Restricted basis set coupled-channel calculations on atom-molecule collisions in magnetic fields

TL;DR

This paper introduces a restricted basis set approach for coupled-channel quantum scattering calculations in atom-molecule collisions under magnetic fields, significantly reducing computational costs while maintaining accuracy for certain processes.

Contribution

The authors demonstrate that limiting the total angular momentum basis states to helicities $K \,\le\, K_{\text{max}}$ yields accurate results with much less computational effort, especially for ultracold spin relaxation.

Findings

Minimal helicity basis ($K_{\text{max}}=0$) achieves accurate ultracold collision results.

Larger basis sets are needed for resonance structure and indirect spin relaxation.

Resonance structures arise from spin-rotation and Coriolis couplings.

Abstract

Rigorous coupled-channel quantum scattering calculations on molecular collisions in external fields are computationally demanding due to the need to account for a large number of coupled channels and multiple total angular momenta $J$ of the collision complex. We show that by restricting the number of total angular momentum basis states to include only the states with helicities $K\le K_\text{max}$ it is possible to obtain accurate elastic and inelastic cross sections for He+CaH, Li+CaH and Li+SrOH collisions at a small fraction of the computational cost of the full coupled-channel calculations (where $K$ is the projection of the molecular rotational angular momentum on the atom-diatom axis). The optimal size of the truncated helicity basis set depends on the mechanism of the inelastic process and on the magnitude of the external magnetic field. For dipolar-mediated spin relaxation in ultracold Li+CaH and Li+SrOH collisions, we find that a minimal helicity basis set ($K_\text{max}=0$) gives quantitatively accurate results at ultralow collision energies, leading to nearly 90-fold gain in computational efficiency. Larger basis sets are required to accurately describe the resonance structure in Li+CaH and Li+SrOH inelastic cross sections in the few partial wave-regime ($K_\text{max}=3$) as well as indirect spin relaxation in He+CaH collisions ($K_\text{max}=1$). Our calculations indicate that the resonance structure is due to an interplay of the spin-rotation and Coriolis couplings between the basis states of different $K$ and the couplings between the rotational states of the same $K$ induced by the anisotropy of the interaction potential.