| The conditions in the solar interior are so extreme that it has so far been impossible to match them in a laboratory. However, for nearly 50 years solar oscillations have been precisely observed, and the wealth of their data has enabled us to study the interior of the Sun as if it were a laboratory. Helioseismology is the name of this branch of astrophysics. It allows a high-precision diagnostic of the thermodynamic quantities in the solar interior. High-quality thermodynamic quantities are crucial for successful solar modeling.;If good solar models are desired, considerable theoretical effort is required. Good solar models, in turn, are fundamental tools for solar physics. The most prominent example of this link between solar physics and basic physics was the resolution of the solar neutrino problem in 2002. The equation of state is a key material property that describes the relation between pressure, density and temperature. If the equation of state is derived from a thermodynamic potential it will also determine all associated thermodynamic quantities. A second key material property is the nuclear-energy production rate, which plays a crucial role in the solar core. Both are important physical properties describing the structure of the Sun. Both derive from microphysical models.;In the equation-of-state part, we have studied two models of the equation of state (EOS). One is the MHD EOS, which is widely used in solar models. In our research, we have incorporated new terms into the MHD EOS. These terms have been borrowed from the major competing formalism, the OPAL EOS. They were missing in the original MHD EOS. Not only do the upgrades bring MHD closer to the OPAL equation of state, which is well known for its better match with observations. Most importantly it will allow solar modelers to use the OPAL equation of state directly, without recourse to the OPAL tables distributed by the Lawrence Livermore National Laboratory. Since the OPAL code is not publicly available, there is no alternative source. The official OPAL tables, however, have disadvantages. First, they are inflexible regarding the chemical mix, which is set once and for all by the producers of the tables. Our equation of state will allow the user to choose, in principle, an arbitrary mix. Second, the OPAL tables by their very nature are limited by the errors of interpolation within tables. The second equation of state model is a density expansion based on the Feynman-Kac path-integral formalism. By making use of the equivalence of quantum Hamiltonian matrix and the classical action of closed and open filaments (paths), an analytic formalism of equation of state. Although the character of density expansion limits its application, the formalism can still be valid in most region in the Sun. Our work provides the link between the abstract theoretical formalism that was developed in the 1990s and a numerically smooth realization that can be used in solar and stellar models. Since it is so far the most exact and systematic approach for an EOS, it provides another way to study the influence of different very fine physical effects, despite considerable limitations in its domain of applicability.;In the nuclear-reaction part of the thesis, we have used a molecular-dynamics method to simulate the motion of protons in a hydrogen plasma (which is a good approximation for this purpose). Quantum tunneling explains why nuclear fusion can occur in the first place, considering the “low” temperature in the solar core. It is well known that this tunneling is enhanced (which leads to higher nuclear reaction rates) in the presence of Coulomb screening. In the 1950, Salpeter formulated a theory based on the static-screened Coulomb potential, as derived by Debye and Hückel in the 1920s. As expected, Salpeter obtained enhanced reaction rates. But from our simulation, we confirmed the results of a recent controversy about the existence of a dynamic effect. Since the bulk of fusion reactions happens at the high end of the Maxwell distribution, this is an relevant issue. Our work is the first independent confirmation of such a dynamic effect. |
