Green's function method for single-particle resonant states in relativistic mean field theory

Abstract

Relativistic mean field theory is formulated with the Green's function method in coordinate space to investigate the single-particle bound states and resonant states on the same footing. Taking the density of states for free particle as a reference, the energies and widths of single-particle resonant states are extracted from the density of states without any ambiguity. As an example, the energies and widths for single-neutron resonant states in 120 Sn are compared with those obtained by the scattering phase-shift method, the analytic continuation in the coupling constant approach, the real stabilization method and the complex scaling method. Excellent agreements are found for the energies and widths of single-neutron resonant states.

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

“…This method has avoided all the defects in the CSM, and has been used to explore the bound states [30,31] and resonant states [32,33] in the nonrelativistic case, and used as the so-called "Berggren representation" in the shellmodel calculations [34,35]. Considering that the relativistic resonances are widely concerned, almost all the methods for resonances have been extended to the relativistic framework [36][37][38][39][40][41][42], including the relativistic CSM [22,27] and relativistic complex scaled Green's function method [25]. Recently, we applied the CMR method to the relativistic mean-field (RMF) framework and established the RMF-CMR method for the resonances in the spherical case [43], in which both bound states and resonant states have been treated on the same footing.…”

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.…”

Single particle states in the Fermi sea and Dirac sea in spherical nuclei

“…郭等 人 [20] 做了一些近似, 曾给出了伍兹 -萨克森势下狄 拉克方程的近似解析解. 目前, 尚没有得到伍兹 -萨 图 1 (网络版彩图) 协变密度泛函理论框架下核子运动的平 均势场、费米海和狄拉克海及其中的束缚能级与连续谱 [21,22] . 如果只 关心束缚态, 则常常采用 "盒子" 边界条件, 这样, 连 续谱被分立化.…”