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The perturbation formulas of the electron paramagnetic resonance (EPR) parameters g(parallel to), g(perpendicular to), A(parallel to) and A(perpendicular to) for a 4f(3)(Nd3+) ion in tetragonal symmetry are established in this work. In these formulas, the contributions to the EPR parameters arising from the second-order perturbation terms and the admixtures of different states are included. Then the above formulas are applied to a tetragonal Nd3+ center in LiYF4, where the related crystal-field parameters are calculated from the superposition model and the local structural parameters of the Y3+ Site occupied by the impurity Nd3+. The EPR parameters and the optical spectra within the I-4(9/2) and I-4(1/2) states obtained in this work agree reasonably with the observed values.

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