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The EPR parameters (g factors g(parallel to), g(perpendicular to) and hyperfine structure constants A(parallel to), A(perpendicular to)) of a tetragonal (C-4v) Sm3+ center in CaF2 and SrF2 crystals are calculated by considering the crystal-field J-mixing among the ground H-6(5/2), the first excited H-6(7/2) and second excited H-6(9/2) state multiplets. In the calculations the free-ion and crystal-field parameters of the tetragonal Sm3+-F- center obtained from polarized laser-selective excitation spectroscopy are used. The calculated results suggest that the tetragonal Sm3+-F- center is the Sm3+ center found by later EPR measurements. The g factors g(parallel to), g(perpendicular to) and hyperfine structure constants A(parallel to), A(perpendicular to) of this EPR center are satisfactorily explained.

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