Bound-to-continuum potential model for the $(p,\gamma)$ reactions of the CNO cycle

TL;DR

This paper introduces a bound-to-continuum potential model based on Skyrme Hartree-Fock calculations to accurately reproduce astrophysical S factors for proton capture reactions in the CNO cycle, advancing microscopic analysis in nuclear astrophysics.

Contribution

The study develops a self-consistent mean-field approach to model proton capture reactions, providing a new microscopic method for analyzing nuclear reactions in astrophysics.

Findings

Successfully reproduced astrophysical S factors for CNO cycle reactions.

Demonstrated the effectiveness of the Hartree-Fock continuum approach.

Highlighted the potential of microscopic models in nuclear astrophysics.

Abstract

The study of CNO cycle involves the examination of the proton radiative capture, or the $(p,\gamma)$ reactions below 2 MeV. The astrophysical $\mathcal{S}$ factor characterizing the $(p,\gamma)$ reaction is usually reduced to the electric dipole transition $E1$ from the scattering state to the bound state. In this work, the partial scattering and the single-particle bound wave functions in the reduced matrix element of the transition are obtained from the single self-consistent mean-field potential deduced from the Skyrme Hartree-Fock calculation. The astrophysical $\mathcal{S}$ factors of the $(p,\gamma)$ reactions in the CNO cycle were successfully reproduced. The self-consistent Hartree-Fock calculation from the discrete to the continuum is a promising approach for the microscopic analysis of the nucleon-induced reactions in nuclear astrophysics.