On exact solutions for quantum particles with spin S= 0, 1/2, 1 and de Sitter event horizon

Exact wave solutions for particles with spin 0, 1/2 and 1 in the static coordinates of the de Sitter space-time model are examined in detail. Firstly, for a scalar particle, two pairs of linearly independent solutions are specified explicitly: running and standing waves. A known algorithm for calculation of the reflection coefficient $R_{\epsilon j}$ on the background of the de Sitter space-time model is analyzed. It is shown that the determination of R_{\epsilon j} requires an additional constrain on quantum numbers \epsilon \rho / \hbar c >> j, where \rho is a curvature radius. When taken into account of this condition, the R_{\epsilon j} vanishes identically. It is claimed that the calculation of the reflection coefficient R_{\epsilon j} is not required at all because there is no barrier in an effective potential curve on the background of the de Sitter space-time. The same conclusion holds for arbitrary particles with higher spins, it is demonstrated explicitly with the help of exact solutions for electromagnetic and Dirac fields.Comment: 30 pages. This paper is an updated and more comprehensive version of the old paper V.M. Red'kov. On Particle penetrating through de Sitter horizon. Minsk (1991) 22 pages Deposited in VINITI 30.09.91, 3842 - B9

The charge state of pt in binary compounds and synthetic minerals determined by x-ray absorption spectroscopy and quantum chemical calculations

The binary synthetic compounds of Pt with chalcogens (O, S, Se, Te), pnictogens (As, Sb, Bi), and intermetallic compounds with Ga, In, and Sn of various stoichiometry were studied via X-ray absorption spectroscopy (XAS). The partial atomic charges of Pt in the compounds were computed using quantum chemical density functional theory (DFT) based methods: the Bader (QTAIM) method, and the density-derived electrostatic and chemical (DDEC6) approach. Strong positive correlations were established between the calculated partial atomic charges of Pt and the electronegativity (χ) of ligands. The partial charge of Pt in PtL2 compounds increases much sharply when the ligand electronegativity increases than the Pt partial charge in PtL compounds. The effect of the ligand-to-Pt atomic ratio on the calculated Pt partial charge depended on ligand electronegativity. The DDEC6 charge of Pt increases sharply with the growth of the number of ligands in PtSn (n = 1, 2; electronegativity χ(S) >> χ(Pt)), weakly depends on the phase composition in PtTen (n = 1, 2; χ(Te) is slightly lower than χ(Pt)), and decreases (becomes more negative) with increase of the ligand-to-Pt ratio in intermetallic compounds with electron donors (χ(L) χ(L)) was overcompensated by the gain of the hybridized s-p electron density, which was confirmed by Pt L1-edge spectra analysis. As a result, the total electron density at the Pt site followed the electronegativity rule, i.e., it increased with the growth of the number of the ligands-electron donors. The empirical correlations between the Pt partial atomic charges and parameters of XANES spectral features were used to identify the state of Pt in pyrite, and can be applied to determine the state of Pt in other ore minerals