“…Full expressions for the terms E z , E c and E ex written in Refs. [2,4,18] including next integrals: ðm 1 9m 2 u Þ -the two electrons two-centers penetrating integral of the wave functions of nl ion and n 0 l 0 ligand; ðm 1 9r À1 Z 2 9m 2 u Þ -one electron two-centers matrix elements of operator describing the interaction of the electron with the strange nucleus, ðm 1 m 2 9r 12 À1 9mu 1 mu 2 Þ-two electrons two-centers matrix element of the Coulomb or exchange interaction. Using Eq.…”
Section: Methods Of the Self-consistent Field For Clustersmentioning
confidence: 98%
“…The theoretical values are compared to experimental ones for optical and X-ray spectra of ME ions in free state and in wide band gap crystals, too [2,4,[18][19][20].…”
Section: Methods Of the Self-consistent Field For Clustersmentioning
confidence: 99%
“…Using the one-electron approximation for the wave functions of the central field approximation, the energy of the cluster may be written as [3,18] EðME n þ :…”
Section: Methods Of the Self-consistent Field For Clustersmentioning
“…Full expressions for the terms E z , E c and E ex written in Refs. [2,4,18] including next integrals: ðm 1 9m 2 u Þ -the two electrons two-centers penetrating integral of the wave functions of nl ion and n 0 l 0 ligand; ðm 1 9r À1 Z 2 9m 2 u Þ -one electron two-centers matrix elements of operator describing the interaction of the electron with the strange nucleus, ðm 1 m 2 9r 12 À1 9mu 1 mu 2 Þ-two electrons two-centers matrix element of the Coulomb or exchange interaction. Using Eq.…”
Section: Methods Of the Self-consistent Field For Clustersmentioning
confidence: 98%
“…The theoretical values are compared to experimental ones for optical and X-ray spectra of ME ions in free state and in wide band gap crystals, too [2,4,[18][19][20].…”
Section: Methods Of the Self-consistent Field For Clustersmentioning
confidence: 99%
“…Using the one-electron approximation for the wave functions of the central field approximation, the energy of the cluster may be written as [3,18] EðME n þ :…”
Section: Methods Of the Self-consistent Field For Clustersmentioning
“…As a result fluorescence X ray radiation of ions is excited in the sample decomposed by a crystal-analyzer (3) and registered by a counter (4). X ray intensity is determined for a reference and examined samples for each step of the crystal-analyzer [18,24]. As an example, the experimental profiles of TiK 1 XRL are given on Figure 10.…”
Section: Oxidation State Of the Ionsmentioning
confidence: 99%
“…More than 20% of Ti +4 ions change valence to Ti +3 state (electronic configuration 3d 1 ) that was observed in non-stoichiometric Sr x Ti y O z and Ti x O y single crystals [17,18].…”
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