# Energy levels and lifetimes of Nd IV, Pm IV, Sm IV, and Eu IV

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V. A. Dzuba, Jul 03, 2015 Available from:- [Show abstract] [Hide abstract]

**ABSTRACT:**We use the relativistic Hartree-Fock method, many-body perturbation theory and configuration-interaction method to calculate the dependence of atomic transition frequencies on the fine structure constant, alpha. The results of these calculations will be used in the search for variation of the fine structure constant in quasar absorption spectra.Physical Review A 05/2004; 70(6). DOI:10.1103/PhysRevA.70.064101 · 2.99 Impact Factor - [Show abstract] [Hide abstract]

**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.The Journal of Chemical Physics 04/2005; 122(9):094714. DOI:10.1063/1.1855880 · 3.12 Impact Factor -
##### Article: Relativistic bound states

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**ABSTRACT:**The Hamiltonian for Dirac's second-order equation depends nonlinearly on the potential V and the energy E. For this reason the magnetic contribution to the Hamiltonian for s-waves, which has a short range, is attractive for a repulsive Coulomb potential (V>0) and repulsive for an attractive Coulomb potential (V<0). Previous studies are confined to the latter case, where strong net attraction near a high-Z nucleus accelerates electrons to velocities close to the speed of light. The Hamiltonian is linear in the product EV/mc2. Usually solutions are found in the regime E=mc2+ɛ, where except for high Z, ɛ≪mc2. Here it is shown that for V>0 the attractive magnetic term and the linear repulsive term combine to support a bound state near E=0.5mc2 corresponding to a binding energy Eb=−ɛ=0.5mc2.Physics Letters A 03/2006; 352(3-352):239-241. DOI:10.1016/j.physleta.2005.12.094 · 1.63 Impact Factor