Probing the resonance in the Dirac equation with quadruple-deformed potentials by complex momentum representation method

TL;DR

This paper extends a complex momentum representation method to deformed nuclei for probing resonances in the Dirac equation, demonstrating accurate identification of narrow and broad resonant states in $^{37}$Mg.

Contribution

The paper introduces a formalism for applying the complex momentum representation method to deformed nuclei, enabling precise resonance analysis beyond spherical cases.

Findings

Successfully applied to $^{37}$Mg with good agreement to coordinate space results.

Effectively identifies both narrow and broad resonances.

Provides a clear visualization of resonant states in the complex momentum plane.

Abstract

Resonance plays critical roles in the formation of many physical phenomena, and many techniques have been developed for the exploration of resonance. In a recent letter [Phys. Rev. Lett. 117, 062502 (2016)], we proposed a new method for probing single-particle resonances by solving the Dirac equation in complex momentum representation for spherical nuclei. Here, we extend this method to deformed nuclei with theoretical formalism presented. We elaborate numerical details, and calculate the bound and resonant states in $^{37}$Mg. The results are compared with those from the coordinate representation calculations with a satisfactory agreement. In particular, the present method can expose clearly the resonant states in complex momentum plane and determine precisely the resonance parameters for not only narrow resonances but also broad resonances that were difficult to obtain before.