Symmetry Considerations in the Spectrum of Ruby

Abstract

The role of the point symmetry of the Cr³⁺ ion in the spectral analysis of Cr³⁺ in Al₂O₃ is reviewed. Previous energy‐level calculations were made on the basis of C_3v symmetry with a reflection plane perpendicular to the unique axis. Little change in the gross spectral features is expected if C₃ (noninversion center) operators are used. However, as noted by McClure, it is necessary to go to C₃(NIC) when calculating electric dipole radiation matrices. For consideration of the axial optical and microwave electric effects it is sufficient to consider C_3v(NIC). For the full microwave electric effect tensor, C₃(NIC) must be used. The interelations between the electric effects and the optical radiation dipole operators are explored. A substantial contribution to the ruby ⁴A₂ ground‐state splitting 2D is expected from the ``odd NIC fields.'' The magnitude of this effect for Cr₂O₃ is considered.