Quantum Defect Theory for High Partial Wave Cold Collisions

TL;DR

This paper extends Multichannel Quantum Defect Theory to high partial wave ultracold collisions, providing a standardized approach and demonstrating its accuracy through calculations of Fano-Feshbach resonances in potassium-rubidium systems.

Contribution

The authors develop a standardized extension of MQDT for high partial wave collisions and validate it with detailed resonance calculations.

Findings

Accurate calculation of Fano-Feshbach resonances for L ≤ 2

Standardized reference wave functions improve theory robustness

Method applicable to ultracold atomic collision studies

Abstract

We extend Multichannel Quantum Defect Theory (MQDT) to ultracold collisions involving high partial wave quantum numbers $L$. This requires a careful standardization of the MQDT reference wave functions at long range to ensure their linear independence. To illustrate the simplicity and accuracy of the resulting theory, we perform a comprehensive calculation of $L\le 2$ Fano-Feshbach resonances in the range 0-1000 G for the scattering of $^{40}$K + $^{87}$Rb in their lowest hyperfine states.