Beyond universality: parametrizing ultracold complex-mediated reactions using statistical assumptions

TL;DR

This paper computes quantum reactive and elastic cross-sections for a prototypical ultracold reaction, testing a quantum theory in a nonuniversal case and relating reaction probability to statistical models for better parameter estimation.

Contribution

It introduces a method to estimate ultracold reaction parameters from first principles using statistical assumptions and tests quantum theory predictions with accurate cross-section calculations.

Findings

Quantum cross-sections calculated across ultracold to Langevin regimes.

Validation of quantum theory in a nonuniversal reaction case.

Reaction probability linked to statistical model assumptions.

Abstract

We have calculated accurate quantum reactive and elastic cross-sections for the prototypical barrierless reaction D$^{+}$ + H$_2$($v$=0, $j$=0) using the hyperspherical scattering method. The considered kinetic energy ranges from the ultracold to the Langevin regimes. The availability of accurate results for this system allows to test the quantum theory by Jachymski et al. [Phys. Rev. Lett. 110, 213202 (2013)] in a nonuniversal case. The short range reaction probability is rationalized using statistical model assumptions and related to a statistical factor. This provides a means to estimate one of the parameters that characterizes ultracold processes from first principles. Possible limitations of the statistical model are considered.