Probing resonances in the Dirac equation with quadrupole-deformed potentials with the complex momentum representation method

Resonances play critical roles in the formation of many physical phenomena, and many techniques have been developed for the exploration of resonances. In a recent letter [Phys. Rev. Lett. 117, 062502 (2016)PRLTAO0031-900710.1103/PhysRevLett.117.062502], we proposed a new method for probing single-particle resonances by solving the Dirac equation in complex momentum representation for spherical nuclei. Here, we develop the theoretical formalism of this method for deformed nuclei. We elaborate numerical details and calculate the bound and resonant states in Mg37. 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 a complex momentum plane and determine precisely the resonance parameters for not only narrow resonances but also broad resonances that were difficult to obtain before.