The electronic isotope shift in diatomic molecules and the partial breakdown of the Born-Oppenheimer approximation

Abstract

The exact rovibronic Hamiltonian of a diatomic molecule is derived, and expressions for the eigenfunctions and eigenvalues are obtained in the adiabatic approximation. This is an improvement over the results obtained using the Born-Oppenheimer approximation. The best possible potential curve of an electronic state of a diatomic molecule is defined and it is shown how this varies with isotopic substitution. The theoretical expression for the electronic isotope shift of a transition is determined from the expressions for the best possible potential curves. This theoretical result is shown to be in good agreement with the observed isotope shifts of the Lyman bands of H 2, HD, and D 2. Since the theoretical determination of an electronic isotope shift demands the ab initio calculation of several expectation values, an approximate expression is derived and shown to give good agreement with experiment. The accuracy of the experimental determination of an electronic isotope shift is also discussed.