Quantum slowdown of thermal barrier crossing: an exact criterion and a universal thin-barrier threshold of seven

Tunneling speeds up barrier crossing; quantum reflection can slow it down. For any one-dimensional barrier, kBT[κ(T) − 1], with κ the tunneling factor, falls with temperature to A, the signed area between quantum and classical transmission. Hence κ < 1 occurs if and only if A < 0, then above a unique temperature. A is the shift of the mean crossing threshold below the barrier top. For any regular thin barrier with heights Vmin ≤ Vmax, A → (7Vmin − Vmax)/6, as a step raises the mean threshold by 1/6 of its height. Numerically, the Eckart threshold Vmax/Vmin lies between 6.8159 and 7 + 4√3. The upload contains the Letter, the Supplemental Material (proofs, ball-arithmetic certificates, numerical methods, reaction data) and the reproducibility package (Python: mpmath, SymPy, NumPy, SciPy, Matplotlib, python-flint/Arb, ELIAH, formerly NETI) with the LaTeX sources.