Statistics of energy levels in the quantum treatment of an elementary reaction

Abstract

Statistical tests (NNLSD, Δ 3 of Dyson and Mehta, correlation coefficients) are applied to the adiabatic energy level distribution of the prototypical reaction F+H 2 → HF+H, depending parametrically on the three-body total inertia measured by the hyperradius ρ. As a function of ρ (proposed as a natural control variable for the quantum mechanical three-body problem), a transition can be identified. At high ρ, the situation of separate partners of the reaction shows a Poissonian behavior while, at low ρ, the transition state (where the triatom can be viewed as a system of coupled oscillators) exhibits some Wigner-like features as signatures of quantum chaos.