Quantum defect model of a reactive collision at finite temperature

TL;DR

This paper develops a quantum defect theory-based model to analytically describe inelastic collisions involving power-law potentials at finite temperatures, accounting for quantum effects like tunneling and resonances.

Contribution

It introduces an analytical formula for the energy-dependent complex scattering length applicable to universal and non-universal collisions, enhancing understanding of reactive collision rates.

Findings

Derived a universal formula for complex scattering length.

Analyzed elastic and reactive collision rates at various energies.

Incorporated quantum corrections such as tunneling and shape resonances.

Abstract

We consider a general problem of inelastic collision of particles interacting with power-law potentials. Using quantum defect theory we derive an analytical formula for the energy-dependent complex scattering length, valid for arbitrary collision energy, and use it to analyze the elastic and reactive collision rates. Our theory is applicable for both universal and non-universal collisions. The former corresponds to the unit reaction probability at short range, while in the latter case the reaction probability is smaller than one. In the high-energy limit we present a method that allows to incorporate quantum corrections to the classical reaction rate due to the shape resonances and the quantum tunneling.