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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.

Enhancement factors for the thermonuclear reaction rates in dense binary-ionic mixtures (BIMs) with charge ratio R Z ≤5 are calculated through detailed examination of the screening potentials at short ranges obtained by the Monte Carlo simulation method. Small but nonnegligible deviations of the screening distances from the constant electron-density, ion-sphere scaling are discovered at R Z ∼5 for the lighter elements; the deviations act further to enhance the reaction rates. The triple-α reactions in He-C mixtures are treated as an example

Through a combination of compositional scaling arguments and examinations of Monte Carlo simulation results for the interparticle separations in binary-ionic mixture (BIM) solids, we have derived parameterized expressions for the BIM pycnonuclear rates as generalizations of those in one-component solids obtained previously by Salpeter and Van Horn and by Ogata et al. We have thereby discovered a catalyzing effect of the heavier elements, which enhances the rates of reactions among the lighter elements when the charge ratio exceeds a critical value of approximately 2.3.

Shear moduli are calculated for bcc crystalline and rapidly quenched Coulomb solids produced by the Monte Carlo simulation method. The shear moduli are calculated up to the transition temperature and include the effects of thermal fluctuations. An effective shear modulus appropriate to an approximate 'isotropic' body is introduced. It is found that the values of the 'average shear modulus' for the quenched solids remain about the same as those for the corresponding bcc crystals, although the individual shear moduli of the former, disordered solids deviate considerably from the cubic symmetry of the latter. These results are applied to analyses of neutron star oscillations. It is found that the periods of the two interfacial modes are increased by about 10 percent compared to previous results, and that s-mode periods are increased by about 30 percent. The periods of the f and p modes are hardly affected at all. The surface g-mode periods are not greatly affected, while the t-mode periods are increased by 20-25 percent.

Relativistic degenerate electrons have a considerable screening effect on Coulomb repulsion between reacting nuclei even in the limit of high densities. The enhancement factor of the thermonuclear reaction rate resulting from such an electron screening is recalculated. It is shown that the enhancement is significant in high-Z materials such as carbon and oxygen at the densities near ignition. 13 refs.

New, first principles calculations of nuclear reaction rates in dense carbon-oxygen mixtures appropriate to Type I supernova progenitors are presented for both fluid and bcc crystalline-solid phases, based on accurate Monte Carlo evaluations of the screening potentials and a correct treatment of the quantum-statistical effects. A blocking effect of oxygen is discovered in the pycnonuclear reaction of carbon. The results are compared with the existing theories in the limit of one-component plasma cases, both for the screening potentials and for the reaction rates. Examples of the carbon ignition curve are shown. 25 refs.

The electric and thermal conductivities in the outer crustal matter of a neutron star quenched into a solid state by cooling are estimated using a Monte Carlo simulation of freezing transition for dense plasmas. The conductivities are calculated by the precise evaluation of the scattering integrals, using the procedure of Ichimaru et al. (1983) and Iyetomi and Ichimaru (1983). The results predict the conductivities lower, by a factor of about 3, than those with the single-phonon approximation.

An accurate calculation is presented of the the phase diagram associated with the solidification transitions in dense carbon-oxygen mixtures appropriate to the interiors of white dwarfs, resulting in a novel prediction of an azeotropic diagram. It is concluded that chemical separations would not take place thermodynamically through such solidification processes. 20 references.