The authors review the present status of self-consistent mean-field (SCMF) models for describing nuclear structure and low-energy dynamics. These models are presented as effective energy-density functionals. The three most widely used variants of SCMF's based on a Skyrme energy functional, a Gogny force, and a relativistic mean-field Lagrangian are considered side by side. The crucial role of the treatment of pairing correlations is pointed out in each case. The authors discuss other related nuclear structure models and present several extensions beyond the mean-field model which are currently used. Phenomenological adjustment of the model parameters is discussed in detail. The performance quality of the SCMF model is demonstrated for a broad range of typical applications.

Self-consistent mean-field models for nuclear structure

http://cds.cern.ch/record/349359/files/9803035.pdf

Microscopic models for ultrarelativistic heavy ion collisions

A Skyrme parametrization from subnuclear to neutron star densities Part II. Nuclei far from stabilities

Recoil-ion and electron momentum spectroscopy is a rapidly developing technique that allows one to measure the vector momenta of several ions and electrons resulting from atomic or molecular fragmentation. In a unique combination, large solid angles close to 4π and superior momentum resolutions around a few per cent of an atomic unit (a.u.) are typically reached in state-of-the art machines, so-called reaction-microscopes. Evolving from recoil-ion and cold target recoil-ion momentum spectroscopy (COLTRIMS), reaction-microscopes—the `bubble chambers of atomic physics'—mark the decisive step forward to investigate many-particle quantum-dynamics occurring when atomic and molecular systems or even surfaces and solids are exposed to time-dependent external electromagnetic fields. This paper concentrates on just these latest technical developments and on at least four new classes of fragmentation experiments that have emerged within about the last five years. First, multi-dimensional images in momentum space brought unprecedented information on the dynamics of single-photon induced fragmentation of fixed-in-space molecules and on their structure. Second, a break-through in the investigation of high-intensity short-pulse laser induced fragmentation of atoms and molecules has been achieved by using reaction-microscopes. Third, for electron and ion-impact, the investigation of two-electron reactions has matured to a state such that the first fully differential cross sections (FDCSs) are reported. Fourth, comprehensive sets of FDCSs for single ionization of atoms by ion-impact, the most basic atomic fragmentation reaction, brought new insight, a couple of surprises and unexpected challenges to theory at keV to GeV collision energies. In addition, a brief summary on the kinematics is provided at the beginning. Finally, the rich future potential of the method is briefly envisaged.

/pdf/recoil-ion-and-electron-momentum-spectroscopy-reaction-c7ai542e3l.pdf

Recoil-ion and electron momentum spectroscopy: reaction-microscopes

The major uncertainties involved in the Chandrasekhar mass models for Type Ia supernovae (SNe Ia) are related to the companion star of their accreting white dwarf progenitor (which determines the accretion rate and consequently the carbon ignition density) and the flame speed after the carbon ignition. We calculate explosive nucleosynthesis in relatively slow deflagrations with a variety of deflagration speeds and ignition densities to put new constraints on the above key quantities. The abundance of the Fe group, in particular of neutron-rich species like 48Ca,50Ti,54Cr,54,58Fe, and 58Ni, is highly sensitive to the electron captures taking place in the central layers. The yields obtained from such a slow central deflagration, and from a fast deflagration or delayed detonation in the outer layers, are combined and put to comparison with solar isotopic abundances. To avoid excessively large ratios of 54Cr/56Fe and 50Ti/56Fe, the central density of the average white dwarf progenitor at ignition should be as low as 2 ? 109 g cm-3. To avoid the overproduction of 58Ni and 54Fe, either the flame speed should not exceed a few percent of the sound speed in the central low Ye layers or the metallicity of the average progenitors has to be lower than solar. Such low central densities can be realized by a rapid accretion as fast as -->img1.gif 1 ? 10-7 M? yr-1. In order to reproduce the solar abundance of 48Ca, one also needs progenitor systems that undergo ignition at higher densities. Even the smallest laminar flame speeds after the low-density ignitions would not produce sufficient amount of this isotope. We also found that the total amount of 56Ni, the Si-Ca/Fe ratio, and the abundance of some elements like Mn and Cr (originating from incomplete Si burning), depend on the density of the deflagration-detonation transition in delayed detonations. Our nucleosynthesis results favor transition densities slightly below 2.2 ? 107 g cm-3.

https://iopscience.iop.org/article/10.1086/313278/pdf

Nucleosynthesis in Chandrasekhar Mass Models for Type Ia Supernovae and Constraints on Progenitor Systems and Burning-Front Propagation

The effective Skyrme interaction has been used extensively in mean-field models for several decades and many different parametrizations of the interaction have been proposed. All of these give similar agreement with the experimental observables of nuclear ground states as well as with the properties of infinite symmetric nuclear matter at the saturation density n0. However, when applied over a wider range of densities (up to ∼3n0) they predict widely varying behavior for the observables of both symmetric and asymmetric nuclear matter. A particularly relevant example of naturally occurring asymmetric nuclear matter is the material of which neutron stars are composed. At around nuclear matter density, this can be well represented as a mixture of neutrons, protons, electrons, and muons (n+p+e+μ matter) in β-equilibrium, and these densities turn out to be the key ones for determining the properties of neutron-star models with masses near to the widely used “canonical” value of 1.4M⊙. By constructing equations of state for neutron-star matter using the different Skyrme parametrizations, calculating corresponding neutron-star models and then comparing these with observational data, an additional constraint can be obtained for the values of the Skyrme parameters. Such a constraint is particularly relevant because the parametrizations are initially determined by fitting to the properties of doubly closed-shell nuclei and it is an open question how suitable they then are for nuclei with high values of isospin, such as those at the neutron drip-line and beyond. The neutron-star environment provides an invaluable testing ground for this. We have carried out an investigation of 87 different Skyrme parametrizations in order to examine how successful they are in predicting the expected properties of infinite nuclear matter and generating plausible neutron-star models. This is the first systematic study of the predictions of the various Skyrme parametrizations for the density dependence of the characteristic observables of nuclear matter; the density dependence of the symmetry energy for β-equilibrium matter turns out to be a crucial property for indicating which Skyrme parameter sets will apply equally well for finite nuclei and for neutron-star matter. Only 27 of the 87 parametrizations investigated pass the test of giving satisfactory neutron-star models and we present a list of these.

Nuclear matter and neutron-star properties calculated with the Skyrme interaction

The Chandrasekhar-mass model for Type Ia supernovae (SNe Ia) has received increasing support from recent comparisons of observations with light-curve predictions and modeling of synthetic spectra. It explains SN Ia events via thermonuclear explosions of accreting white dwarfs in binary stellar systems, being caused by central carbon ignition when the white dwarf approaches the Chandrasekhar mass. As the electron gas in white dwarfs is degenerate, characterized by high Fermi energies for the high-density regions in the center, electron capture on intermediate-mass and Fe group nuclei plays an important role in explosive burning. Electron capture affects the central electron fraction Ye, which determines the composition of the ejecta from such explosions. Up to the present, astrophysical tabulations based on shell model matrix elements were available only for light nuclei in the sd-shell. Recently, new shell model Monte Carlo and large-scale shell model diagonalization calculations have also been performed for pf-shell nuclei. These lead in general to a reduction of electron capture rates in comparison with previous, more phenomenological, approaches. Making use of these new shell model-based rates, we present the first results for the composition of Fe group nuclei produced in the central regions of SNe Ia and possible changes in the constraints on model parameters like ignition densities ρign and burning front speeds vdef.

The Role of Electron Captures in Chandrasekhar-Mass Models for Type Ia Supernovae

We study a relativistic model of the nucleus consisting of nucleons coupled to mesonic degrees of freedom via an effective Lagrangian whose parameters are determined by a fit to selected nuclear ground-state data. We find that the model allows a very good description of nuclear ground-state properties. Because of the relativistic nature of the model, the spin properties are uniquely fixed. We discuss variations of the parametrization and of the data which suggest that the present fit has exhausted the limits of the mean-field approximation, and discuss extensions which go beyond the mean field.

/pdf/optimal-parametrization-for-the-relativistic-mean-field-15ab2v3t0b.pdf

Optimal parametrization for the relativistic mean-field model of the nucleus

The spectral distribution of isovector dipole strength is computed using the time-dependent Skyrme-Hartree-Fock method with subsequent spectral analysis The calculations are done without any imposed symmetry restriction, allowing any nuclear shape to be dealt with The scheme is used to study the deformation dependence of giant resonances and its interplay with Landau fragmentation (owing to 1 ph states) Results are shown for the chain of Nd isotopes, superdeformed Dy-152, triaxial Os-188, and U-238

https://epubs.surrey.ac.uk/234/1/fulltext.pdf

Dipole Giant Resonances in Deformed Heavy Nuclei

Properties of proton-rich nuclei around doubly magic $_{28}^{48}\mathrm{Ni}_{20}$ are studied in the framework of the self-consistent mean-field theory (Hartree-Fock, Hartree-Fock-Bogoliubov, and relativistic mean field). Various effective interactions are employed to investigate two-proton separation energies, deformations, single-particle levels, proton average potentials, and diproton partial decay half-lives in this mass region. \textcopyright{} 1996 The American Physical Society.

M. R. Strayer

Papers

Nuclear matter and neutron-star properties calculated with the Skyrme interaction

The Role of Electron Captures in Chandrasekhar-Mass Models for Type Ia Supernovae

Optimal parametrization for the relativistic mean-field model of the nucleus

Dipole Giant Resonances in Deformed Heavy Nuclei

Structure of proton drip-line nuclei around doubly magic 48Ni.