Complete symmetry characterization in collisions involving four identical atoms

Abstract

We discuss symmetry properties of a quantum system comprised of four identical atoms in different large - distance molecular configurations and derive general selection rules with possible nuclei exchange after a four-atom collision, e.g. a molecular reaction. We focus on the following important collisional processes: (1) two bound diatomic molecules, (2) a bound triatomic molecule and a free atom, and (3) a bound diatomic molecule and two free atoms. The approach employed to treat this problem is based on analyzing eigenspaces of the large-distance Hamiltonians and the corresponding constants of motion. The symmetry is then studied by decomposing a given eigenspace of the large-distance Hamiltonian in irreducible representations of the complete nuclear permutation inversion group G 48 of four identical nuclei appropriate for short distances using appropriate symmetry subgroups. The final results provide selection rules for collisions of four identical atoms.