Characterizing quasibound states and scattering resonances

Matthew D Frye,Jeremy M Hutson

doi:10.1103/physrevresearch.2.013291

Abstract

Characterizing quasibound states from coupled-channel scattering calculations can be a laborious task, involving extensive manual iteration and fitting. We present an automated procedure, based on the phase shift or S-matrix eigenphase sum, that reliably converges on a quasibound state (or scattering resonance) from some distance away. It may be used for both single-channel and multichannel scattering. It produces the energy and width of the state and the phase shift of the background scattering, and hence the lifetime of the state. It also allows extraction of partial widths for decay to individual open channels. We demonstrate the method on a very narrow state in the Van der Waals complex Ar--H$_2$, which decays only by vibrational predissociation, and on near-threshold states of $^{85}$Rb$_2$, whose lifetime varies over 4 orders of magnitude as a function of magnetic field.

Highlights

Scattering resonances are important in many areas of physics and chemistry
We use a space-fixed basis set that includes all functions with j 10 for v = 0 and with j 8 for v = 1 and solve the coupled equations using the symplectic log-derivative propagator of Manolopoulos and Gray [14] with the six-step fifth-order symplectic integrator of McLachlan and Atela [15]. This state has previously been characterized in coupledchannel calculations [8], but the purpose of this example is to show the efficiency of the present method
We have sometimes found that this procedure converges successfully, even for resonances where uncorrected energy dependence in the background prevents convergence based on the eigenphase sum

Summary

INTRODUCTION

Scattering resonances are important in many areas of physics and chemistry These include nuclear physics [1], electron scattering from atoms [2] and molecules [3], the spectroscopy of Van der Waals complexes [4], and chemical reaction dynamics [5]. They have manifestations in both spectroscopy and collisions, and describe both the decay properties of a quasibound state and the resonant scattering that occurs at energies close to the state. Once the location is approximately known, the procedure can often characterize the resonance position, width and background phase shift with calculations at fewer than 10 energies, without the need for manual intervention. We will describe our method in terms of the phase shift, but it applies to the eigenphase sum

THEORY

Vibrational predissociation of Ar–H2

Lifetimes of 85Rb2 Feshbach molecules

Energy dependence of background scattering

Findings

CONCLUSIONS