Analytic continuation of single-particle resonance energy and wave function in relativistic mean field theory

Abstract

Single-particle resonant states in spherical nuclei are studied by an analytic continuation in the coupling constant (ACCC) method within the framework of the self-consistent relativistic mean field (RMF) theory. Taking the neutron resonant state ν1g 9/2 in 60 Ca as an example, we examine the analyticity of the eigenvalue and eigenfunction for the Dirac equation with respect to the coupling constant by means of a Padé approximant of the second kind. The RMF-ACCC approach is then applied to 122 Zr and, for the first time, this approach is employed to investigate both the energies, widths and wave functions for l = 0 resonant states close to the continuum threshold.Predictions are also compared with corresponding results obtained from the scattering phase shift method.

Shell-model-like Approach (SLAP) for the Nuclear Properties in Relativistic Mean Field Theory

“…In order to justify the description for nuclei close to the drip line, the analytical continuation in coupling constant (ACCC) method or the S-matrix method [22,24,25] should be adopted to resort the resonance states. The works along this line is in progress.…”

“…This aspect becomes all the more important when considering the continuum effects, which are crucial for the description of drip line nuclei. So far the most commonly used methods, the Bardeen-Cooper-Schrieffer (BCS) approximation and Bogoliubov transformation, have become standard in the nuclear physics literatures [18,19], even for exotic nuclei where the Bogoliubov transformation is required to be done in coordinate space [4,8,20,21] or the introduction of the resonant states is necessary [22,23,24,25].…”

Real stabilization method for nuclear single-particle resonances

“…[22] where resonant parameters of some low lying resonant states in 16 O and 48 Ca obtained from the ACCC calculations are comparable with available data. The wave functions of nuclear resonant states were also determined by the ACCC method where the bound states are obtained by solving either the Schrödinger equation with a Woods-Saxon potential [23] or the Dirac equation with self-consistent RMF potentials [24].…”

Exploration of direct neutron capture with covariant density functional theory inputs

“…This RMF+ACCC+BCS approach [18,19], denoted by RAB for simplicity below, was recently used to describe s.p. levels in unstable nuclei including 131,133 Sn [12], and the p-wave halo nucleus 31 Ne [16].…”

“…The s.p. level energies, normalized to one-neutron separation energy, are crucial inputs for FRESCO, for which we used three sources: available data [28]; RMF model predic- tions; and our developed RAB approach [18] with the NL3 effective interactions [29]. The FRESCO code internally optimizes Woods-Saxon shape potential to reproduce the input bound s.p.…”