Collect. Czech. Chem. Commun.
2005, 70, 905-922
https://doi.org/10.1135/cccc20050905
Borrowing Intensity in Rare Earth Doped Materials; Magnetic Dipole Transitions
Brian G. Wybournea, Lidia Smentekb,a,* and Andrzej Kędziorskia
a Instytut Fizyki, Uniwersytet Mikołaja Kopernika, Toruń, Poland
b Department of Chemistry, Vanderbilt University, Nashville, U.S.A.
Abstract
A theoretical model of magnetic dipole transitions in crystals doped by the lanthanide ions is based on the fourth-order perturbation theory applied for the Hamiltonian in which two perturbing mechanisms are taken into account. Namely, the impact due to the crystal field potential and also spin-orbit interaction operator is included in the transition amplitude. The analysis is performed in the language of Racah algebra applied for the formulation of the effective operators expressed in terms of unit double tensor operators. The radial integrals of the terms contributing at the fourth order are defined within the perturbed function approach, due to which their values are evaluated for the complete radial basis sets of one-electron states of given symmetry. The numerical analysis performed for the Eu3+ ion provides the information on the relative importance of various effective operators and allows one to establish a hierarchy of important terms contributing to the transition amplitude. The results of the analysis lead also to the verification of possible importance of magnetic dipole transitions in the description of 0 ↔ 0 and 0 ↔ 1 electric dipole transitions via the so-called borrowing mechanism introduced by Wybourne.
Keywords: Hamiltonian; Magnetic dipoles; Lanthanides; Spin-orbit interaction; Racah algebra; Borrowing mechanism; Double perturbation theory.
References: 15 live references.
