Theoretical Model of Dense Plasmas

Abstract

AbstractIn the dawn of quantum mechanics, scientists had challenged to formulate the equation of many-electron system, such as atom and solid matter, just after the success of Schrodinger equation to explain a hydrogen atom. It is found, however, that a system of multi-electron requires the self-consistent treatment of exchange interaction stemming from Pauli exclusive principle.In 1930s, Hartree and Fock has derived the equation with use of Slater determinant. It is called Hartree-Fock (HF) equation. This is the equation for many-electron system and if we can solve it, almost exact solution is obtained. However, it was difficult to solve it analytically and numerically. Scientists proposed a variety of approximate theoretical models to solve such many-electron system.Slater has proposed screened-hydrogenic model (SHM) in 1930. Thomas and Fermi have proposed a statistical model, now called Thomas-Fermi (TF) model. These two models have been widely used, modified, extended, and applied to many purposes even now. Their physical image is very simple and useful as comprehensive understanding of the physics. The examples of applications to the equation of state (EOS) for shock compression (shock Hugoniot) are explained here. Such models can be used to single atom (ion) or statistically averaged ion, so-called average ion model (AIM).Even with the atomic data are supplied, the ionization potential depression (IPD) is essential to solve Saha equation of ionization population, especially at high-density plasma. Thanks to a rapid progress of computer capability, even HF equation can be solved numerically in some cases. It is very hard to solve, for example, the band structure of condensed matters. Kohn-Sham proposed density-functional theory (DFT) in 1960s. DFT solves one-electron Schrodinger equation for all electrons in the self-consistent potential. It is proved that the self-consistent potential is formulated as a function of only the density profile.