This paper presents a detailed assessment of the ability of the 240 Skyrme interaction parameter sets in the literature to satisfy a series of criteria derived from macroscopic properties of nuclear matter in the vicinity of nuclear saturation density at zero temperature and their density dependence, derived by the liquid-drop model, in experiments with giant resonances and heavy-ion collisions. The objective is to identify those parametrizations which best satisfy the current understanding of the physics of nuclear matter over a wide range of applications. Out of the 240 models, only 16 are shown to satisfy all these constraints. Additional, more microscopic, constraints on the density dependence of the neutron and proton effective mass $\beta$-equilibrium matter, Landau parameters of symmetric and pure neutron nuclear matter, and observational data on high- and low-mass cold neutron stars further reduce this number to 5, a very small group of recommended Skyrme parametrizations to be used in future applications of the Skyrme interaction of nuclear-matter-related observables. Full information on partial fulfillment of individual constraints by all Skyrme models considered is given. The results are discussed in terms of the physical interpretation of the Skyrme interaction and the validity of its use in mean-field models. Future work on application of the Skyrme forces, selected on the basis of variables of nuclear matter, in the Hartree-Fock calculation of properties of finite nuclei, is outlined.

The nuclear mean-field model based on Skyrme forces or related density functionals has found widespread application to the description of nuclear ground states, collective vibrational excitations, and heavy-ion collisions. The code Sky3D solves the static or dynamic equations on a three-dimensional Cartesian mesh with isolated or periodic boundary conditions and no further symmetry assumptions. Pairing can be included in the BCS approximation for the static case. The code is implemented with a view to allow easy modifications for including additional physics or special analysis of the results.Program summaryProgram title: Sky3DCatalogue identifier: AESW_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AESW_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 43187No. of bytes in distributed program, including test data, etc.: 1423973Distribution format: tar.gzProgramming language: Fortran 90. The OpenMP version requires a relatively recent compiler; it was found to work using gfortran 4.6.2 or later and the Intel compiler version 12 or later.Computer: All computers with a Fortran compiler supporting at least Fortran 90.Operating system: All operating systems with such a compiler. Some of the Makefiles and scripts depend on a Unix-like system and need modification under Windows.Has the code been vectorized or parallelized?: Yes, Runs under OpenMP and MPI, unlimited number of processors can be used.RAM: 1 GBClassification: 17.16, 17.22, 17.23.External routines: LAPACK, FFTW3Nature of problem:The time-dependent Hartree–Fock equations can be used to simulate nuclear vibrations and collisions between nuclei for low energies. This code implements the equations based on a Skyrme energy functional and also allows the determination of the ground-state structure of nuclei through the static version of the equations. For the case of vibrations the principal aim is to calculate the excitation spectra by Fourier-analyzing the time dependence of suitable observables. In collisions, the formation of a neck between nuclei, the dissipation of energy from collective motion, processes like charge transfer and the approach to fusion are of principal interest.Solution method:The nucleonic wave function spinors are represented on a three-dimensional Cartesian mesh with no further symmetry restrictions. The boundary conditions are always periodic for the wave functions, while the Coulomb potential can also be calculated for an isolated charge distribution. All spatial derivatives are evaluated using the finite Fourier transform method. The code solves the static Hartree–Fock equations with a damped gradient iteration method and the time-dependent Hartree–Fock equations with an expansion of the time-development operator. Any number of initial nuclei can be placed into the mesh in with arbitrary positions and initial velocities.Restrictions:The reliability of the mean-field approximation is limited by the absence of hard nucleon–nucleon collisions. This limits the scope of applications to collision energies about a few MeV per nucleon above the Coulomb barrier and to relatively short interaction times. Similarly, some of the missing time-odd terms in the implementation of the Skyrme interaction may restrict the applications to even–even nuclei.Unusual features:The possibility of periodic boundary conditions and the highly flexible initialization make the code also suitable for astrophysical nuclear-matter applications.Running time:The running time depends strongly on the size of the grid, the number of nucleons, and the duration of the collision. For a single-processor PC-type computer it can vary between a few minutes and weeks

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 $n_0.$ However, when applied over a wider range of densities (up to $\sim {3n}_0)$ 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 $(n+p+e+\mu$ matter) in $\beta$-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 ${1.4M}_{\odot }.$ 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 $\beta$-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.

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 1ph states). Results are shown for the chain of Nd isotopes, superdeformed ${}^{152}\mathrm{Dy}$, triaxial ${}^{188}\mathrm{Os}$, and ${}^{238}\mathrm{U}$.

Background: Nuclear fission is a complex large-amplitude collective decay mode in heavy nuclei. Microscopic density functional studies of fission have previously concentrated on adiabatic approaches based on constrained static calculations ignoring dynamical excitations of the fissioning nucleus and the daughter products.