Simplified diagrammatic expansion for effective operators

Duan, Chang‐Kui; Gong, Yungui; Dong, Hui; Reid, Michael F.

doi:10.1063/1.1782071

Cited by 3 publications

(1 citation statement)

References 21 publications

(35 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, perturbations from the crystal field together with electron-electron interactions have large influences [24,[26][27][28][29][30][31]. Interesting evaluation rules for effective transition operators have recently been developed in [32]. A great part of the correlation contributions can be expressed in the one-particle parameterization scheme of an effective dipole operator [33]:…”

Section: Forced Electric Dipole Transitionsmentioning

confidence: 99%

The connection between the dynamic intensity model and the vibronic intensity model for f–f transitions

Edvardsson

Ning

Åberg

2006

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

In this paper we discuss intensity mechanisms of interest for rare-earth ions in optical materials. More specifically, we investigate the character of two models-first, a semi-classical dynamic intensity model, and second, a more traditional quantum mechanical vibronic intensity model. We focus on the case of f-f transitions and show that the predicted oscillator strengths then are the same under very reasonable approximations. We emphasize that this connection between the models cannot be made in the case of f-d transitions. The dynamic intensity model has an interesting classical interpretation. We show that it is very convenient to apply this approach together with classical dynamical techniques such as molecular dynamics simulation or the classical Monte Carlo method. The classical approach simplifies both the interpretation and calculation of vibronic oscillator strengths in complex systems. The concept of an effective temperature works as a bridge between the two models; so realistic predictions can be obtained even at low temperatures.

show abstract

Section: Forced Electric Dipole Transitionsmentioning

confidence: 99%

The connection between the dynamic intensity model and the vibronic intensity model for f–f transitions

Edvardsson

Ning

Åberg

2006

J. Phys. B: At. Mol. Opt. Phys.

View full text Add to dashboard Cite

show abstract

Calculation of single-beam two-photon absorption transition rate of rare-earth ions using effective operator and diagrammatic representation

Duan

Reid

Ruan

et al. 2006

Journal of Alloys and Compounds

Self Cite

View full text Add to dashboard Cite

Effective operators needed in single-beam two-photon transition calculations have been represented with modified Goldstone diagrams similar to the type suggested by Duan et al. [C.-K. Duan, G. Ruan, M.F. Reid, J. Chem. Phys. 121 (2004) 5071]. The rules to evaluate these diagrams are different from those for effective Hamiltonian and one-photon transition operators. It is verified that the perturbation terms considered contain only connected diagrams and the evaluation rules are simplified and given explicitly.

show abstract

General calculation of 4f-5d transition rates for rare-earth ions using many-body perturbation theory

Duan

Reid

2005

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

The 4f-5d transition rates for rare-earth ions in crystals can be calculated with an effective transition operator acting between model 4f(N) and 4f(N-1)5d states calculated with effective Hamiltonian, such as semiempirical crystal Hamiltonian. The difference of the effective transition operator from the original transition operator is the corrections due to mixing in transition initial and final states of excited configurations from both the center ion and the ligand ions. These corrections are calculated using many-body perturbation theory. For free ions, there are important one-body and two-body corrections. The one-body correction is proportional to the original electric dipole operator with magnitude of approximately 40% of the uncorrected electric dipole moment. Its effect is equivalent to scaling down the radial integral (5d/r/4f) to about 60% of the uncorrected HF value. The two-body correction has magnitude of approximately 25% relative to the uncorrected electric dipole moment. For ions in crystals, there is an additional one-body correction due to ligand polarization, whose magnitude is shown to be about 10% of the uncorrected electric dipole moment.

show abstract

Simplified diagrammatic expansion for effective operators

Cited by 3 publications

References 21 publications

The connection between the dynamic intensity model and the vibronic intensity model for f–f transitions

The connection between the dynamic intensity model and the vibronic intensity model for f–f transitions

Calculation of single-beam two-photon absorption transition rate of rare-earth ions using effective operator and diagrammatic representation

General calculation of 4f-5d transition rates for rare-earth ions using many-body perturbation theory

Contact Info

Product

Resources

About