By using temperature-and-density dependent atomic models, a method for uncertainty of electron EOS of plasmas is described via 35 functional exchange-correlation potentials. A fast method for roughly evaluating uncertainty is designed, and checked in Thomas-Fermi model. Taking gold as an example, calculations of uncertainties of total inner energy, electron pressure and ionization degree, with their ‘quasi true value’, are carried out in the range of temperatures from 1.0 to 10 000.0 eV with three densities 1.0, 10.0, 100.0 g·cm^-3,respectively. The results can be applied in engineering design.

Main cause for uncertainty of atomic structure theory is indicated. A method for uncertainty of temperature-and-density-dependent atomic models in radiative opacity calculation is described via various functional exchange potentials. Uncertainty quantification(UQ) calculation of atomic structures in density-functional at arbitrary temperature and density is carried out by definition of algorithms of modulus. Several procedures indispensable for uncertainty study, and formulae about UQ of electron energy levels and of matrix elements are given. A criterion is proposed to estimate atomic models quantificationally. Feasibility of UQ method is verified by of data of mercury, gold and iron compared with data from‘quasi true’atomic model.

Based on fully relativistic HFS self-consistent field AA model, the emerging probabilities of ionic types are determined in analytic formula using the principle of the maximum entropy, and the ionic structures are obtained in peturbation way. All the contributions from over millions of ionic types are taken into account in statistical method according to convolution principle. Finally the formula of extinction coefficient for bound free transition in hot matter with the statistical effects is given, and some results for iron are discussed.

This paper is based on the relativistic self-consistent ion-sphere model. The densi-ty and the continuum wave function are determined consistently with the model. The free-free Gaunt factor is calculated by using partial wave phase-shift method, and the results are compared with the predictions of the Born-Elwert approximation.

Schrödinger wave equation is solved for arbitrary matter density and temperature in the Hartree-Fock-Slater (HFS) self-consistent field method. In order to describe relativistic effects, the mass-velocity, the Darwin and spin-orbit coupling terms are included in the wave equation. Some of our results are compared with experimental data and with other theoretical model, the present results are consistent with experiment better and are close to that of Reference.

Schrodinger wave equation is solved in TF Statistical potential including modification of electronic self-interaction for arbitrary temperature and matter density. In order to deal with relativistic effects on atom, relativistic mass-velocity correction, relativistic Darwin correction and spin-orbit coupling correction are introduced into the wave equation. Calculations are presented for Fe, Rb at a few temperature and various densities and comparison with more accurate one's is made in tables. The datas obtained by present method show our results may be compared even with one of relativistic HFS model.