Scattering Angle Dependence of Fano Resonance Profiles in Cold Atomic Collisions Analyzed with the Complex Valued $w$ Parameter

TL;DR

This paper introduces a complex-valued parameter to describe the angle-dependent asymmetry of Fano resonance profiles in cold atomic collisions, providing a new analytical framework for understanding scattering phenomena.

Contribution

It proposes a novel complex parameter $w$ that generalizes Fano's $q$ parameter to include scattering angle dependence, advancing theoretical analysis of atomic collision resonances.

Findings

Strong angle dependence of resonance asymmetry observed in hydrogen-krypton collisions

The asymmetry parameter $w$ is highly sensitive to inter-atomic potentials

The approach enhances understanding of interaction potentials through resonance profiles

Abstract

The scattering angle dependence of Fano resonance profiles in cold atomic collisions has been theoretically studied. A complex-valued parameter $ w $ with an analytical formula describing the asymmetry of the resonance profile is proposed as a new development from previous work on electron resonance scattering from atoms [F. Koike, J. Phys. $\mathbf{B10}$, 2883 (1977)]. It serves as the general formulation which leads to the angle-dependence of Fano's $ q $ parameter. Calculations for the case of cold elastic collisions of hydrogen atoms with krypton atoms have been accomplished. The strong angle dependence of the resonance profile asymmetry in the differential scattering cross section due to the interference with non-resonant partial waves is demonstrated. The scattering angle dependence of the resonance profile and thus the newly proposed asymmetry parameter is highly sensitive to the inter-atomic interaction potentials. This is likely to prove useful for the study of interaction potentials themselves.