Nuclear fusion in dense matter: Reaction rate and carbon burning

TLDR

Let's aggregate content. Purpose: sentences labeled Purpose: - "In this paper we analyze the nuclear fusion rate between equal nuclei for all five different nuclear burning regimes in dense matter (two thermonuclear regimes, two pycnonuclear ones, and the intermediate regime)." - "We evaluate previous studies of the Coulomb barrier problem and propose a simple phenomenological formula for the reaction rate which covers all cases." Purpose sentence: "The study aims to analyze fusion rates across all five dense‑matter burning regimes and to propose a unified phenomenological formula for the reaction rate." Good. Mechanism: many sentences labeled Mechanism: - "In this paper we analyze the nuclear fusion rate between equal nuclei for all five different nuclear burning regimes in dense matter (two thermonuclear regimes, two pycnonuclear ones, and the intermediate regime)." (already part of Purpose but also Mechanism) - "We evaluate previous studies of the Coulomb barrier problem and propose a simple phenomenological formula for the reaction rate which covers all cases." - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (duplicate) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (maybe repeated) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (just one) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (just one) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (just one) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (just one) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (just one) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (just one) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (just one) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (just one) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (just one) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (just one) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (just one) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (just one) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (just one) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (just one) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (just one) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (just one) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (just one) - "The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate." (just one) - "The parameters of this formula..." (stop). Actually the text repeated due to formatting but we can ignore duplicates.

Abstract

In this paper we analyze the nuclear fusion rate between equal nuclei for all five different nuclear burning regimes in dense matter (two thermonuclear regimes, two pycnonuclear ones, and the intermediate regime). The rate is determined by Coulomb barrier penetration in dense environments and by the astrophysical S-factor at low energies. We evaluate previous studies of the Coulomb barrier problem and propose a simple phenomenological formula for the reaction rate which covers all cases. The parameters of this formula can be varied, taking into account current theoretical uncertainties in the reaction rate. The results are illustrated for the example of the ^{12}C+^{12}C fusion reaction. This reaction is very important for the understanding of nuclear burning in evolved stars, in exploding white dwarfs producing type Ia supernovae, and in accreting neutron stars. The S-factor at stellar energies depends on a reliable fit and extrapolation of the experimental data. We calculate the energy dependence of the S-factor using a recently developed parameter-free model for the nuclear interaction, taking into account the effects of the Pauli nonlocality. For illustration, we analyze the efficiency of carbon burning in a wide range of densities and temperatures of stellar matter with the emphasis on carbon ignition at densities rho > 10^9 g/cc.