# Theoretical exploration of $S$-factors for nuclear reactions of astrophysical importance

## TL;DR

This paper develops an analytical nuclear reaction model to accurately predict astrophysical S-factors for fusion reactions involving various isotopes near the Coulomb barrier, aiding understanding of stellar nucleosynthesis.

## Contribution

It introduces a formalism based on tunneling through combined nuclear, Coulomb, and centrifugal barriers to predict S-factors, including suppression at sub-barrier energies, for the first time.

## Key findings

- Accurately predicts S-factor suppression at sub-barrier energies.
- Calculates fusion cross sections for isotopes of C, O, Ne, Mg, Si.
- Provides reaction rates relevant to stellar nucleosynthesis and neutron star crusts.

## Abstract

We present here a robust analytical model based on nuclear reaction theory for non-resonant fusion cross sections near Coulomb barrier. The astrophysical $S$-factors involving stable and neutron rich isotopes of C, O, Ne, Mg and Si for fusion reactions have been calculated in the centre of mass energy range of 2-30 MeV. The model is based on the tunneling through barrier arising out of nuclear, Coulomb and centrifugal potentials. Our formalism predicts precisely the suppression of $S$-factor at sub-barrier energies which are of astrophysical interest. The cross sections can be convoluted with Maxwell-Boltzmann distribution of energies to obtain thermo- or pycno- nuclear reaction rates relevant to nucleosynthesis at high density environments and stellar burning at high temperatures as well as for $^{34}$Ne $+$ $^{34}$Ne fusion occurring in the inner crust of accreting neutron stars.