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The influence of the long range forces between an atom and a diatomic fragment on the density of vibrational bound states is studied theoretically in the vicinity of the dissociation threshold of a model triatomic molecule. In the two-dimensional case (2D), where the non dissociating bond is frozen at the equilibrium geometry, the number of quantum states and their density is shown to increase quickly in a small energy interval close to the dissociation threshold  D  0 , due to the long range forces between the fragments. In addition to the strongly coupled states already known at low energies, a new family of states emerges, whose wavefunctions extend to large internuclear distances and correspond to orbiting motion of the two fragments around each other. The semiclassical number of states in 2D is shown to be in excellent agreement with the exact quantum mechanical result. In contrast, semiclassical calculations of the three-dimensional (3D) density and number of states completely fail in the vicinity of the dissociation limit, because of the quantum character of the high frequency vibration of the diatomic fragment. An adiabatic approach is proposed and discussed, that allows one to estimate the 3D density of states close to the dissociation threshold.

Density of Loosely Bound States in a Triatomic Molecule: The Role of Long Range Interactions