Theoretical description of the spectroscopic properties of rare earth ions in crystals |
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| Affiliation: | 2. Department of Chemistry, Vanderbilt University, Nashville, TN 37235, USA;1. Département des Sciences et Techniques, Faculté des Sciences et de la Technologie, Université Mohamed El Bachir El Ibrahimi, Bordj Bou Arreridj 34000, Algeria;2. Laboratoire d''étude des Surfaces et Interfaces des Matériaux Solides (LESIMS), Université de Sétif 1, 19000 Algeria;3. Institut d''Electronique, de Microélectronique et de Nanotechnologie (IEMN), UMR 8520, Université Lille 1, Avenue Poincaré, BP 60069, 59652 Villeneuve d''Ascq Cédex, France;4. Département de Physique, Université de Sétif 1, Sétif 19000, Algeria;1. Grupo de Pesquisa em Química de Materiais – (GPQM), Departamento de Ciências Naturais, Universidade Federal de São João del-Rei, Campus Dom Bosco, Praça Dom Helvécio, 74, CEP: 36301-160, São João del-Rei, MG, Brazil;2. Instituto de Química, UNESP, P.O. Box 355, CEP: 14800-970, Araraquara, SP, Brazil;3. Research Group of Materials Chemistry, Universidade Federal de Alfenas, Campus de Poços de Caldas, Poços de Caldas, MG, Brazil;4. Departamento de Química, Faculdade de Filosofia Ciências e Letras de Ribeirão Preto, USP, Avenida Bandeirantes, 3900, 14040-901, Ribeirão Preto, SP, Brazil;5. Department of Chemistry and Physics, University of Tennessee at Martin, Martin, TN, USA;6. Desenvolvimento de Materiais Inorgânicos com Terras Raras - DeMITeR, Instituto de Química – (IQ), Universidade Federal de Uberlândia – (UFU), Av. João Naves de Ávila, 2121 – Bairro Santa Mônica, CEP: 38400-902, Uberlândia, MG, Brazil;1. Department of Physics, Nagoya University, Nagoya 464-8602, Japan;2. Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), University of Tokyo, Kashiwa 277-8568, Japan;1. Kazan Zavoisky Physical-Technical Institute, 420029 Kazan, Russian Federation;2. Kazan (Volga Region) Federal University, 420008 Kazan, Russian Federation;3. South Westphalia University of Applied Sciences, Department of Electrical Engineering, 59494 Soest, Germany;4. University of Paderborn, Department of Physics, 33098 Paderborn, Germany |
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| Abstract: | In this article the present state of knowledge of the theory of one- and two-photon processes observed in rare earth ions in crystals is presented. The conclusions are based on the results of ab initio calculations performed for various ions across the lanthanide series. The model applied for the calculations is based on the Rayleigh–Schrödinger perturbation theory, and the amplitude of a certain electric dipole transition is expressed in terms of effective operators. The radial integrals of the effective operators are defined by the perturbed functions that contain the perturbing influence of single excitations from the 4f shell to all one-electron states of a given symmetry, discrete and continuum. In this approach the interactions between the 4fN and the excited configurations via the crystal field potential, the electron correlation operator and the spin–orbit interaction operator are discussed; it is believed that the presented theory contains the most important physical mechanisms responsible for the f↔f electric dipole transitions. Two alternative formulations of the theory of one-photon electric dipole transitions are presented. Consequently, the transition amplitude is defined within the standard theory based on the length formula and within a new approach which is based on the velocity form of the electric dipole radiation operator. |
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