High order corrections to the time-independent Born-Oppenheimer approximation II: Diatomic Coulomb systems

We study the bound states of diatomic molecular systems. We prove that if the nuclear masses are proportional to ε^?4 then certain eigenvalues and eigenvectors of the Hamiltonian have asymptotic expansions to arbitrarily high order in powers of ε, as ε→0. The zeroth through fourth order terms in the expansions for the eigenvalues are those of the well-known Born-Oppenheimer approximation. The fifth order term is zero.