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 quasi-classic approximations widely used in the literature, such as factoring out the tunnelling process, tunnelling 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 Γ ∼ 100 is found. For a very strongly coupled liquid 100 ≲ Γ ≤ 175, a deviation from currently used parametrizations 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 crystallized phases of stellar matter.

Metals, the plasma of the poor man?

The electron screening effect in the d(d,p)t reaction has been studied for deuterated metals, insulators, and semiconductors, i.e. 58 samples in total. As compared to measurements performed with a gaseous D2 target, a large effect has been observed in most metals, while a small (gaseous) effect is found e.g. for the insulators, semiconductors, and lanthanides. The periodic table provides the ordering of the observed small and large effects in the samples. An explanation of the large effects in metals is possibly provided by the classical plasma screening of Debye applied to the quasi-free metallic electrons. The data also provide information on the solubility of hydrogen in the samples.

Ionization potential depression and ionization balance in dense carbon plasma under solar and stellar interior conditions

Recent quantitative experiments on the ionization potential depression (IPD) in dense plasma show that the observational results are difficult to explain with the widely used analytical models for plasma screening. Here, we investigate the effect of plasma screening on the IPD and ionization balance of dense carbon plasma under solar and stellar interior conditions using our developed consistent nonanalytical model. The screening potential can be primarily attributed to the free electrons in the plasma and is determined by the microspace distribution of these free electrons. The ionization balance is determined by solving the Saha equation, including the effect of IPD. The predicted IPD and average ionization degree are larger than those obtained using the Stewart–Pyatt model for mass densities that are greater than 3.0 g cm−3. Under solar interior conditions, our results are in better agreement with the Ecker–Kröll model at electron temperatures and densities lower than 250 eV and 2.1 × 1023 cm−3 and in the best agreement with the ion-sphere model at 303 eV and 4.3 × 1023 cm−3. Finally, our results are compared with those obtained via a recent experiment on a CH-mixture plasma that has been compressed six times. The predicted average ionization degree of C in a CH mixture agrees better with the experiment than the Stewart–Pyatt and Thomas–Fermi models when the screening from free electrons contributed by hydrogen atoms is included. Our results provide useful information concerning the ionization balance and can be applied to investigate the opacity and equations of state for dense plasma under the solar and stellar interior conditions.