We analyze enhancement of thermonuclear fusion reactions due to strong plasma screening in dense matter using a simple electron drop model. The model assumes fusion in a potential that is screened by an effective electron cloud around colliding nucle
i (extended Salpeter ion-sphere model). We calculate the mean field screened Coulomb potentials for atomic nuclei with equal and nonequal charges, appropriate astrophysical S factors, and enhancement factors of reaction rates. As a byproduct, we study analytic behavior of the screening potential at small separations between the reactants. In this model, astrophysical S factors depend not only on nuclear physics but on plasma screening as well. The enhancement factors are in good agreement with calculations by other methods. This allows us to formulate the combined, pure analytic model of strong plasma screening in thermonuclear reactions. The results can be useful for simulating nuclear burning in white dwarfs and neutron stars.
We analyze diffusion equations in strongly coupled Coulomb mixtures of ions in dense stellar matter. Strong coupling of ions in the presence of gravitational forces and electric fields (induced by plasma polarization in the presence of gravity) produ
ces a specific diffusion current which can separate ions with the same A/Z (mass to charge number) ratios but different Z. This Coulomb separation of ions can be important for the evolution of white dwarfs and neutron stars.
We review the history of neutron star physics in the 1930s that is related to L. Landau. According to recollections of Rosenfeld (1974, Proc. 16th Solvay Conference on Physics, p. 174), Landau improvised the concept of neutron stars in a discussion w
ith Bohr and Rosenfeld just after the news of the discovery of the neutron reached Copenhagen in February 1932. We present arguments that the discussion took place in March 1931, before the discovery of the neutron, and that they in fact discussed the paper written by Landau in Zurich in February 1931 but not published until February 1932 (Phys. Z. Sowjetunion, 1, 285). In his paper Landau mentioned the possible existence of dense stars which look like one giant nucleus; this can be regarded as an early theoretical prediction or anticipation of neutron stars, prior to the discovery of the neutron. The coincidence of the dates of the neutrons discovery and the papers publication has led to an erroneous association of the paper with the discovery of the neutron. In passing, we outline the contribution of Landau to the theory of white dwarfs and to the hypothesis of stars with neutron cores.
Numerous nuclear reactions in the crust of accreting neutron stars are strongly affected by dense plasma environment. Simulations of superbursts, deep crustal heating and other nuclear burning phenomena in neutron stars require astrophysical S-factor
s for these reactions (as a function of center-of-mass energy E of colliding nuclei). A large database of S-factors is created for about 5000 non-resonant fusion reactions involving stable and unstable isotopes of Be, B, C, N, O, F, Ne, Na, Mg, and Si. It extends the previous database of about 1000 reactions involving isotopes of C, O, Ne, and Mg. The calculations are performed using the Sao Paulo potential and the barrier penetration formalism. All calculated S-data are parameterized by an analytic model for S(E) proposed before [Phys. Rev. C 82, 044609 (2010)] and further elaborated here. For a given reaction, the present S(E)-model contains three parameters. These parameters are easily interpolated along reactions involving isotopes of the same elements with only seven input parameters, giving an ultracompact, accurate, simple, and uniform database. The S(E) approximation can also be used to estimate theoretical uncertainties of S(E) and nuclear reaction rates in dense matter, as illustrated for the case of the 34Ne+34Ne reaction in the inner crust of an accreting neutron star.
We propose a physically transparent analytic model of astrophysical S-factors as a function of a center-of-mass energy E of colliding nuclei (below and above the Coulomb barrier) for non-resonant fusion reactions. For any given reaction, the S(E)-mod
el contains four parameters [two of which approximate the barrier potential, U(r)]. They are easily interpolated along many reactions involving isotopes of the same elements; they give accurate practical expressions for S(E) with only several input parameters for many reactions. The model reproduces the suppression of S(E) at low energies (of astrophysical importance) due to the shape of the low-r wing of U(r). The model can be used to reconstruct U(r) from computed or measured S(E). For illustration, we parameterize our recent calculations of S(E) (using the Sao Paulo potential and the barrier penetration formalism) for 946 reactions involving stable and unstable isotopes of C, O, Ne, and Mg (with 9 parameters for all reactions involving many isotopes of the same elements, e.g., C+O). In addition, we analyze astrophysically important 12C+12C reaction, compare theoretical models with experimental data, and discuss the problem of interpolating reliably known S(E) values to low energies (E <= 2-3 MeV).
Using the Sao Paulo potential and the barrier penetration formalism we have calculated the astrophysical factor S(E) for 946 fusion reactions involving stable and neutron-rich isotopes of C, O, Ne, and Mg for center-of-mass energies E varying from 2
MeV to 18-30 MeV (covering the range below and above the Coulomb barrier). We have parameterized the energy dependence S(E) by an accurate universal 9-parameter analytic expression and present tables of fit parameters for all the reactions. We also discuss the reduced 3-parameter version of our fit which is highly accurate at energies below the Coulomb barrier, and outline the procedure for calculating the reaction rates. The results can be easily converted to thermonuclear or pycnonuclear reaction rates to simulate various nuclear burning phenomena, in particular, stellar burning at high temperatures and nucleosynthesis in high density environments.
We calculate the shear viscosity $eta = eta_{emu}+eta_{n}$ in a neutron star core composed of nucleons, electrons and muons ($eta_{emu}$ being the electron-muon viscosity, mediated by collisions of electrons and muons with charged particles, and $eta
_{n}$ the neutron viscosity, mediated by neutron-neutron and neutron-proton collisions). Deriving $eta_{emu}$, we take into account the Landau damping in collisions of electrons and muons with charged particles via the exchange of transverse plasmons. It lowers $eta_{emu}$ and leads to the non-standard temperature behavior $eta_{emu}propto T^{-5/3}$. The viscosity $eta_{n}$ is calculated taking into account that in-medium effects modify nucleon effective masses in dense matter. Both viscosities, $eta_{emu}$ and $eta_{n}$, can be important, and both are calculated including the effects of proton superfluidity. They are presented in the form valid for any equation of state of nucleon dense matter. We analyze the density and temperature dependence of $eta$ for different equations of state in neutron star cores, and compare $eta$ with the bulk viscosity in the core and with the shear viscosity in the crust.
We calculate the thermal conductivity of electrons and muons kappa_{e-mu} produced owing to electromagnetic interactions of charged particles in neutron star cores and show that these interactions are dominated by the exchange of transverse plasmons
(via the Landau damping of these plasmons in nonsuperconducting matter and via a specific plasma screening in the presence of proton superconductivity). For normal protons, the Landau damping strongly reduces kappa_{e-mu} and makes it temperature independent. Proton superconductivity suppresses the reduction and restores the Fermi-liquid behavior kappa_{e-mu} ~ 1/T. Comparing with the thermal conductivity of neutrons kappa_n, we obtain kappa_{e-mu}> kappa_n for T>2 GK in normal matter and for any T in superconducting matter with proton critical temperatures T_c>3e9 K. The results are described by simple analytic formulae.
