Abstract
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.
Highlights
The vast majority of microscopic models of many-body systems rely on a description in terms of the single-particle (s.p.) wave functions
Self-consistent mean-field models (SCMF) automatically generate the optimal one-body potentials corresponding to the s.p. wave functions
A more practical approach is provided by the Density Functional Theory (DFT), which incorporates the involved many-body effects into effective interactions, or effective energy–density functionals
Summary
The vast majority of microscopic models of many-body systems rely on a description in terms of the single-particle (s.p.) wave functions. There are no symmetry restrictions and the full Skyrme energy functional is used including the spin–orbit and most important time-odd terms Such fully-fledged 3D calculations became possible only over the last decade with the steadily increasing computing capabilities. The conservation of total energy excluding the pairing energy is not impaired for the case of constant occupation, while the pairing energy is not even computed It should be noted, that once the wave functions change dynamically, this approach is not correct as the occupation probabilities will change with time. That once the wave functions change dynamically, this approach is not correct as the occupation probabilities will change with time In this case the TDHF-Bogolyubov equations should be used. Using this code as is with pairing included in the timedependent case might be useful for schematic or exploratory studies but extreme caution is advised when interpreting such results
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