Relativistic third-order MBPT is applied to obtain energies of ions with two valence electrons in the no virtual-pair approximation (NVPA). A total of 302 third-order Goldstone diagrams are organized into 12 one-body and 23 two-body terms. Only third-order two-body terms and diagrams are presented here, owing to the fact that the one-body terms are identical to the previously studied third-order terms in monovalent ions. Dominant classes of diagrams are identified. The model potential is a Dirac-Hartree-Fock V N−2 potential, and B-spline basis functions in a cavity of finite radius are employed in the numerical calculations. The Breit interaction is taken into account through second order of perturbation theory and the lowest-order Lamb shift is also evaluated. Sample calculations are performed for berylliumlike ions with Z = 4-7, and for the magnesiumlike ion P IV. The third-order energies are in excellent agreement with measurement with an accuracy at 0.2% level for the cases considered. Comparisons are made with previous second-order MBPT results and with other calculations. The third-order energy correction is shown to be significant, improving second-order correlation energies by an order of magnitude.
Based on the idea that different temperatures generate different carrier densities and the resulting diffusion causes the thermal emf, a new formula for the Seebeck coefficient S is obtained: [Formula: see text], where q, n, εF, [Formula: see text]. and [Formula: see text]. are respectively charge, carrier density, Fermi energy, density of states at ∊F and volume. Ohmic and Seebeck currents are fundamentally different in nature. This difference can cause significantly different transport behaviors. For a multi-carrier metal the Einstein relation between the conductivity and the diffusion coefficient does not hold in general. Seebeck (S) and Hall (RH) coefficients in noble metals have opposite signs. This is shown to arise from the Fermi surface having "necks" at the Brillouin boundary.
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