J. Dobaczewski

Hartree-Fock-Bogolyubov description of nuclei near the neutron-drip line

Abstract We consider the Hartree-Fock-Bogolyubov theory of nuclei in the coordinate representation and derive and solve the HFB equation for the Skyrme effective interaction. Ground-state wave functions and energies of the tin isotopes with 100 ⩽ A ⩽ 176 have been determined and the results have been compared with the predictions of the HF+BCS and macroscopic-microscopic models. The lightest tin isotope which is unstable with respect to a neutron emission is predicted by the HFB method to be 153 Sn. In the region of nuclei where experimental data are not available the macroscopic-microscopic and self-consistent approximations give substantially different results.

Mean-field description of ground-state properties of drip-line nuclei: Pairing and continuum effects

Ground-state properties of exotic even-even nuclei with extreme neutron-to-proton ratios are described in the framework of self-consistent mean-field theory with pairing formulated in coordinate space. This theory properly accounts for the influence of the particle continuum, which is particularly important for weakly bound systems. The pairing properties of nuclei far from stability are studied with several interactions emphasizing different aspects, such as the range and density dependence of the effective interaction. Measurable consequences of spatially extended pairing fields are presented, and the sensitivity of the theoretical predictions to model details is discussed. {copyright} {ital 1996 The American Physical Society.}

Shell structure of the superheavy elements

Abstract Ground-state properties of the superheavy elements (SHE) with 108 ⩽ Z ⩽ 128 and 150 ⩽ N ⩽ 192 are investigated using both the Skyrem-Hartree-Fock method with a density-independent contact pairing interaction and the macroscopic-microscopic approach with an average Woods-Saxon potential and a monopole pairing interaction. Detailed analysis of binding energies, separation energies, shell effects, single-proton and neutron states, equilibrium deformations, Qα-values, and other observables is given.

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. {copyright} {ital 1999} {ital The American Physical Society}

Systematic study of deformed nuclei at the drip lines and beyond

An improved prescription for choosing a transformed harmonic oscillator (THO) basis for use in configuration-space Hartree-Fock-Bogoliubov (HFB) calculations is presented. The new HFB+THO framework that follows accurately reproduces the results of coordinate-space HFB calculations for spherical nuclei, including those that are weakly bound. Furthermore, it is fully automated, facilitating its use in systematic investigations of large sets of nuclei throughout the periodic table. As a first application, we have carried out calculations using the Skyrme Force SLy4 and volume pairing, with exact particle number projection following application of the Lipkin-Nogami prescription. Calculations were performed for all even-even nuclei from the proton drip line to the neutron drip line having proton numbers Z=2,4,...,108 and neutron numbers N=2,4,...,188. We focus on nuclei near the neutron drip line and find that there exist numerous particle-bound even-even nuclei (i.e., nuclei with negative Fermi energies) that have at the same time negative two-neutron separation energies. This phenomenon, which was earlier noted for light nuclei, is attributed to bound shape isomers beyond the drip line.

Odd-Even Staggering of Nuclear Masses: Pairing or Shape Effect?

The odd-even staggering of nuclear masses was recognized in the early days of nuclear physics. Recently, a similar effect was discovered in other finite fermion systems, such as ultrasmall metallic grains and metal clusters. It is believed that the staggering in nuclei and grains is primarily due to pairing correlations (superconductivity), while in clusters it is caused by the Jahn-Teller effect. We find that, for light- and medium-mass nuclei, the staggering has two components. The first originates from pairing while the second, comparable in magnitude, has its roots in the deformed mean field. {copyright} {ital 1998} {ital The American Physical Society }

Analysis of the generator coordinate method in a study of shape isomerism in 194Hg

Abstract We investigate the properties of the generator coordinate method (GCM) on a collective basis of BCS states. The method is applied to a study of large-amplitude quadrupole dynamics in the nucleus 194 Hg. Among the GCM levels, we discuss candidates for a possible shape isomerism associated with a secondary deformed minimum at large deformation ( Q ≈ 45b). We also analyze standard approximation schemes based on the gaussian overlap approximation which lead to a collective Schrodinger equation. We compare their predictions with the exact GCM results for the particular case of 194 Hg.

Influence of shell-quenching far from stability on the astrophysical r-process

Abstract Comparison of results from r-process calculations within the waiting-point assumption and the r-process component ( N r ,⊙ ) of the solar-system composition of heavy elements, permits to test nuclear structure far from stability. Previous investigations, making use of nuclear mass predictions from global macroscopic-microscopic models, showed abundance deficiencies around A ∼- 120 and 140, indicating an overly strong N = 82 strength(some models also showed problems around A ∼- 180 related to the N = 126 shell). In this paper we calculate masses based on Skyrme interactions locally around N = 82, within the HF+BCS method with the SIII interaction and the HFB theory with SkP interaction. The shell-quenching obtained in the latter approach results in a considerable improvement of the global N r ,⊙ fit, indicating a solution to a puzzle existing in r-process nucleosynthesis.

Error Estimates of Theoretical Models: a Guide

This guide offers suggestions/insights on uncertainty quantification of nuclear structure models. We discuss a simple approach to statistical-error estimates, strategies to assess systematic errors, and show how to uncover inter-dependences by correlation analysis. The basic concepts are illustrated through simple examples. By providing theoretical error bars on predicted quantities and using statistical methods to study correlations between observables, theory can significantly enhance the feedback between experiment and nuclear modeling.

Coordinate-space solution of the Skyrme-Hartree-Fock-Bogolyubov equations within spherical symmetry. The program HFBRAD (v1.00)

Abstract We describe the first version (v1.00) of the code hfbrad which solves the Skyrme–Hartree–Fock or Skyrme–Hartree–Fock–Bogolyubov equations in the coordinate representation with spherical symmetry. A realistic representation of the quasiparticle wave functions on the space lattice allows calculations to be performed up to the particle drip lines. Zero-range density-dependent interactions are used in the pairing channel. The pairing energy is calculated by either using a cut-off energy in the quasiparticle spectrum or the regularization scheme proposed by A. Bulgac and Y. Yu. Program summary Title of the program: hfbrad (v1.00) Catalogue indentifier:ADVM Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADVM Program obtainable from: CPC Program Library, Queens University of Belfast, N. Ireland Licensing provisions: none Computers on which the program has been tested: Pentium-III, Pentium-IV Operating systems: LINUX, Windows Programming language used:FORTRAN-95 Memory required to execute with typical data: 30 MBytes No. of bits in a word: The code is written with a type real and uses the intrinsic function selected_real_kind at the beginning of the code to ask for at least 12 significant digits. This can be easily modified by asking for more significant digits if the architecture of the computer can handle it. No. of processors used:1 Has the code been vectorized?:No No. of bytes in distributed program, including test data, etc.: 40 308 No. of lines in distributed program, including test data, etc.: 5370 Distribution format:tar.gz Nature of physical problem: For a self-consistent description of nuclear pair correlations, both the particle–hole (field) and particle–particle (pairing) channels of the nuclear mean field must be treated within a common approach, which is the Hartree–Fock–Bogolyubov theory. By expressing these fields in spatial coordinates one can obtain the best possible solutions of the problem; however, without assuming specific symmetries the numerical task is often too difficult. This is not the case when the spherical symmetry is assumed, because then the one-dimensional differential equations can be solved very efficiently. Although the spherically symmetric solutions are physically meaningful only for magic and semi-magic nuclei, the possibility of obtaining them within tens of seconds of the CPU makes them a valuable element for studying nuclei across the nuclear chart, including those near or at the drip lines. Method of solution: The program determines the two-component Hartree–Fock–Bogolyubov quasiparticle wave functions on the lattice of equidistant points in the radial coordinate. This is done by solving the eigensystem of two second-order differential equations using the Numerov method. A standard iterative procedure is then used to find self-consistent solutions for the nuclear product wave functions and densities. Restrictions on the complexity of the problem: The main restriction is related to the assumed spherical symmetry. Typical running time: One Hartree–Fock iteration takes about 0.4 s for a medium mass nucleus, convergence is achieved in about 40 s. Unusual features of the program: none