应用晶体场理论和不可约张量算符方法构造了3d2/3d8态离子在C3v对称晶场中包含自旋-轨道相互作用、自旋-自旋相互作用、自旋-其它轨道相互作用和其它轨道-其它轨道相互作用四种微观磁效应的45阶可完全对角化的能量哈密顿矩阵.利用该矩阵，计算了Ni2+∶α-Al2O3晶体的光谱精细结构和晶体局域结构，深入研究了Ni2+∶α-Al2O3晶体的自旋-轨道相互作用、自旋-自旋相互作用、自旋-其它轨道相互作用和其它轨道-其它轨道相互作用和它们对光谱精细结构的影响及Jahn-Teller效应.理论计算值和实验值相符合.研究发现，掺杂没有改变晶体的对称性、同时发现并合理解释了Ni2+对α-Al2O3晶体基态精细光谱中Jahn-Teller效应的存在机理.

The completely diagonalized Hamiltonian matrixes of order 45 of 3d2/3d8 ion configurations in the trigonal symmetry sites were established by means of crystal field theory and irreducible representation method. The Hamiltonian matrixes include four kinds of microscopic magnetic interactions: spin-orbit interaction, spin-spin interaction, spin-other-orbit interaction and other-orbit-other-orbit interaction. The spectral fine structure and crystal local structure of Ni2+∶α-Al2O3 crystal were calculated by the Hamiltonian matrixes. Meanwhile, the four kinds of interactions and their effects to the spectral fine structure and the Jahn-Teller effect were also analyzed. The calculated values were conformed with the experimental values. The results show that doping Ni2+ ions cannot change the symmetry, and it was discovered and explained the existence mechanism of Jahn-Teller effect in spectral fine structure of α-Al2O3 doped with Ni2+.