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

Multiscale quantum-defect theory and its application to atomic spectrum