The effect of crystal-field Hamiltonian with cubic symmetry acting upon different angular momenta J-manifolds between 2 and 8 has been investigated considering the quantization axis along body diagonal [111] axis of the cube. The eigen-values and eigen-functions are numerically computed as a function of the ratio between the fourth and sixth degree terms of the cubic Hamiltonian, expressed in terms of the two parameters, e.g., x and W, in the notation of LLW [J. Phys. Chem. Solids 23 (1962) 1381]. The analytical expressions of eigen-values are also presented for few J values. The effect of external magnetic field as a perturbation on the crystal-field level scheme is discussed toward calculations of magnetic susceptibility and axial magnetizations and compared with the LLW Hamiltonian.

考虑到沿着立方体的对角线[111]轴的量化轴，研究了立方对称的晶体场哈密顿量对2至8之间的不同角动量J流形的影响。本征值和本征函数是根据三次哈密顿量的第四和第六阶项之间的比率进行数值计算的，该比率用两个参数（例如x和W）以LLW表示[J 。物理 化学 Solids 23（1962）1381]。还给出了几个J的特征值的解析表达式价值观。为了计算磁化率和轴向磁化强度，并与LLW哈密顿量进行了比较，讨论了外部磁场作为摄动对晶体场能级的影响。