A complete image energy level diagram for all trivalent lanthanide ions

We describe the calculations of the image energy levels, reduced matrix elements for image-image transitions and the simulation of absorption and emission spectra. A complete image energy level diagram is calculated for all trivalent lanthanide ions in image. The calculated energy levels are compared with experimentally obtained energies. For Ce, Pr, Nd, Eu, Gd, Ho, Er, Tm and Yb many, and in some cases all, energy levels have been observed. This work provides a starting point for future investigation of as yet unobserved VUV energy levels.