Probing Resonances In Deformed Nuclei 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,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 37Mg.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.The detailed content is in the following:Firstly,this paper introduces the physical meanings of resonant states for deformed nuclei,and the methods for exploring the resonant states in recent years,including:the R matrix method,the extended the R matrix method,the K-matrix method,the S-matrix method,the Jost function method and the Green functions method,the real stabilization method(RSM),the analytic continuation in the coupling constant approach method(ACCC),the complex scaling method(CSM)and the complex momentum representation method(CMR),and so on.Secondly,the theoretical framework of the RMF-CMR theory is introduced in detail,which includes the relativistic mean field theory(RMF),the complex momentum representation method(CMR)and the calculation of deformation nuclei by combining relativistic mean field theory with the complex momentum represent ion method(RMF-CMR).Finally,the single particle bound states and the resonant states properties of the quadrupole-deformed nuclei are explored with the RMF-CMR method,and compared with the ACCC method under the coordinate representation.In addition,the level density,widths and the wave functions in the momentum representation and the coordinate representations are calculated.The physical mechanism of halo in 37Mg is clarified,which comes from a resonance of p-wave.