Atomic Entanglements in Three-Body Molecular Dissociation,

Theoretical studies are reported of atomic state entanglements in the three-body dissociation of molecules employing tri-atomic hydrogen (H3) as a prototypical example. The predictions made employ methods based on orthonormal outer-products of atomic eigenstates, providing a separable Hilbert space in support of totally antisymmetric solutions of the molecular Schr\"odinger equation. Adiabatic Born-Oppenheimer molecular energies are obtained in the form of sums of the energies of the individual atomic constituents and of their pairwise interactions. Detailed descriptions of the electronic states of constitute atoms within a molecule are provided which allows predictions of atomic entanglements upon dissociation in cases involving at least one internally excited atom. Energy sharing among the three atoms gives rise to complex fractional populations of ground and excited atomic states consequent of the congestion and degeneracy of atomic spectra, which entanglements are accessible to measurement under coherent dissociation conditions. These possibilities are described in detail in the particular cases of symmetric collinear and C3v dissociations, providing specific potential sources for experimental formation and trapping methodologies and related information theory applications.