应用不可约张量方法和群的理论构造了三角对称晶场中考虑自旋－轨道相互作用，自旋－自旋相互作用和自旋－其它轨道相互作用的3d³／3d⁷态离子的可完全对角化的120阶微扰哈密顿矩阵．利用该矩阵计算了绿宝石晶体的基态能级、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－自旋相互作用、自旋－其它轨道相互作用和自旋－轨道相互作用对绿宝石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－其它轨道相互作用对绿宝石晶体基态能级和零场分裂参量的影响都是不可忽略的．从而通过理论计算值和实验值的比较，证实了在绿宝石晶体中Jahn－Teller效应的存在，它能够对光谱精细结构的分裂提出一些更加合理的解释．

The complete diagonalized Hamiltonian matrixes of order 120 of 3d³ /3d⁷ ions configuration in the trigonal symmetry have been established by irreducible representation method and group theory,taking spin-orbit interaction,spin-spin interaction and spin-other-orbit interaction into account. Ground-state energy levels and zero-field splitting parameter were calculated by the matrixes,and the effects of spin doublets on the ground-state energy levels were studied. The calculated values were conformed with the experimental values. The results show that the contributions of doublets cannot be omitted. 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 emerald crystal were studied further. It was found that the effects of spin-spin interaction and spin-other-orbit interaction on the ground-state energy levels and the zero-field splitting parameter cannot be omitted. By comparing the values of theoretical calculation with the experimental values,the existence of Jahn-Teller effects in emerald crystal is confirmed and this can give more reasonable explain on the splitting of fine structures of spectra.