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

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