| Summary: | The 8-coordinated crystalline environment in optical materials is a common type of crystal field potential. Due to the large polyhedral volume, it is beneficial for lanthanide elements doping. Therefore, it is important to understand the crystal-field effect in 8-coordinated potential. This work provides a quantitatively analysis of the perfect cubic crystal field effect. The potential is expressed by the vertex coordinates, and expanded by Legendre polynomials. Then the perturbation secular matrix is constructed by the ϕ, θ integration and substitution of the radial wavefunction part. Finally, the split energy levels are given. This work provides a deeper understanding of the crystal-field effect.
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