Eur. Phys. J. D (2016) 70: 228
https://doi.org/10.1140/epjd/e2016-60587-9

Regular Article

Complete symmetry characterization in collisions involving four identical atoms

¹ Department of Chemical Engineering and Material Sciences, University of California, Davis, California 95616, USA
² Department of Theoretical Physics, Saarland University, 66123 Saarbrücken, Germany
³ Department of Physics, University of Central Florida, Orlando, Florida 32816, USA

^a e-mail: nicolas.douguet@drake.edu

Received: 18 October 2015
Received in final form: 7 August 2016
Published online: 1 November 2016

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.