8,527 research outputs found
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
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
A Configuration Model with Triadic Closure
In this paper we present a configuration model with random triadic closure.
This model possesses five fundamental properties: large transitivity, power law
degree distributions, short path lengths, non-zero Pearson degree correlation,
and the existence of community structures. We analytically derive the Pearson
degree correlation and the clustering coefficient of the proposed model. By
simulation we also test three well-known community detection algorithms on our
model as well as other two benchmark models that are the LFR model and the ABCD
model
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