Multichannel quantum defect theory for ro-vibrational transitions in ultracold molecule-molecule collisions

TL;DR

This paper introduces a hybrid quantum defect theory approach combining MQDT and close-coupling calculations to efficiently model ultracold molecule-molecule collisions, accurately reproducing cross sections across a wide energy range.

Contribution

It develops a hybrid CC-MQDT method that simplifies ultracold molecular collision calculations while maintaining accuracy, reducing computational costs compared to full CC methods.

Findings

Accurately reproduces cross sections for H2-H2 collisions across 1μK to 10 K.

Shows energy-independent short-range K-matrix suffices in certain regimes.

Provides a computationally efficient alternative to full CC calculations.

Abstract

Multichannel quantum defect theory (MQDT) has been widely applied to resonant and non-resonant scattering in a variety of atomic collision processes. In recent years, the method has been applied to cold collisions with considerable success, and it has proven to be a computationally viable alternative to full-close coupling (CC) calculations when spin, hyperfine and external field effects are included. In this paper, we describe a hybrid approach for molecule-molecule scattering that includes the simplicity of MQDT while treating the short-range interaction explicitly using CC calculations. This hybrid approach, demonstrated for H$_2$-H$_2$ collisions in full-dimensionality, is shown to adequately reproduce cross sections for quasi-resonant rotational and vibrational transitions in the ultracold (1$\mu$K) and $\sim$ 1-10 K regime spanning seven orders of magnitude. It is further shown that an energy-independent short-range $K$-matrix evaluated in the ultracold regime (1$\mu$K) can adequately characterize cross sections in the mK-K regime when no shape resonances are present. The hybrid CC-MQDT formalism provides an alternative approach to full CC calculations at considerably less computational expense for cold and ultracold molecular scattering.