  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.
