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 G48 of four identical nuclei appropriate for short distances using appropriate symmetry subgroups. The final results provide selection rules for collisions of four identical atoms. Graphical abstract: [Figure not available: see fulltext.