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

Statistical tests (NNLSD, Δ3 of Dyson and Mehta, correlation coefficients) are applied to the adiabatic energy level distribution of the prototypical reaction F+H2 → 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.