A rigorous adiabatic approach to ultracold atom-molecule collisions in a magnetic field

TL;DR

This paper develops an efficient adiabatic coupled-channel method for ultracold atom-molecule collisions in magnetic fields, reducing computational cost while maintaining accuracy, and introduces a basis truncation protocol applicable to complex collision systems.

Contribution

The authors extend the adiabatic formalism to ultracold collisions with magnetic fields and introduce an R-dependent basis truncation protocol that enhances computational efficiency.

Findings

Adiabatic approach yields accurate cross sections with fewer channels.

RBT basis truncation reduces computational cost by 15-30 times.

Method is effective for anisotropic collisions and reactions in magnetic fields.

Abstract

We extend the rigorous adiabatic coupled-channel formalism to ultracold nonreactive atom-molecule collisions in the presence of an external magnetic field. The wavefunction of the collision complex is expanded in adiabatic basis states obtained by solving the eigenvalue problem for the adiabatic Hamiltonian (the total Hamiltonian of the collision complex minus the radial kinetic energy) on a grid of atom-molecule distances $R$. The resulting coupled-channel equations are solved using the diabatic-by-sector method. We show that the adiabatic approach provides accurate cross sections for cold and ultracold Mg ($^1$S) + NH ($^3\Sigma^-$) collisions in a magnetic field with ~2 times fewer channels than the standard diabatic basis. We further develop an efficient $R$-dependent basis truncation protocol (RBT), in which the elements of the log-derivative matrix are sampled and discarded as it is propagated from small to large $R$. While RBT can be applied in both the adiabatic and diabatic bases, we show that the adiabatic basis can be reduced to just the open channels at long range, leading to an overall computational gain of ~15-30 for the propagation part of the calculation. The gain is particularly significant in situations where substantial errors in the calculated cross sections ($<$50\%) can be tolerated or long-range interactions are involved, making the adiabatic basis formulation a promising approach to strongly anisotropic collisions and chemical reactions in the presence of an external magnetic field.