Energy spectrum of a particle in potentials with strongly differing ranges

Equations are derived that determine the spectrum of weakly bound states of systems in which the interaction is described by a superposition of potentials with strongly differing interaction ranges. The level shifts in a long-range potential due to the influence of a short-range center are found. The interaction of levels that exist in the isolated potentials is investigated. Expressions for the renormalization of the scattering length by an external field are obtained. The Stark effect under conditions of degeneracy is considered.