Bypassing translation factors in molecular dissociation and reactions

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Abstract
Recent calculations of three-body systems have obtained correct dissociating states in a hyperspherical adiabatic framework. The hyperradius scrR, a measure of the size of the system, commutes with the kinematic rotations connecting united-atom and dissociation limits. This result has general significance. The widely discussed translation factors were included in the Born-Oppenheimer basis to compensate an intrinsic shortcoming rooted in the separation of nuclear and electronic kinetic energies. The treatment of kinetic energy in the adiabatic hyperspherical procedure eliminates the need for translation factors entirely, even though this procedure departs from the Born-Oppenheimer model only slightly in other respects.

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