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A unified theoretical method is established to determine the charge-compensated C3v (II) centers of Er3+ ions in CdF2 and CaF2 crystals by simulating the electron paramagnetic resonance (EPR) parameters and Stark energy levels. The potential (Er3+–F−–) and (Er3+– –O2–) structures for the C3v (II) centers of Er3+ ions in CdF2 and CaF2 crystals are checked by diagonalizing 364 × 364 complete energy matrices in the scheme of superposition model. Our studies indicate that the C3v (II) centers of Er3+ ions in CdF2 and CaF2 may be ascribed to the local (Er3+–F−–) structure, where the upper ligand ion F− undergoes an off-center displacement by ΔZ ≈ 0.3 Ĺ for CdF2 and ΔZ ≈ 0.29 Ĺ for the CaF2 along the C3 axis. Meanwhile, a local compressed distortion of the cluster is expected to be ΔR ≈ 0.07 Ĺ for CdF2:Er3+ and ΔR ≈ 0.079 Ĺ for CaF2:Er3+. The considerable g-factor anisotropy for Er3+ ions in each of both crystals is explained reasonably by the obtained local parameters. Furthermore, our studies show that a stronger covalent effect exists in the C3v (II) center for Er3+ in CaF2 or CaF2, which may be due to the stronger electrostatic interaction and closer distance between the central Er3+ ion and ligand O2– with the (Er3+–F−–) structure. [ABSTRACT FROM AUTHOR]

This paper systematically investigates the local distortion and electron paramagnetic resonance (EPR) parameter for CdCl2:V2+ and CdCl2:V2+ systems on the basis of the complete energy matrix, in which not only the contributions due to the spin-orbit coupling of the central ions but also that of the ligands are considered. To describe the difference of overlapping between d-orbits and p orbit, two spin-orbit coupling coefficients are introduced. By simulating the crystal field parameter and EPR parameter, the local distortion parameters are studied and the relationships between the EPR parameter and the spin-orbit coupling coefficients as well as divergent parameter are discussed. These results show that the local structures exhibit compression distortion for CdCl2:V2+ and elongation distortions for CdCl2:V2+, respectively. It notes that the empirical formula R ≈ RH + (ri-rh)=2 is not suitable for CdCl2:V2+ and CdCl2:V2+ systems. The contributions of ligand to spin-orbit coupling interaction cannot be neglected for strong covalent systems, especially for V2+ doped in CsMgBr3:V2+. [ABSTRACT FROM AUTHOR]

Magic wavelengths for laser trapping of barium atoms in the optical lattices are calculated with considering the optical clock transition at 1107 nm between the 6s2 1S0 state and 6s5d 3D1 state. Theoretical calculation shows that there are several magic wavelengths with the linearly polarized trapping laser. The trap depths of the optical lattice and the slope of light shift difference with different magic wavelengths are also calculated. Some of these magic wavelengths are selected and recommended as potentially suitable magic wavelengths for the optical lattice trapping laser. [ABSTRACT FROM AUTHOR]