A model for nuclear spin product-state distributions of ultracold chemical reactions in magnetic fields

TL;DR

This paper introduces a theoretical model to predict nuclear spin state distributions in ultracold chemical reactions under magnetic fields, emphasizing the role of molecular eigenfunctions and explaining experimental observations.

Contribution

It provides an analytical expression for nuclear spin distributions in ultracold reactions considering magnetic fields, a novel approach in this research area.

Findings

The model accurately predicts the magnetic field dependence of product-state distributions.

The simplified expression only requires reactant eigenfunctions for summed distributions.

The formalism successfully explains experimental results with ultracold KRb molecules.

Abstract

Based on a theoretical model where the nuclear spins remain unchanged during a collision, we provide an analytical and general expression for the nuclear spin state-to-state distribution of an ultracold chemical reaction in a magnetic field, for given rotational transitions of the molecules. It simply requires knowledge of the field-dependent eigenfunctions of the molecular reactants and products of the chemical reaction. The final state-to-state distribution drastically changes with the magnetic field. When the distribution is summed over all the final products, a simplified expression is found where only the knowledge of the eigenfunctions of the molecular reactants is required. The present theoretical formalism has been successfully used to explain the magnetic field behavior of the product-state distribution in chemical reactions of ultracold KRb molecules [Hu et al., Nat. Chem. 13, 435 (2021)].