Elastic and inelastic collisions of $^2\Sigma$ molecules in a magnetic field

TL;DR

This study calculates elastic and inelastic collision cross sections for $^2\Sigma$ molecules in a magnetic field, revealing conditions for stable trapping and identifying molecules likely to be collisionally unstable at ultra-cold temperatures.

Contribution

It provides the first comprehensive analysis of collision cross sections for $^2\Sigma$ molecules in magnetic traps, including averaged results over multiple interaction potentials.

Findings

Elastic-to-inelastic cross section ratios exceed 100 at T ~ 10^{-3} K for most $^2\Sigma$ molecules.

Collisionally unstable molecules at T < 10^{-3} K have $\gamma_{SR} > 0.5$ cm$^{-1}$ and $B_e < 4$ cm$^{-1}$.

Most $^2\Sigma$ molecules are stable in magnetic traps at ultra-cold temperatures.

Abstract

We calculate the cross sections for elastic scattering and Zeeman relaxation in binary collisions of molecules in the ro-vibrational ground state of a $^2\Sigma$ electronic state and the Zeeman state with the electron spin projection $M_S=1/2$ on the magnetic field axis. This is the lowest-energy state of $^2\Sigma$ molecules confined in a magnetic trap. The results are averaged over calculations with multiple molecule - molecule interaction potentials, which yields the expectation intervals for the cross sections and the elastic-to-inelastic cross section ratios. We find that the elastic-to-inelastic cross section ratios under conditions corresponding to trapped molecular ensembles at $T \sim 10^{-3}$ K exceed 100 for the majority of $^2\Sigma$ molecules. The range of $^2\Sigma$ molecules expected to be collisionally unstable in magnetic traps at $T < 10^{-3}$ K is limited to molecules with the spin-rotation interaction constant $\gamma_{\rm SR} > 0.5$ cm$^{-1}$ and the rotational constant $B_e < 4$ cm$^{-1}$.