J. Mod. Phys. E 29, 1930007 (2020).
4. S. B. Dubovichenko, et al. arXiv:2303.14680 [nucl-th]
5. H. Costantini, et al. Rep. Prog. Phys. 72, 086301 (2009).
6. J. Skowronski, et al. J. Physi. G: Nucl. Part. Phys. (2023).
7. LUNA Collaboration: Lemut A, et al. Phys. Lett. B 634, 483 (2006).
