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Register a new userSymmetry-unrestricted Skyrme mean-field study of heavy nuclei
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In the light of recent experimental developments, increasing attention is devoted to nuclear phenomena related to rotational excitations of exotic intrinsic nuclear configurations that often lack symmetries present in the majority of nuclei. Examples include configurations with a non-vanishing octupole moment. In order to describe this kind of states, we have developed a new computer code to solve the self-consistent mean-field equations, able to use most of todays effective Skyrme interactions and working in coordinate-space. We report on the development of MOCCa, a code based on the same principles as EV8, but offering the user individual control on many symmetry assumptions. In addition, the HF+BCS pairing treatment of EV8 has been generalised to the full machinery of Hartree-Fock-Bogoliubov transformations. We discuss as example the static fission barrier of $^{226}$Ra, prefacing extended studies in the region, using the recent series of Skyrme parameterizations SLy5s1 through SLy5s8.
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{Full three dimensional static and dynamic mean field calculations using collocation basis splines with a Skyrme type Hamiltonian are described. This program is developed to address the difficult theoretical challenges offered by exotic nuclei. Ground state and deformation properties are calculated using static Hartree-Fock, Hartree-Fock+BCS and constrained Hartree-Fock models. Collective properties, such as reaction rates and resonances, are described using a new alternate method for evaluating linear response theory, which is constructed directly on top of the static calculation. This provides a consistent description of the ground state, deformation and collective nuclear properties. Sample results are presented for the giant multiple resonances of $^{16}$O. }
The E1(T=1) isovector dipole giant resonance (GDR) in heavy and super-heavy deformed nuclei is analyzed over a sample of 18 rare-earth nuclei, 4 actinides and three chains of super-heavy elements (Z=102, 114 and 120). Basis of the description is self-consistent separable RPA (SRPA) using the Skyrme force SLy6. The self-consistent model well reproduces the experimental data (energies and widths) in the rare-earth and actinide region. The trend of the resonance peak energies follows the estimates from collective models, showing a bias to the volume mode for the rare-earths isotopes and a mix of volume and surface modes for actinides and super-heavy elements. The widths of the GDR are mainly determined by the Landau fragmentation which in turn is found to be strongly influenced by deformation. A deformation splitting of the GDR can contribute about one third to the width and about 1 MeV further broadening can be associated to mechanism beyond the mean-field description (escape, coupling with complex configurations).
We report on cranked Skyrme-HFB calculations of rotational bands of the octupole-deformed nucleus $^{222}$Th. A sudden change in configuration is observed, with the shape of the yrast state jumping from large octupole deformation at low spin to small octupole deformation at high spin.
In these proceedings, we report first results for particle-number and angular-momentum projection of self-consistently blocked triaxial one-quasiparticle HFB states for the description of odd-A nuclei in the context of regularized multi-reference energy density functionals, using the entire model space of occupied single-particle states. The SIII parameterization of the Skyrme energy functional and a volume-type pairing interaction are used.
The mean-field approximation based on effective interactions or density functionals plays a pivotal role in the description of finite quantum many-body systems that are too large to be treated by ab initio methods. Examples are strongly interacting atomic nuclei and mesoscopic condensed matter systems. In this approach, the linear Schrodinger equation for the exact many-body wave function is mapped onto a non-linear density-dependent one-body potential problem. This approximation, not only provides computationally very simple solutions even for systems with many particles, but due to the non-linearity, it also allows for obtaining solutions that break essential symmetries of the system, often connected with phase transitions. However, mean-field approach suffers from the drawback that the corresponding wave functions do not have sharp quantum numbers and, therefore, many results cannot be compared directly with experimental data. In this article, we discuss general group theoretical techniques to restore the broken symmetries, and provide detailed expressions on the restoration of translational, rotational, spin, isospin, parity and gauge symmetries. In order to avoid the numerical complexity of exact projection techniques, various approximation methods available in the literature are examined. We present applications of the projection methods to simple nuclear models, realistic calculations in relatively small configuration spaces, nuclear energy density functional theory, as well as in other mesoscopic systems. We also discuss applications of projection techniques to quantum statistics in order to treat the averaging over restricted ensembles with fixed quantum numbers. Further, unresolved problems in the application of the symmetry restoration methods to the energy density functional theories are highlighted.
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