  The exciton on a single polydiacetylene chain is considered in a Wannier
approach, taking into account the surrounding polarizable medium. The
electron-hole Coulomb interaction potential is explictly obtained for a quantum
wire of circular cross-section, and numerically calculated for a rectangular
one. The predicted binding energy and Bohr radius, starting from the chain
conformation, are in good agreement with experimental values. This shows the
importance of considering the monomer matrix embedding the chain, and the major
role of confinement, together with electron correlations, for describing the
exciton. The method is general and applicable to any quantum wire.
