7. Summary of Universal (Semi)­classical Scaling Laws for Two-Body s-Wave Endothermic Collisions Subject to Short-Range Potentials in Varied Dimensionality (1D to ND), the Attractive Coulomb Potential in Three Dimensions (Coulomb), and the Wannier Double Ionization System in Full Dimensionality (Wannier) .

^aBoth (semi)­classical (class) and quantum (quant) scalings are provided for the probability density |ψ|², cross section σ, and rate $\mathcal{R}$ in terms of the wavenumber k, with (semi)­classical scalings also provided for the density of states ρ _class. The semiclassical 1D-ND and Coulomb scaling laws are determined according to the classical analogue of the Fermi Golden Rule, , with classical scaling laws determined for the Wannier system according to phase-space counting. Quantum threshold laws (quant) are included for direct comparison, with instances of quantum-classical correspondence bolded and emphasized in blue.