137 research outputs found
General calculation of transition rates for rare-earth ions using many-body perturbation theory
The transition rates for rare-earth ions in crystals can be
calculated with an effective transition operator acting between model
and states calculated with effective Hamiltonian, such as
semi-empirical 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 \ME {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.Comment: 10 pages, 1 figur
Calculation of single-beam two-photon absorption transition rate of rare-earth ions using effective operator and diagrammatic representation
Effective operators needed in single-beam two-photon transition calculations
have been represented with modified Goldstone diagrams similar to the type
suggested by Duan and co-workers [J. Chem. Phys. 121, 5071 (2004) ]. 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.Comment: 10 preprint pages, to appear in Journal of Alloys and Compound
Conservation of connectivity of model-space effective interactions under a class of similarity transformation
Effective interaction operators usually act on a restricted model space and
give the same energies (for Hamiltonian) and matrix elements (for transition
operators etc.) as those of the original operators between the corresponding
true eigenstates. Various types of effective operators are possible. Those well
defined effective operators have been shown being related to each other by
similarity transformation. Some of the effective operators have been shown to
have connected-diagram expansions. It is shown in this paper that under a class
of very general similarity transformations, the connectivity is conserved. The
similarity transformation between hermitian and non-hermitian
Rayleigh-Schr\"{o}dinger perturbative effective operators is one of such
transformation and hence the connectivity can be deducted from each other.Comment: 12 preprint page
Calculation of single-beam two-photon absorption rate of lanthanides: effective operator method and perturbative expansion
Perturbative contributions to single-beam two-photon transition rates may be
divided into two types. The first, involving low-energy intermediate states,
require a high-order perturbation treatment, or an exact diagonalization. The
other, involving high energy intermediate states, only require a low-order
perturbation treatment. We show how to partition the effective transition
operator into two terms, corresponding to these two types, in such a way that a
many-body perturbation expansion may be generated that obeys the linked cluster
theorem and has a simple diagrammatic representation.Comment: 11 preprint page
Local Field effects on the radiative lifetime of emitters in surrounding media: virtual- or real-cavity model?
For emitters embedded in media of various refractive indices, different
macroscopic or microscopic theoretical models predict different dependencies of
the spontaneous emission lifetime on refractive index. Among those models are
the two most promising models: the virtual-cavity model and the real-cavity
model. It is a priori not clear which model is more relevant for a given
situation. By close analysis of the available experimental results and
examining the assumptions underlying the two models, we reach a consistent
interpretation of the experimental results and give the criteria which model
should apply for a given situation.Comment: 12 pages with 4 figure
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