Possible New Type of Molecular Bound State

Abstract

It is shown that the corrections to the Born–Oppenheimer approximation may lead to the appearance of a new type of bound state, the theory of which is mathematically analogous to that of Cooper pair states in superconductivity theory. Some of the properties of these states, and the conditions for their existence, are studied for the special case of diatomic molecules. In all cases of interest, one such state at most can appear below the continuum threshold belonging to the ground electronic state of the molecule, i.e., they have no rotational or vibrational structure. In the case most likely to arise, the binding energy, considered as a function of the Born–Oppenheimer expansion parameter κ, has an essential singularity at zero, so the state could never have been discovered by the power-series expansion method. Experimental observation of these states is expected to be difficult since their wavefunctions do not differ importantly from those for ordinary bound states of the same energy. However, the theory predicts that an accurate Born–Oppenheimer calculation of the number of bound states should sometimes be too low by one, and the isotope effect on the binding energy is different from that of ordinary bound states.