Application of point-group bases to fN−fN−1d transitions of lanthanide and actinide ions doped in crystals

The application of point-group coupling coefficients to the modeling of fN↔fN−1d transitions is discussed. There are several possible coupling schemes for the states of the fN−1d configuration. Formulae for matrix elements of the Hamiltonian for the fN−1d configuration and the relative line strengths for fN↔fN−1d transitions are derived. As an example, the f-d absorption spectrum of the crystal Yb2+: SrCl2 is calculated using coupling coefficients based on the software developed by Butler and co-workers, which makes use of the Racah-Wigner calculus. The advantages and disadvantages of various coupling schemes are demonstrated. These coupling schemes are related to the simple model for f-d transitions.