Chang-Kui Duan

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

By close analysis of the available experimental results on the spontaneous emission lifetime of various emitters in different media and examining the assumptions underlying the two titled models, we reach a consistent interpretation of the experimental results and give a practical criterion on which model is applicable for a given situation.

Extraction of crystal-field parameters for lanthanide ions from quantum-chemical calculations

A simple method for constructing effective Hamiltonians for the 4f(N) and 4f(N - 1)5d energy levels of lanthanide ions in crystals from quantum-chemical calculations is presented. The method is demonstrated by deriving crystal-field and spin-orbit parameters for Ce(3 + ) ions doped in LiYF(4), Cs(2)NaYCl(6), CaF(2), KY(3)F(10) and YAG host crystals from quantum-chemical calculations based on the DV-Xα method. Good agreement between calculated and fitted values of the crystal-field parameters is obtained. The method can be used to calculate parameters even for low-symmetry sites where there are more parameters than energy levels.

Supernova constraints on alternative models to dark energy

The recent observations of type Ia supernovae suggest that the universe is accelerating now and decelerated in the recent past. This may be the evidence of the breakdown of the standard Friedmann equation. The Friedmann equation H 2 � ρ is modified to be a general form H 2 = g(ρ). Three models with particular form of g(ρ) are considered in detail. The supernova data published by Tonry et al. (2003), Daly & Djorgovski (2003) and Knop et al. (2003) are used to analyze the models. After the best fit parameters are obtained, we then find out the transition redshift zT when the universe switched from the deceleration phase to the acceleration phase.

Spectroscopy of High-Energy States of Lanthanide Ions

We discuss recent progress and future prospects for the analysis of the 4f N-1 5d excited states of lanthanide ions in host materials. We demonstrate how ab initio calculations for Ce 3+ in LiYF 4 may be used to estimate crystal-field and spin-orbit parameters for the 4f 1 and 5d 1 configurations. We show how excited-state absorption may be used to probe the electronic and geometric structure of the 4f N-1 5d excited states in more detail and we illustrate the possibilities with calculations for Yb 2+ ions in SrCl 2 .

Constraints on alternative models to dark energy

Recent observations of type Ia supernovae strongly support that the universe is accelerating now and decelerated in the recent past. This may be evidence of the breakdown of the standard Friedmann equation. We consider a general modified Friedmann equation. Three different models are analysed in detail. The current supernova data and the Wilkinson microwave anisotropy probe data are used to constrain these models. A detailed analysis of the transition from the deceleration to acceleration phase is also performed.

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

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.

DFT calculations of crystal-field parameters for the lanthanide ions in the LaCl3 crystal.

We present herein a calculation of crystal-field (CF) parameters for the lanthanide ions in the LaCl(3) crystal, using the density functional theory-based orbital-free embedding formalism in conjunction with the effective Hamiltonian method. The calculated values for the second- and fourth-rank CF parameters agree fairly well with the experimental data. It is found that the effect of ligand polarization plays a crucial role in determining the sign and magnitude of the second-rank CF parameters, while the effect of Pauli repulsion between 4f electrons and the ligands is important for the fourth-rank CF parameters. The usefulness of the present approach is illustrated by a study of the relative preference of Eu(3 + ) occupation on the two distinct Pb(2 + ) sites in the KPb(2)Cl(5) crystal. The computational approach and results discussed in this work are useful for a better understanding and simulation of the CF effect in the lanthanide-containing systems.

A New alternative model to dark energy

The recent observations of type Ia supernovae strongly support that the universe is accelerating now and decelerated in the recent past. This may be the evidence of the breakdown of the standard Friedmann equation. Instead of a linear function of the matter density, we consider a general function of the matter density to modify the Freidmann equation. We propose a new model which explains the recent acceleration and the past deceleration. Furthermore, the new model also gives a decelerated universe in the future. The new model gives Ωm0=0.46 and zT=0.44.

Simplified diagrammatic expansion for effective operators

For a quantum many-body problem, effective Hamiltonians that give exact eigenvalues in reduced model space usually have different expressions, diagrams, and evaluation rules from effective transition operators that give exact transition matrix elements between effective eigenvectors in reduced model space. By modifying these diagrams slightly and considering the linked diagrams for all the terms of the same order, we find that the evaluation rules can be made the same for both effective Hamiltonian and effective transition operator diagrams, and in many cases it is possible to combine many diagrams into one modified diagram. We give the rules to evaluate these modified diagrams and show their validity.

Crystal-field analysis and calculation of two-photon absorption line strengths of dicesium sodium hexachlorogadolinate(III)

The crystal-field energy level calculation of the 4f(7) ion Gd(3+) in the crystal Cs(2)NaGdCl(6) has fitted 45 levels with standard deviation 12 cm(-1), with the energy parameters being consistent with those from other studies. The resulting eigenvectors have been employed in the calculation of two-photon absorption (TPA) intensities of transitions from the electronic ground state (8)S(7/2) to the crystal-field levels of excited (6)P, (6)I and (6)D multiplet terms. The TPA line strengths are highly polarization dependent and exhibit striking differences for linearly polarized incident radiation compared with circularly polarized radiation. The relative intensities are compared with those available from previous experimental studies and some reassignments have been made. Good agreement of calculated and experimental TPA spectra is found, except for the intensity ratio of the transitions to (6)P(7/2) or (6)P(5/2) compared with that to (6)P(3/2), for linear and circular polarizations, where the calculation overestimates the ratio. Reasons for this disagreement are presented.