The 13N(d,n)14O Reaction and the Astrophysical 13N(p,g)14O Reaction Rate

TL;DR

This study measures the $^{13}$N($d,n$)$^{14}$O reaction to better understand the $^{13}$N($p, extgamma$)$^{14}$O reaction rate, crucial for stellar nucleosynthesis, using experimental data and theoretical analysis to refine astrophysical models.

Contribution

First measurement of the $^{13}$N($d,n$)$^{14}$O angular distribution at 8.9 MeV and derivation of the ANC, improving the accuracy of the $^{13}$N($p, extgamma$)$^{14}$O reaction rate for astrophysics.

Findings

Derived ANC value: 5.42 ± 0.48 fm$^{-1/2}$

Calculated astrophysical S-factors and reaction rates

Discussed implications for nova evolution

Abstract

$^{13}$N($p,\gamma$)$^{14}$O is one of the key reactions in the hot CNO cycle which occurs at stellar temperatures around $T_9$ $\geq$ 0.1. Up to now, some uncertainties still exist for the direct capture component in this reaction, thus an independent measurement is of importance. In present work, the angular distribution of the $^{13}$N($d,n$)$^{14}$O reaction at $E_{\rm{c.m.}}$ = 8.9 MeV has been measured in inverse kinematics, for the first time. Based on the distorted wave Born approximation (DWBA) analysis, the nuclear asymptotic normalization coefficient (ANC), $C^{^{14}O}_{1,1/2}$, for the ground state of $^{14}$O $\to$ $^{13}$N + $p$ is derived to be $5.42 \pm 0.48$ fm$^{-1/2}$. The $^{13}$N($p,\gamma$)$^{14}$O reaction is analyzed with the R-matrix approach, its astrophysical S-factors and reaction rates at energies of astrophysical relevance are then determined with the ANC. The implications of the present reaction rates on the evolution of novae are then discussed with the reaction network calculations.