  The Anderson model with the Coulomb interaction between the local and
conduction electrons is studied in the semiconducting phase. Based on a
perturbation theory from the atomic limit, leading contributions for the c-f
Coulomb interaction are incorporated as a vertex correction to hybridization.
An analytical solution shows that the effective attraction in the intermediate
states leads to a bound state localized at the local electron site.
Self-consistent equations are constructed as an extension of the non-crossing
approximation (NCA) to include the vertex part yielding the bound state. A
numerical calculation demonstrates the excitonic bound state inside the
semiconducting gap for single-particle excitations, and a discontinuity at the
gap edge for magnetic excitations.
