Optimized Multichannel Quantum Defect Theory for cold molecular collisions

TL;DR

This paper improves multichannel quantum defect theory (MQDT) for cold molecular collisions by optimizing the reference phases to eliminate poles in the Y matrix, enabling efficient and accurate interpolation over broader energy and magnetic field ranges.

Contribution

It introduces a method to choose MQDT reference phases that remove poles from the Y matrix, significantly enhancing interpolation efficiency for cold molecular collision calculations.

Findings

Y matrix can be interpolated smoothly over several Kelvin and 1000 G

Computational cost scales linearly with channels N after optimization

Method demonstrated on Mg+NH collision system

Abstract

Multichannel quantum defect theory (MQDT) can provide an efficient alternative to full coupled-channel calculations for low-energy molecular collisions. However, the efficiency relies on interpolation of the Y matrix that encapsulates the short-range dynamics, and there are poles in Y that may prevent interpolation over the range of energies of interest for cold molecular collisions. We show how the phases of the MQDT reference functions may be chosen so as to remove such poles from the vicinity of a reference energy and dramatically increase the range of interpolation. For the test case of Mg+NH, the resulting optimized Y matrix may be interpolated smoothly over an energy range of several Kelvin and a magnetic field range of over 1000 G. Calculations at additional energies and fields can then be performed at a computational cost that is proportional to the number of channels N and not to N^3.