Particles in classically forbidden area, neutron skin and halo, and pure neutron matter in Ca isotopes

The nucleon density distributions and the thickness of pure neutron matter in Ca isotopes were systematically studied using the Skyrme-Hartree-Fock model (SHF) from the $\beta$-stability line to the neutron drip-line. The pure neutron matter, related with the neutron skin or halo, was shown to depend not only on the Fermi levels of the neutrons but also on the orbital angular momentum of the valence neutrons. New definitions for the thickness of pure neutron matter are proposed.Comment: 6 pages, 5 figure

First order shape transition and critical point nuclei in Sm isotopes from relativistic mean field approach

The critical point nuclei in Sm isotopes, which marks the first order phase transition between spherical U(5) and axially deformed shapes SU(3), have been investigated in the microscopic quadrupole constrained relativistic mean field (RMF) model plus BCS method with all the most used interactions, i.e., NL1, NL3, NLSH and TM1. The calculated potential energy surfaces show a clear shape transition for the even-even Sm isotopes with $N = 82\sim 96$ and the critical point nuclei are found to be $^{148}$Sm, $^{150}$Sm and $^{152}$Sm. Similar conclusions can also be drawn from the microscopic neutron and proton single particle spectra.Comment: 6 figure

Spherical Relativistic Hartree theory in a Woods-Saxon basis

The Woods-Saxon basis has been suggested to replace the widely used harmonic oscillator basis for solving the relativistic mean field (RMF) theory in order to generalize it to study exotic nuclei. As examples, relativistic Hartree theory is solved for spherical nuclei in a Woods-Saxon basis obtained by solving either the Schr\"odinger equation or the Dirac equation (labelled as SRHSWS and SRHDWS, respectively and SRHWS for both). In SRHDWS, the negative levels in the Dirac Sea must be properly included. The basis in SRHDWS could be smaller than that in SRHSWS which will simplify the deformed problem. The results from SRHWS are compared in detail with those from solving the spherical relativistic Hartree theory in the harmonic oscillator basis (SRHHO) and those in the coordinate space (SRHR). All of these approaches give identical nuclear properties such as total binding energies and root mean square radii for stable nuclei. For exotic nuclei, e.g., $^{72}$Ca, SRHWS satisfactorily reproduces the neutron density distribution from SRHR, while SRHHO fails. It is shown that the Woods-Saxon basis can be extended to more complicated situations for exotic nuclei where both deformation and pairing have to be taken into account.Comment: 12 pages, 9 figure

A systematic study of Zr and Sn isotopes in the Relativistic Mean Field theory

The ground-state properties of Zr and Sn isotopes are studied within the relativistic mean field theory. Zr and Sn isotopes have received tremendous attention due to various reasons, including the predicted giant halos in the neutron-rich Zr isotopes, the unique feature of being robustly spherical in the region of $^{100}$Sn $\sim$ $^{132}$Sn and the particular interest of Sn isotopes to nuclear astrophysics. Furthermore, four (semi-) magic neutron numbers, 40, 50, 82 and 126, make these two isotopic chains particularly important to test the pairing correlations and the deformations in a microscopic model. In the present work, we carry out a systematic study of Zr and Sn isotopes from the proton drip line to the neutron drip line with deformation effects, pairing correlations and blocking effects for nuclei with odd number of neutrons properly treated. A constrained calculation with quadrupole deformations is performed to find the absolute minimum for each nucleus on the deformation surface. All ground-state properties, including the separation energies, the odd-even staggerings, the nuclear radii, the deformations and the single-particle spectra are analyzed and discussed in detail.Comment: the final version to appear in Modern Physics Letters A. more figures, discussions, and references added. the data remain unchange

Proton drip-line nuclei in Relativistic Hartree-Bogoliubov theory

Ground-state properties of spherical even-even nuclei $14\leq Z \leq 28$ and $N=18,20,22$ are described in the framework of Relativistic Hartree Bogoliubov (RHB) theory. The model uses the NL3 effective interaction in the mean-field Lagrangian, and describes pairing correlations by the pairing part of the finite range Gogny interaction D1S. Binding energies, two-proton separation energies, and proton $rms$ radii that result from fully self-consistent RHB solutions are compared with experimental data. The model predicts the location of the proton drip-line. The isospin dependence of the effective spin-orbit potential is discussed, as well as pairing properties that result from the finite range interaction in the $pp$ channel.Comment: 12 pages, RevTex, 10 p.s figures, submitted to Phys. Rev.

Halos and related structures

The halo structure originated in nuclear physics but is now encountered more widely. It appears in loosely bound, clustered systems where the spatial extension of the system is significantly larger than that of the binding potentials. A review is given on our current understanding of these structures, with an emphasis on how the structures evolve as more cluster components are added, and on the experimental situation concerning halo states in light nuclei.Comment: 27 pages, 3 figures, Contribution to Nobel Symposium 152 "Physics With Radioactive Beams

Neutron density distributions for atomic parity nonconservation experiments

The neutron distributions of Cs, Ba, Yb and Pb isotopes are described in the framework of relativistic mean-field theory. The self-consistent ground state proton and neutron density distributions are calculated with the relativistic Hartree-Bogoliubov model. The binding energies, the proton and neutron radii, and the quadrupole deformations are compared with available experimental data, as well as with recent theoretical studies of the nuclear structure corrections to the weak charge in atomic parity nonconservation experiments.Comment: 16 pages, RevTex, 11 eps figs, submitted to Phys. Rev.

A Dirac-Hartree-Bogoliubov approximation for finite nuclei

We develop a complete Dirac-Hartree-Fock-Bogoliubov approximation to the ground state wave function and energy of finite nuclei. We apply it to spin-zero proton-proton and neutron-neutron pairing within the Dirac-Hartree-Bogoliubov approximation (we neglect the Fock term), using a zero-range approximation to the relativistic pairing tensor. We study the effects of the pairing on the properties of the even-even nuclei of the isotopic chains of Ca, Ni and Sn (spherical) and Kr and Sr (deformed), as well as the $N$=28 isotonic chain, and compare our results with experimental data and with other recent calculations.Comment: 43 pages, RevTex, 13 figure

Shell Effects in Nuclei with Vector Self-Coupling of Omega Meson in Relativistic Hartree-Bogoliubov Theory

Shell effects in nuclei about the stability line are investigated within the framework of the Relativistic Hartree-Bogoliubov (RHB) theory with self-consistent finite-range pairing. Using 2-neutron separation energies of Ni and Sn isotopes, the role of $\sigma$- and $\omega$-meson couplings on the shell effects in nuclei is examined. It is observed that the existing successful nuclear forces (Lagrangian parameter sets) based upon the nonlinear scalar coupling of $\sigma$-meson exhibit shell effects which are stronger than suggested by the experimental data. We have introduced nonlinear vector self-coupling of $\omega$-meson in the RHB theory. It is shown that the inclusion of the vector self-coupling of $\omega$-meson in addition to the nonlinear scalar coupling of $\sigma$-meson provides a good agreement with the experimental data on shell effects in nuclei about the stability line. A comparison of the shell effects in the RHB theory is made with the Hartree-Fock Bogoliubov approach using the Skyrme force SkP. It is shown that the oft-discussed shell quenching with SkP is not consistent with the available experimental data.Comment: 34 pages latex, 18 ps figures, replaced with minor corrections in some figures, accepted for publication in Phys. Rev.