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

Department of Physics, University of Notre Dame, South Bend, Indiana, United States

Physical Review A (Impact Factor: 2.81). 09/2003; 68(3). DOI: 10.1103/PhysRevA.68.032503 Source: arXiv

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##### 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.