Plasma screening of nuclear fusion reactions in liquid layers of compact degenerate stars: a first-principle study

Abstract

A reliable description of nuclear fusion reactions in inner layers of white dwarfs and envelopes of neutron stars is important for realistic modelling of a wide range of observable astrophysical phenomena from accreting neutron stars to type Ia supernovae. We study the problem of screening of the Coulomb barrier impeding the reactions, by a plasma surrounding the fusing nuclei. Numerical calculations of the screening factor are performed from the first principles with the aid of quantum-mechanical path integrals in the model of a one-component plasma of atomic nuclei for temperatures and densities typical for dense liquid layers of compact degenerate stars. We do not rely on various quasiclassic approximations widely used in the literature, such as factoring-out the tunneling process, tunneling in an average spherically symmetric mean-force potential, usage of classic free energies and pair correlation functions, linear mixing rule and so on. In general, a good agreement with earlier results from the thermonuclear limit to $\Gamma \sim 100$ is found. For a very strongly coupled liquid $100\lesssim \Gamma \le 175$, a deviation from currently used parametrisations of the reaction rates is discovered and approximated by a simple analytic expression. The developed method of nuclear reaction rate calculations with account of plasma screening can be extended to ion mixtures and crystallised phases of stellar matter.

arXiv comment8 pages, 6 figures, accepted to MNRAS

References in corpus (12)

• Coulomb tunneling for fusion reactions in dense matter: Path integral Monte Carlo versus mean field
• Double white dwarf mergers and elemental surface abundances in extreme helium and R Coronae Borealis stars
• Supernovae Ia in 2019 (review): a rising demand for spherical explosions
• Nuclear Reaction Rates in a Plasma
• Type Ia Supernova Sub-classes and Progenitor Origin
• Nuclear fusion reaction rates for strongly coupled ionic mixtures
• Deep crustal heating for realistic compositions of thermonuclear ashes
• Electron screening effect on stellar thermonuclear fusion
• Quantum ion thermodynamics in liquid interiors of white dwarfs
• Energy of Quantum Coulomb Liquid
• Corrections to linear mixing in binary ionic mixtures and plasma screening at zero separation
• Nuclear fusion in a dense plasma

Cited by in corpus (2)

• $Abinitio$ thermodynamics of one-component plasma for astrophysics of white dwarfs and neutron stars
• Phase diagrams of binary ionic mixtures and white dwarf cooling