Calculation and analysis of hyperfine and quadrupole interactions in praseodymium-doped image

We present characterization of the hyperfine and quadrupole interactions of praseodymium in image. The hyperfine structure of the image transition is calculated from a crystal-field analysis and is compared to experimental values retrieved from previous holeburning experiments. The crystal-field wavefunctions are obtained by fitting 42 experimental energy levels, with a good rms standard deviation of image. It is noteworthy that the energy-level scheme of image is reported for the first time. The experimental branching ratios between individual image hyperfine transitions are also fitted. Two different approaches are undertaken, one with a complete diagonalization of a Hamiltonian including the crystal-field, the hyperfine and the quadrupole interactions, another using a spin-Hamiltonian approach based on a second-order perturbation treatment.