Optical Absorption Intensities of Rare-Earth Ions Export

@article{citeulike:2328496, abstract = {Electric dipole transitions within the 4 f shell of a rare-earth ion are permitted if the surroundings of the ion are such that its nucleus is not situated at a center of inversion. An expression is found for the oscillator strength of a transition between two states of the ground configuration 4 f N ; on the assumption that the levels of each excited configuration of the type 4 f N n ′ d or 4 f N n ′ g extend over an energy range small as compared to the energy of the configuration above the ground configuration. On summing over all transitions between the components of the ground level ψ J and those of an excited level ψ ′ J ′ ; both of 4 f N ; the oscillator strength P corresponding to the transition ψ J →ψ ′ J ′ of frequency ν is found to be given by P =Σ T λ ν(ψ J ∥ U (λ) ∥ψ ′ J ′ ) 2 ; where U (λ) is a tensor operator of rank λ; and the sum runs over the three values 2; 4; and 6 of λ. Transitions that also involve changes in the vibrational modes of the complex comprising a rare-earth ion and its surroundings; provide a contribution to P of precisely similar form. It is shown that sets of parameters T λ can be chosen to give a good fit with the experimental data on aqueous solutions of NdCl 3 and ErCl 3 . A calculation on the basis of a model; in which the first hydration layer of the rare-earth ion does not possess a center of symmetry; leads to parameters T λ that are smaller than those observed for Nd 3+ and Er 3+ by factors of 2 and 8; respectively. Reasons for the discrepancies are discussed.}, author = {Judd, B. R.}, citeulike-article-id = {2328496}, citeulike-linkout-0 = {http://dx.doi.org/10.1103/PhysRev.127.750}, citeulike-linkout-1 = {http://link.aps.org/abstract/PR/v127/i3/p750_1}, citeulike-linkout-2 = {http://link.aps.org/pdf/PR/v127/i3/p750_1}, day = {1}, doi = {10.1103/PhysRev.127.750}, journal = {Physical Review}, keywords = {judd, prb}, number = {3}, pages = {750+}, posted-at = {2008-02-04 07:05:46}, priority = {2}, publisher = {American Physical Society}, title = {Optical Absorption Intensities of Rare-Earth Ions}, url = {http://dx.doi.org/10.1103/PhysRev.127.750}, volume = {127}, year = {1962} }

TY - JOUR ID - citeulike:2328496 L3 - citeulike-article-id:2328496 N2 - Electric dipole transitions within the 4 f shell of a rare-earth ion are permitted if the surroundings of the ion are such that its nucleus is not situated at a center of inversion. An expression is found for the oscillator strength of a transition between two states of the ground configuration 4 f N ; on the assumption that the levels of each excited configuration of the type 4 f N n ′ d or 4 f N n ′ g extend over an energy range small as compared to the energy of the configuration above the ground configuration. On summing over all transitions between the components of the ground level ψ J and those of an excited level ψ ′ J ′ ; both of 4 f N ; the oscillator strength P corresponding to the transition ψ J →ψ ′ J ′ of frequency ν is found to be given by P =Σ T λ ν(ψ J ∥ U (λ) ∥ψ ′ J ′ ) 2 ; where U (λ) is a tensor operator of rank λ; and the sum runs over the three values 2; 4; and 6 of λ. Transitions that also involve changes in the vibrational modes of the complex comprising a rare-earth ion and its surroundings; provide a contribution to P of precisely similar form. It is shown that sets of parameters T λ can be chosen to give a good fit with the experimental data on aqueous solutions of NdCl 3 and ErCl 3 . A calculation on the basis of a model; in which the first hydration layer of the rare-earth ion does not possess a center of symmetry; leads to parameters T λ that are smaller than those observed for Nd 3+ and Er 3+ by factors of 2 and 8; respectively. Reasons for the discrepancies are discussed. IS - 3 JF - Physical Review TI - Optical Absorption Intensities of Rare-Earth Ions PB - American Physical Society VL - 127 SP - 750 KW - judd KW - prb AU - Judd, BR PY - 1962//01/ UR - http://dx.doi.org/10.1103/PhysRev.127.750 ER -