Quantum theory of reactive collisions for 1/r^n potentials

TL;DR

This paper develops a comprehensive quantum framework for reactive collisions involving power-law potentials, extending traditional models to include non-universal reaction probabilities and applicable across a wide temperature range.

Contribution

It introduces a quantum defect theory that generalizes capture models to account for partial reaction probabilities in power-law potentials.

Findings

Derived explicit analytical formulas for reaction rates.

Numerical analysis for van der Waals and polarization potentials.

Connected theory to recent low-energy collision experiments.

Abstract

We develop a general quantum theory for reactive collisions involving power-law potentials (-1/r^n) valid from the ultracold up to the high-temperature limit. Our quantum defect framework extends the conventional capture models to include the non-universal case when the short-range reaction probability P^{re} < 1. We present explicit analytical formulas as well as numerical studies for the van der Waals (n = 6) and polarization (n = 4) potentials, and relate our work to recent merged beam experiments on Penning ionization for collision energies below 0.1 meV [Henson et al, Science 338, 234(2012)].