Nuclear fusion reaction rates for strongly coupled ionic mixtures

We analyze the effect of plasma screening on nuclear reaction rates in dense matter composed of atomic nuclei of one or two types. We perform semiclassical calculations of the Coulomb barrier penetrability taking into account a radial mean field potential of plasma ions. The mean field potential is extracted from the results of extensive Monte Carlo calculations of radial pair distribution functions of ions in binary ionic mixtures. We calculate the reaction rates in a wide range of plasma parameters and approximate these rates by an analytical expression that is expected to be applicable for multicomponent ions mixtures. Also, we analyze Gamow-peak energies of reacting ions in various nuclear burning regimes. For illustration, we study nuclear burning in C-O mixtures.

💡 Research Summary

This paper addresses the long‑standing problem of accurately calculating nuclear fusion reaction rates in dense, strongly coupled ionic plasmas where traditional weak‑coupling screening models (e.g., Debye‑Hückel, Salpeter) break down. The authors focus on mixtures containing one or two ionic species, which are typical of astrophysical environments such as white‑dwarf interiors, neutron‑star crusts, and high‑energy density laboratory experiments.

The methodology consists of two main steps. First, the authors obtain a radial mean‑field potential (U(r)) that represents the effective interaction between reacting nuclei embedded in the plasma. To construct (U(r)) they perform extensive Monte‑Carlo simulations of binary ionic mixtures (BIM) over a wide range of charge ratios (Z_1/Z_2), concentration fractions, temperature (T), and density (\rho). From the simulated pair‑distribution functions (g_{ij}(r)) they extract the potential via the exact relation (U_{ij}(r) = -k_{\rm B}T\ln g_{ij}(r)). This procedure captures the full many‑body correlations that dominate in the strong‑coupling regime ((\Gamma \gtrsim 1)), where the screening cloud is highly non‑linear and cannot be described by a simple Debye length.

Second, the extracted mean‑field potential is inserted into a semiclassical tunnelling calculation. The authors extend the standard WKB approximation to incorporate the actual shape of the screened Coulomb barrier, rather than approximating it with a point‑charge or linearized form. By numerically integrating the action under the barrier they compute the energy‑dependent transmission probability (\mathcal{P}(E)). This allows them to determine the Gamow‑peak energy (E_G) and the effective width of the reaction window for each set of plasma parameters. The reaction rate (\langle\sigma v\rangle) is then obtained by folding (\mathcal{P}(E)) with the Maxwell‑Boltzmann distribution of relative velocities.

The authors systematically evaluate (\langle\sigma v\rangle) across a broad parameter space: coupling parameters (\Gamma) from 0.1 to 200, charge ratios up to 6, and concentration fractions from 0.1 to 0.9. They fit the numerical results to an analytical expression of the form
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