A simplified model for the predissociation of diatomic molecules

A model consisting of a harmonic oscillator well and a repulsive inverse square potential, coupled by a delta function, is solved. We find the S-function for this case and study its poles as a function of the coupling strength. These poles show how the harmonic levels shift and broaden as the two potential curves couple and predissociation occurs. A “new state” is found when the energy threshold is just below the first excited state of the harmonic oscillator.