| Study of the optical spectra and the electron paramagnetic resonance(EPR) spectrum is an important method to study substance property. It also plays a key role in dealing with the problems such as the micro interaction of inner structure and local structure of transitional metal ions in some host crystals (for example,substitution, local symmetry, bond-length, bond-angle and vacancy……). 3d2(V3+) and 3d8(Ni2+) ions are relatively active transitional metal ions, and play a key role in the study of the optical spectra. The study of optical and paramagnetic properties of crystal by doped transitional metal ions such as 3d2(V3+)and 3d8(Ni2+) can obviously provid new optical materials with theoretical evidence and experimental conduct.Crystal field theory is an available method in dealing with the problems of the energy levels of transitional metal ions in crystals. There are two ordinary methods developed by Slater and Racah, respectively, where the physical picture of the Slater method is clearer relatively, but its calculation process is more complex. The Racah irreducible tensor operator method is very simple in calculation process,but its physical picture is not as clear as Slater method. This method has already been broadly applied in the theory of free ions (or atoms) spectrum and crystal field theory sufficiently.In the cubic crystal field, the d-orbit splits into e-orbit and t2-orbit which are distinct from each other on the covalency. The difference between the 2 kinds of orbital was neglected in the classical crystal-field theory that is a good approach at dealing with transition-metal (TM) impurity in ionic crystal. Because there is strong covalence inⅡ-VI compounds, i.e., large electronic overlap between ligands and TM impurity, the different covalence between the t2-orbital and the e-orbital must be considered.In this thesis, based on analysis of precedent works, adopting the Tanabe-Sugano strong-field scheme, the influence of the different covalency to the inner Coulomb electron-electron repulsion(Racah)and the spin-orbi(tSO)coupling of 3d2 ions, and the outer crystal-field (CF)is discussed in detail, and a full Hamiltonian matrix for 3d2 ions within different covalent reduction factors Ne and Nt is deduced including the Coulomb electron-electron repulsion, the spin-orbit coupling, and the crystal-field interaction. In classical crystal field theory dealing with transitional metal ions , there are four parameters B,C (Racah), Dq(CF)andζd(SO )used to fit the optical spectra data generally. In this thesis, using a molecular-orbital approach, the Racah parameters are changed into a,b,c,d,e,f,g,h,i, and j,the crystal-field parameter is changed into Dq1 and Dq 2and the spin-orbit coupling parameter is changed intoζd1andζd2.Using the present full Hamiltonian matrices for 3d2 ions and the complete diagonalizing procedure (CDP), absorption specta of V3+ ions in GaP crystal with Td symmetry have been calculated, and the results agree well with the experimental data. And this thesis gets following conclusions: (1) for the difference between e-orbital and t2-orbital, the contributions of the Racah parameter A to the spectra can not be neglected; (2) the influence of the covalent factors Ne and Nt is existed on both the spin-orbital coupling, the electron-electron repulsion, and the crystal-field parameter, and a small change of these factors greatly influences the calculating spectra result in GaP:V3+ crystal with Td symmetry.
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