We present a simple scheme for taking into account the resonant continuum coupling in the Relativistic Mean Field-BCS (RMF-BCS) calculations. In this scheme, applied before in nonrelativistic calculations, the effect of the resonant continuum on pairing correlations is introduced through the scattering wave functions located in the region of the resonant states. These states are found by solving the relativistic mean field equations with scattering-type boundary conditions for continuum spectrum. The calculations are done for the neutron-rich Zr isotopes. It is shown that the sudden increase of the neutron radii close to the neutron drip line, the so-called giant halo, is determined by a few resonant states close to the continuum threshold.

The relationship between the nucleon density at large radii and the value of the rms radius is investigated in the framework of Skyrme Hartree-Fock and relativistic mean-field models. From a comparison to the charge density we constrain the models in terms of the nuclear matter incompressibility and effective mass properties required to reproduce the density shape. The results are used to extract the rms neutron radius for 208 Pb from antiprotonic atom data. The result for the difference between the neutron and proton rms radii, the so-called neutron-skin thickness, is S = 0.20(±0.04)(±0.05) fm, where ±0.04 fm is experimental error from the antiprotonic line width, and ±0.05 fm is the theoretical error suggested from the comparison of the models with the experimental charge density.The neutron-skin thickness is defined by S = R n − R p where R n and R p are the rms radii for point neutrons and protons, respectively. The neutron skin in heavy nuclei has been shown to be a unique measure of the density dependence of the neutron equation of state (EOS) near nuclear saturation density [1][2][3]. The density-dependent properties of the neutron EOS have a strong impact on the models of neutron stars [3][4][5][6][7]. Proton rms radii R p for stable nuclei are determined at a high level accuracy from electron scattering and muonic atom data. The charge rms radius obtained for 208 Pb is R ch = 5.5013(7) fm [8], which gives R p = 5.45 fm after taking into account the finite-size effects of the protons and neutrons [9]. Neutron rms radii are much more difficult to accurately determine. A model independent method of using the parity violating asymmetry in elastic scattering of electrons from 208 Pb to measure R n to a 1% (± 0.05 fm) accuracy is proposed for the PREX experiment at JLab [10]. There have been renewed attempts to obtain R n from hadronic scattering data [11,12], but the error due to the many-body strong interaction effects is difficult to quantify [13]. A third method has been to use antiprotonic atom data to constrain the properties of the matter density at large radii [14]. In this article we will explore how the densities at large radii are related to nuclear matter properties and to the neutron rms radius.A recent analysis of the x-ray cascade of antiprotonic atoms [15] has been carried out with zero-range and finite range models for the antiproton nucleus interactions. The analysis is based on two-parameter Fermi (2pF) shapes for the densities; ρ(r) = ρ 0 /[1 + exp(r − c)/a]. The proton density was fixed from the measured charge density using the 2pF shape fit obtianed by Fricke et al. [8] transformed to a 2pF shape for point-protons with the formula of Oset et al. [16]. Then a 2pF shape for neutrons was added. The matter density is the sum of the 2pF densities for protons and neutrons. In [15] equally good fits are obtained for a wide range of correlated c and a combinations for the neutron density with the resulting matter density curves shown in Fig. 1. The curves cross near r = 9.8 fm indicating that th...

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.