Probing resonances in the Dirac equation with quadrupole-deformed potentials with the 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.

Microscopic studies on nuclear spin-isospin properties—a personal perspective on covariant density functional theory

“…In order to probe the single-particle resonances in the relativistic scheme, a method for solving the Dirac equation in the complex momentum space was developed recently. It has been found that this method is not only very effective for the narrow resonances, but also can be reliably applied to the broad resonances [15,16]. This is potentially crucial for understanding some exotic properties of halo nuclei.…”

“…In the right panel of Fig. 1, the SD excitations in 16 O are shown as an example. Note that the three components could not be distinguished experimentally until an experiment with the high-quality polarized proton beam performed in RCNP in 2011 [23].…”

“…Figure 3 shows the results of RBHF calculations for 16 O with Bonn A interaction. First of all, the non-relativistic BHF calculation without the three-body force is away from the data.…”

“…Figure 1: Strength distributions of the Gamow-Teller resonances in 208 Pb (left) and the spin-dipole excitations in16 O (right) by the self-consistent RHF+RPA approach. Taken from Refs [21,22]…”

Structure of Exotic Nuclei: a Theoretical Review

“…Besides the conventional scattering phase shift method [54], several bound-state-like approaches [55,56], such as the analytical continuation in coupling constant [57,58,59,60,61,62], the real stabilization method [63,64,65] and the complex scaling method (CSM) [66,67,68,69], are often used to study single particle resonances in atomic nuclei. Several other methods, e.g., the Jost function method [70,71], the Green's function method [72,73], the Green's function + CSM [69,74], and solving Schrödinger or Dirac equations in the complex momentum representation [75,76], have also been implemented in nuclear models.…”