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Multiscale quantum-defect theory and its application to atomic spectrum

We present a multiscale quantum-defect theory based on the first analytic solution for a two-scale long range potential consisting of a Coulomb potential and a polarization potential. In its application to atomic structure, the theory extends the systematic understanding of atomic Rydberg states, as afforded by the standard single-scale quantum-defect theory, to a much greater range of energies to include the first few excited states and even the ground state. Such a level of understanding has important implications not only on atomic structure, but also on the electronic structure of molecules and on atomic and molecular interactions and reactions. We demonstrate the theory by showing that it provides an analytic description of the energy variations of the standard Coulomb quantum defects for alkali-metal atoms.