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 β-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

The spectral distribution of isovector dipole strength is computed using the time-dependent Skyrme-HartreeFock 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 Dy, triaxial 188 Os, and 238 U.

Absorbing boundary conditions are often employed in time-dependent mean-field calculations to cope with the problem of emitted particles which would otherwise return back onto the system and falsify the dynamical evolution. We scrutinize two widely used methods, imaginary potentials and gradual attenuation by a mask function. To that end, we consider breathing oscillations of a 16 O nucleus computed on a radial onedimensional grid in coordinate space. The most critical test case is the computation of resonance spectra in the ͑linear͒ domain of small amplitude motion. Absorbing bounds turn out to provide a reliable alternative to fully fledged continuum random phase approximation ͑RPA͒ calculations, although rather large absorbing bounds are required to simulate reliably well continuum conditions. We also investigate the computation of observables in the nonlinear domain. This regime turns out to be less demanding. Smaller absorbing margin suffice to achieve the wanted absorption effect.

We investigate the role of odd-odd (with respect to time inversion) couplings in the Skyrme force on collisions of light nuclei, employing a fully three-dimensional numerical treatment without any symmetry restrictions and with modern Skyrme functionals. We demonstrate the necessity of these couplings to suppress spurious spin excitations owing to the spin-orbit force in free translational motion of a nucleus but show that in a collision situation there is a strong spin excitation even in spin-saturated systems which persists in the departing fragments. The energy loss is considerably increased by the odd-odd terms. Time-dependent Hartree-Fock (TDHF) enjoyed a period of large attention in nuclear physics about 30 years ago; for reviews see, e.g., Refs. [1][2][3]. These early calculations delivered a great number of useful insights into the basic mechanisms of heavy-ion collisions, even with the large practical restrictions of that time concerning the model, degrees of freedom, and symmetries. However, it was soon recognized not to be as comprehensive a description as originally expected. For example, widths in the distributions of fragments and kinetic energies are systematically underestimated, a fact which had been traced back in parts to missing correlations [4,5]. More puzzling was that average quantities, such as fusion cross sections, did not come out all that well although they should be predictable by mean field dynamics. Already at that time there were indications that the many restrictions in the calculations spoil their predictive value and that, for example, simply the proper handling of the spin-orbit (l * s) force can improve the results considerably towards the experimentally observed dissipation [6,7]. Computer limitations halted these developments for a while. The subsequent dramatic advance in computational power now allows three-dimensional TDHF calculations with a full-fledged Skyrme force, without any symmetry restrictions, and for any nuclear size. Accordingly, there is a renewed interest in TDHF studies as seen from recent publications on resonance dynamics [8-10] and heavy-ion collisions [11]. The present manuscript also deals with recent 3D TDHF calculations and aims to investigate the importance of a full treatment of the l * s force and related dissipation mechanisms.TDHF in a nuclear context means a time-dependent meanfield theory derived from an effective energy functional. The most widely used is the Skyrme functional which was proposed long ago as a quantitative self-consistent model for the nuclear ground state [12] and dynamics [13]. The Skyrme energydensity functional consists of free kinetic energy, Coulomb energy with exchange in the Slater approximation, and an effective-interaction part depending on density ρ, kinetic density τ , l * s density J , current  , and spin density σ , for a detailed explicit expression see, e.g., Ref. [14]. Pairing is not considered in the present case where we deal mostly with closed shell nuclei. For the purpose of later discussions, we display...

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.Purpose: We explore the ability of dynamic mean-field methods to describe fast fission processes beyond the fission barrier, using the nuclide 240 Pu as an example.Methods: Time-dependent Hartree-Fock calculations based on the Skyrme interaction are used to calculate nonadiabatic fission paths, beginning from static constrained Hartree-Fock calculations. The properties of the dynamic states are interpreted in terms of the nature of their collective motion. Fission product properties are compared to data.Results: Parent nuclei constrained to begin dynamic evolution with a deformation less than the fission barrier exhibit giant-resonance-type behaviour. Those beginning just beyond the barrier explore large amplitude motion but do not fission, whereas those beginning beyond the two-fragment pathway crossing fission to final states which differ according to the exact initial deformation.Conclusions: Time-dependent Hartree-Fock is able to give a good qualitative and quantitative description of fast fission, provided one begins from a sufficiently deformed state.

The Skyrme effective interaction, with its multitude of parameterisations, along with its implementation using the static and time-dependent density functional (TDHF) formalism have allowed for a range of microscopic calculations of low-energy heavy-ion collisions. These calculations allow variation of the effective interaction along with an interpretation of the results of this variation informed by a comparison to experimental data. Initial progress in implementing TDHF for heavy-ion collisions necessarily used many approximations in the geometry or the interaction. Over the last decade or so, the implementations have overcome all restrictions, and studies have begun to be made where details of the effective interaction are being probed. This review surveys these studies in low energy heavy-ion reactions, finding significant effects on observables from the form of the spin-orbit interaction, the use of the tensor force, and the inclusion of time-odd terms in the density functional.Heavy-ion collisions combine the rich dynamics of a many-body out-of-equilibrium open quantum system with the complexities of the residual part of the strong interaction which leaks out of the small, but neither fundamental or point-like, nucleons, causing them to stick loosely together some of the time, and to fall apart at others. Understanding heavy-ion reactions across all energy scales is necessary to understand stellar nucleosynthesis [1], the synthesis of superheavy nuclei [2,3], the properties of nuclear matter [4][5][6], the QCD phase diagram [7,8] as well as the understanding of reaction mechanisms themselves [9][10][11][12][13].Among the theoretical techniques used to study heavy-ion reactions, methods based on timedependent Hartree-Fock have recently achieved the status of having sufficiently mature implementations free of limiting approximations, and running at a suitable speed, such that systematically varying the effective interaction in the calculations is possible. It is such studies that form the main subject of the present review. The practical implementations, using the Skyrme interaction, are in some sense parameter-free, in that one has a framework using an effective interaction fitted to ground state data and nuclear matter properties, with no further adjustment to dynamics. Structure and reaction effects are together determined self-consistently from the interaction, subject to the approximations of the mean-field and one gives no further adjustment. In another sense, the variation among the sets of available effective interactions are parameters of the calculations. We attempt to summarise here what has been learnt from exploring different Skyrme force parameterisations within low-energy heavy-ion reaction calculations.Overlapping this subject area are other recent review articles, to which the reader is referred: A review in which extensive coverage of theoretical approaches to dynamics of heavy-ion collisions in TDHF and its extensions is presented by Simenel and Umar [14]. This review extensively covers the...

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