A single continuum description of molecular dissociations

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Abstract
The definition of Eckart coordinates for a N-particle system and the Hamiltonian form of the classical kinetic energy are given. The important role of the Jacobian in the definition of the configuration domain is emphasized. It is shown that no singularity of the wavefunction occurs at the frontier of this domain. The dissociations of the system into p subsystems (2 ≤ p ≤ N) are described, in Eckart coordinates, within the single continuum r1 → oo, where r1 is the largest radial Eckart coordinate. Each dissociation channel is identified by means of a unit RN-1 vector Γ called the « chemical pointer» : in a p-ary dissociation, the locus of Γ is a (p - 2) manifold. A Gram matrix algebra is constructed to describe the partitions of the system into several subsystems. Owing to a power expansion on the single-continuum variable, the behaviour of Γ in the vicinity of its loci is explicited

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