Scalar ground-state observables in the random phase approximation

We calculate the ground-state expectation value of scalar observables in the matrix formulation of the random phase approximation (RPA). Our expression, derived using the quasiboson approximation, is a straightforward generalization of the RPA correlation energy. We test the reliability of our expression by comparing against full diagonalization in 0 h-bar omega shell-model spaces. In general the RPA values are an improvement over mean-field (Hartree-Fock) results, but are not always consistent with shell-model results. We also consider exact symmetries broken in the mean-field state and whether or not they are restored in RPA.Comment: 7 pages, 3 figure

Combinatorial Level Densities from a Microscopic Relativistic Structure Model

A new model for calculating nuclear level densities is investigated. The single-nucleon spectra are calculated in a relativistic mean-field model with energy-dependent effective mass, which yields a realistic density of single-particle states at the Fermi energy. These microscopic single-nucleon states are used in a fast combinatorial algorithm for calculating the non-collective excitations of nuclei. The method, when applied to magic and semi-magic nuclei, such as $^{60}$Ni, $^{114}$Sn and $^{208}$Pb, reproduces the cumulative number of experimental states at low excitation energy, as well as the s-wave neutron resonance spacing at the neutron binding energy. Experimental level densities above 10 MeV are reproduced by multiplying the non-collective level densities by a simple vibrational enhancement factor. Problems to be solved in the extension to open-shell nuclei are discussedComment: 22 pages, 5 figures, revised version, to appear in Nucl. Phys.

Combinatorial nuclear level density by a Monte Carlo method

We present a new combinatorial method for the calculation of the nuclear level density. It is based on a Monte Carlo technique, in order to avoid a direct counting procedure which is generally impracticable for high-A nuclei. The Monte Carlo simulation, making use of the Metropolis sampling scheme, allows a computationally fast estimate of the level density for many fermion systems in large shell model spaces. We emphasize the advantages of this Monte Carlo approach, particularly concerning the prediction of the spin and parity distributions of the excited states, and compare our results with those derived from a traditional combinatorial or a statistical method. Such a Monte Carlo technique seems very promising to determine accurate level densities in a large energy range for nuclear reaction calculations.Comment: 30 pages, LaTex, 7 figures (6 Postscript figures included). Fig. 6 upon request to the autho

Pairing Properties In Relativistic Mean Field Models Obtained From Effective Field Theory

We apply recently developed effective field theory nuclear models in mean field approximation (parameter sets G1 and G2) to describe ground-state properties of nuclei from the valley of $\beta$-stability up to the drip lines. For faster calculations of open-shell nuclei we employ a modified BCS approach which takes into account quasi-bound levels owing to their centrifugal barrier, with a constant pairing strength. We test this simple prescription by comparing with available Hartree-plus-Bogoliubov results. Using the new effective parameter sets we then compute separation energies, density distributions and spin--orbit potentials in isotopic (isotonic) chains of nuclei with magic neutron (proton) numbers. The new forces describe the experimental systematics similarly to conventional non-linear $\sigma-\omega$ relativistic force parameters like NL3.Comment: 29 pages, 17 figures, accepted for publication in PR

Cohomological tautness for Riemannian foliations

In this paper we present some new results on the tautness of Riemannian foliations in their historical context. The first part of the paper gives a short history of the problem. For a closed manifold, the tautness of a Riemannian foliation can be characterized cohomologically. We extend this cohomological characterization to a class of foliations which includes the foliated strata of any singular Riemannian foliation of a closed manifold

Shape Coexistence and the Effective Nucleon-Nucleon Interaction

The phenomenon of shape coexistence is discussed within the self-consistent Hartree-Fock method and the nuclear shell model. The occurrence of the coexisting configurations with different intrinsic shapes is traced back to the properties of the effective Hamiltonian.Comment: 40 pages (16 text, 24 figures). The file may also be retrieved at http://csep2.phy.ornl.gov/theory_group/people/dean/shape_coex/shapes.htm

Axially symmetric Hartree-Fock-Bogoliubov Calculations for Nuclei Near the Drip-Lines

Nuclei far from stability are studied by solving the Hartree-Fock-Bogoliubov (HFB) equations, which describe the self-consistent mean field theory with pairing interaction. Calculations for even-even nuclei are carried out on two-dimensional axially symmetric lattice, in coordinate space. The quasiparticle continuum wavefunctions are considered for energies up to 60 MeV. Nuclei near the drip lines have a strong coupling between weakly bound states and the particle continuum. This method gives a proper description of the ground state properties of such nuclei. High accuracy is achieved by representing the operators and wavefunctions using the technique of basis-splines. The detailed representation of the HFB equations in cylindrical coordinates is discussed. Calculations of observables for nuclei near the neutron drip line are presented to demonstrate the reliability of the method.Comment: 13 pages, 4 figures. Submitted to Physical Review C on 05/08/02. Revised on Dec/0

Shell structure of superheavy nuclei in self-consistent mean-field models

We study the extrapolation of nuclear shell structure to the region of superheavy nuclei in self-consistent mean-field models -- the Skyrme-Hartree-Fock approach and the relativistic mean-field model -- using a large number of parameterizations. Results obtained with the Folded-Yukawa potential are shown for comparison. We focus on differences in the isospin dependence of the spin-orbit interaction and the effective mass between the models and their influence on single-particle spectra. While all relativistic models give a reasonable description of spin-orbit splittings, all non-relativistic models show a wrong trend with mass number. The spin-orbit splitting of heavy nuclei might be overestimated by 40%-80%. Spherical doubly-magic superheavy nuclei are found at (Z=114,N=184), (Z=120,N=172) or (Z=126,N=184) depending on the parameterization. The Z=114 proton shell closure, which is related to a large spin-orbit splitting of proton 2f states, is predicted only by forces which by far overestimate the proton spin-orbit splitting in Pb208. The Z=120 and N=172 shell closures predicted by the relativistic models and some Skyrme interactions are found to be related to a central depression of the nuclear density distribution. This effect cannot appear in macroscopic-microscopic models which have a limited freedom for the density distribution only. In summary, our findings give a strong argument for (Z=120,N=172) to be the next spherical doubly-magic superheavy nucleus.Comment: 22 pages REVTeX, 16 eps figures, accepted for publication in Phys. Rev.

Shell Corrections of Superheavy Nuclei in Self-Consistent Calculations

Shell corrections to the nuclear binding energy as a measure of shell effects in superheavy nuclei are studied within the self-consistent Skyrme-Hartree-Fock and Relativistic Mean-Field theories. Due to the presence of low-lying proton continuum resulting in a free particle gas, special attention is paid to the treatment of single-particle level density. To cure the pathological behavior of shell correction around the particle threshold, the method based on the Green's function approach has been adopted. It is demonstrated that for the vast majority of Skyrme interactions commonly employed in nuclear structure calculations, the strongest shell stabilization appears for Z=124, and 126, and for N=184. On the other hand, in the relativistic approaches the strongest spherical shell effect appears systematically for Z=120 and N=172. This difference has probably its roots in the spin-orbit potential. We have also shown that, in contrast to shell corrections which are fairly independent on the force, macroscopic energies extracted from self-consistent calculations strongly depend on the actual force parametrisation used. That is, the A and Z dependence of mass surface when extrapolating to unknown superheavy nuclei is prone to significant theoretical uncertainties.Comment: 14 pages REVTeX, 8 eps figures, submitted to Phys. Rev.

Continuum effects for the mean-field and pairing properties of weakly bound nuclei

Continuum effects in the weakly bound nuclei close to the drip-line are investigated using the analytically soluble Poschl-Teller-Ginocchio potential. Pairing correlations are studied within the Hartree-Fock-Bogoliubov method. We show that both resonant and non-resonant continuum phase space is active in creating the pairing field. The influence of positive-energy phase space is quantified in terms of localizations of states within the nuclear volume.Comment: 27 RevTeX pages, 12 EPS figures included, submitted to Physical Review