Energy levels, luminescence and electronic structure of ZnS:Tm³⁺

Energy levels, densities of states, electronic densities, electrostatic interaction integral parameters F_k and spin-orbit coupling parameters ζ_4f for ZnS: Tm³⁺ are calculated self-consistently, using both one-electron local density discrete variational non-relativistic Hartree-Fock-Slater (HFS) and relativistic Dirac-Slater (DS) cluster models. In these calculations, both spin-restricted and spin-polarized models are considered. The finite clusters calculated include TmS₄ and TmS₄Zn₁₂ clusters for cubic ZnS, which are embedded in the crystal environment. The spin-orbit coupling parameter ζ_4f derived from DS cluster calculations is equal to 2689 cm^-1, rather near the result of the relativistic Hartree-Fock free ion model. The parameters F_k and ζ_4f are further calculated from the 4f radial wave function obtained by solving the HFS and the DS atomic equations. It is shown that by decreasing the effective exchange-correlation potential, these parameters can be reduced to approximately match empirical values. A comparison of the excited energy level scheme of ZnS:Tm derived from the calculated parameters and the experimental spectra is presented.