$^{14}$N(p,$γ)^{15}$O $S$ factor and the puzzling solar composition problem

Abstract

In stellar hydrogen burning, the CNO cycle dominates, with the $^{14}$N(p,$γ)^{15}$O reaction being the slowest process. Consequently, this reaction critically influences the solar composition, CNO neutrino fluxes, and the evolution of star clusters and galaxies. Recent direct measurements of $^{14}$N(p,$γ)^{15}$O have reported an enhanced astrophysical $S$-factor. This work presents a microscopic theoretical study of the $^{14}$N(p,$γ)^{15}$O reaction using the Gamow shell model in the coupled-channel representation (GSM-CC). The calculations achieve good agreement with experimental data for both the total $S$-factors and the separate contributions from transitions to the ground state and excited states of $^{15}\mathrm{O}$. However, the predicted $S$-factor at zero energy exceeds the experimental value. Based on the computed $S$-factors, the derived carbon and nitrogen abundances align closely with predictions from recent $^{14}$N(p,$γ)^{15}$O cross-section measurements, yet remain significantly lower than the latest solar neutrino observation values.

Figures (3)

• Figure 1: The calculated energy levels of $^{15}$O are compared with the experimental data nndc. The ground state energy is set to zero and energies of the excited states are given relative to the ground state energy. The energy of the proton capture threshold is indicated by the dashed line. Two sets of GSM-CC calculations are shown, the details of which are explained in the text.
• Figure 2: The astrophysical factor of the $^{14}$N(p,$\gamma)^{15}$O reaction is shown as the function of the proton projectile energy in the $p$ + $^{14}$N center of mass frame. The total S factor is given in Panel (a). The contributions by the capture to the ground state and to other excited states of $^{15}$O are plotted in Panel (b)-(h) respectively. The experimental data are listed for comparisons Imbriani200514NRunkle200514NBemmerer200614NATOMKI14NLi201614NWagner201814NFrentz202214Nchen202414npg.
• Figure 3: The comparison of S factors at the zero energy. The experimental data are taken from Refs. ANGULO2001755Runkle200514NMarta0814NImbriani200514NFrentz202214Nchen202414npg. The shaded area is for the recommendation value in SF-III SF-III.