Analysis of f-d excitation spectra of heavy lanthanide ions in various crystals based on the simple model for f-d transition and its correction caused by the 5d spin-orbit interaction

► A quasi-angular-momentum approach is used to calculate energy levels of 4fN−15d configurations. ► Racah-Wigner algebra was applied to derive the 4f-5d transition energies and line strengths. ► The developed model can be used to predict the 4f-5d spectra of heavy lanthanides. ► The impact of the 5d spin-orbit interaction was revealed.