Enhancement of Nuclear Reaction Rates in Dense Stellar Matter: A Path‐Integral Monte Carlo Simulation Study

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Abstract
The rate of nuclear reactions, which is proportional to the tunnel-contact probabilities of a reacting pair of nuclei, is enhanced significantly in dense stellar matter by the many-body correlations of the surrounding nuclei. Path-integral Monte Carlo (PIMC) calculations for the contact probabilities of a tunneling pair in a dense Coulomb liquid of nuclei, an accurate model for the matter in the interiors and surfaces of white dwarfs and neutron stars, are performed to investigate quantum effects of the surrounding nuclei. We thereby show that the probabilities are enhanced significantly by the wave-mechanical spreading of the surrounding nuclei. The mechanisms for such enhancement are investigated. By performing separate PIMC runs in which the exchange of Bose nuclei is explicitly taken into account, we find that the exchange processes alter the probabilities by negligible amounts at conditions of astrophysical interest. The present results for the enhancement factors of the nuclear reaction rates are applied directly to calculations of the carbon ignition curve in a white dwarf.