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

Abstract

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.

Thermal quenching of Ce3+emission in PrX3(X = Cl, Br) by intervalence charge transfer

“…For the Ce 3+ free ion, | 5d|r |4f | eff is 0.025 nm [29]. The lifetimes τ r , peak wavelengths of emission spectra λ, and refractive indices n of Ce 3+ in REX 3 (RE = La, Pr and X = Cl, Br) are summarized in table 2.…”

Local field effects on the radiative lifetime of emitters in surrounding media: Virtual- or real-cavity model?

“…The lifetimes of CdTe and CdSe quantum dots in media 14 15 since the media are expelled from the space occupied by the quantum dots, the real-cavity model should apply. The relaxation in the quantum dots is partly due to nonradiative relaxation, which shall not depend on the refractive index of the media.…”

A many-body perturbation calculation of 4f –4f−15d electric dipole moments for lanthanide ions

“…a The δ value 0.3571 in Ref. [13] should be corrected to 0.3464. 5d|r|4f is the zeroth-order radial integral between the 4f N and 4f N−1 5d configurations.…”

“…To correctly predict the transition rates, configuration mixing needs to be taken into account. This can be done by introducing an effective operator for the electric dipole moment, whose matrix elements between the pure 4f N and 4f N−1 5d configurations give exact results [13]. Such an effective operator has been given in Ref.…”

“…Actually Zhang et al [9] considered 12 even-parity and 12 odd-parity configurations mixed into 4f N and 4f N−1 5d configurations, and the consequent RHF theoretical calculation results agreed with the experimental radiative lifetime of the Ce 3+ free ion very well. Based on many-body perturbation theory (MBPT), Duan and Reid [13] performed a quantitative calculation concerning the effective electric-dipole operator of the 4f-5d transition. The * Corresponding author.…”