应用不可约张量法和群的理论构造了三角对称晶场中3d3/3d7态离子的可完全对角化的120阶微扰哈密顿矩阵。矩阵中考虑了自旋轨道相互作用,自旋自旋相互作用和自旋其他轨道相互作用,利用该矩阵计算了YAG∶Cr3+晶体的基态能级、零场分裂参量,研究了自旋二重态对基态能级的贡献,理论计算值与实验值相符合,证明二重态对基态的贡献是不可忽略的。在此基础上,进一步研究了自旋轨道相互作用、自旋自旋相互作用和自旋其他轨道相互作用对YAG∶Cr3+晶体的光谱精细结构和零场分裂参量的影响,发现自旋自旋和自旋其他轨道相互作用对YAG晶体基态光谱精细结构和零场分裂参量的影响都是不可忽略的。通过理论计算值和实验值的比较,证实了在YAG∶Cr3+晶体光谱中扬特勒效应的存在。

The completely diagonalized Hamiltonian matrixes of 120 orders of 3d3/3d7 ions configuration in the trigonal symmetry were established by irreducible representation method and group theory, taking into account spin-orbit interaction, spin-spin interaction and spin-other-orbit interaction. The ground-state energy levels, the zero-field splitting parameter were calculated with the matrixes. The contributions of spin doublets for the ground-state energy levels were studied. The values of theoretical calculation were consistent with the experimental ones. The results showed that the contributions of doublets could not be neglected. On these bases, the effects of spin-spin interaction and spin-other-orbit interaction on the fine structures of spectra and zero-field splitting parameter of YAG∶Cr3+ crystal were further studied, and we found that the influence of spin-spin interaction and spin-other-orbit interaction on the fine structures of spectra and the zero-field splitting parameter could not be neglected. By comparing the values of theoretical calculation with the experiments, the existence of Jahn-Teller effect in the YAG:Cr3+ crystal spectra was confirmed.