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

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.

arXiv comment10pages,7figures

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Cited by in corpus (8)

• Missed prediction of the neutron halo in ${}^{37}$Mg
• Green's function method for the single-particle resonances in a deformed Dirac equation
• Green's function method for the spin and pseudospin symmetries in the single-particle resonant states
• Combination of complex momentum representation and Green's function methods in relativistic mean-field theory
• Research on the halo in ${}^{31}$Ne with complex momentum representation method
• Role of quadrupole deformation and continuum effects in the "island of inversion'' nuclei ${}^{28,29,31}$F
• Time-dependent Dirac equation applied to one-proton radioactive emission
• Dirac Equation Solution with Generalized tanh-Shaped Hyperbolic Potential: Application to Charmonium and Bottomonium Mass Spectra