Scattering theory is used to calculate the vibronic energy levels of the interacting double-minimum states in H 2. The calculation is based on the accurate ab initio fixed-nuclei energies of Wolniewicz and Dressler. From these a nondiagonal reaction matrix is extracted whose elements are nuclear-coordinate dependent and involve singly and doubly excited channels. The treatment bypasses the state-by-state evaluation of vibronic coupling, and yields in principle the entire vibronic Rydberg spectrum associated with the H 2+ 1 σ g and 1 σ u cores. The first forty experimental levels are reproduced quite accurately.