Resonant spectra of multipole-bound anions

TL;DR

This paper investigates the resonant spectra of multipole-bound anions using a nonadiabatic model and Berggren expansion, revealing critical behavior, resonant states, and exceptional points near the electron detachment threshold.

Contribution

It introduces a Gaussian multipole potential model and applies the Berggren expansion to analyze resonant states and critical phenomena in multipole-bound anions.

Findings

Predicted the critical transition at the electron detachment threshold.

Identified and characterized various resonant states including bound, resonances, and antibound states.

Predicted exceptional points where resonant states coalesce.

Abstract

In multipole-bound anions, the excess electron is attached by a short-range multipole potential of a neutral molecule. Such anions are prototypical marginally-bound open quantum systems. In particular, around the critical multipole moment required to attach the valence electron, multipole-bound anions exhibit critical behavior associated with a transition from bound states dominated by low-$\ell$ partial waves to the electron continuum. In this work, multipole-bound anions are described using a nonadiabatic electron-plus-rotor model. The electron-molecule pseudo-potential is represented by a short-range multipole field with a Gaussian form-factor. The resulting coupled-channel Schr\"odinger equation is solved by means of the Berggren expansion method, in which the electron's wave function is decomposed into bound states, narrow resonances, and the non-resonant scattering continuum. We show that the Gaussian model predicts the critical transition at the detachment threshold. Resonant states, including bound states, decaying resonances, subthreshold resonances, and antibound states are studied, and exceptional points where two resonant states coalesce are predicted. We discuss the transition of rotational band structures around the threshold and study the effects of channel coupling on the decay width of resonant poles.