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Register a new userSymmetry restoration in mean-field approaches
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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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We show that the symmetry-restored paired mean-field states (quasiparticle vacua) properly account for isoscalar versus isovector nuclear pairing properties. Full particle-number, spin, and isospin symmetries are restored in a simple SO(8) proton-neutron pairing model, and prospects to implement a similar approach in a realistic setting are delineated. Our results show that, provided all symmetries are restored, the pictures based on pair-condensate and quartet-condensate wave functions represent equivalent ways of looking at the physics of nuclear proton-neutron pairing.
Basic properties of the nuclear tensor mean fields are reviewed, and their role in changing the shell structure and masses of nuclei is analyzed within the spherical Hartree-Fock-Bogolyubov approach.
We review recent results on intermediate mass cluster production in heavy ion collisions at Fermi energy and in spallation reactions. Our studies are based on modern transport theories, employing effective interactions for the nuclear mean-field and incorporating two-body correlations and fluctuations. Namely we will consider the Stochastic Mean Field (SMF) approach and the recently developed Boltzmann-Langevin One Body (BLOB) model. We focus on cluster production emerging from the possible occurrence of low-density mean-field instabilities in heavy ion reactions. Within such a framework, the respective role of one and two-body effects, in the two models considered, will be carefully analysed. We will discuss, in particular, fragment production in central and semi-peripheral heavy ion collisions, which is the object of many recent experimental investigations. Moreover, in the context of spallation reactions, we will show how thermal expansion may trigger the development of mean-field instabilities, leading to a cluster formation process which competes with important re-aggregation effects.
We report the recent progress in relativistic mean-field (RMF) and beyond approaches for the low-energy structure of deformed hypernuclei. We show that the $Lambda$ hyperon with orbital angular momentum $ell=0$ (or $ell>1$) generally reduces (enhances) nuclear quadrupole collectivity. The beyond mean-field studies of hypernuclear low-lying states demonstrate that there is generally a large configuration mixing between the two components $[^{A-1}Z (I^+) otimes Lambda p_{1/2}]^J$ and $[^{A-1}Z (Ipm2 ^+) otimes Lambda p_{3/2}]^J$ in the hypernuclear $1/2^-_1, 3/2^-_1$ states. The mixing weight increases as the collective correlation of nuclear core becomes stronger. Finally, we show how the energies of hypernuclear low-lying states are sensitive to parameters in the effective $N Lambda $ interaction, the uncertainty of which has a large impact on the predicted maximal mass of neutron stars.
The time-dependent energy density functional with pairing allows to describe a large variety of phenomena from small to large amplitude collective motion. Here, we briefly summarize the recent progresses made in the field using the TD-BCS approach. A focus is made on the mapping of the microscopic mean-field dynamic to the macroscopic dynamic in collective space. A method is developed to extract the collective mass parameter from TD-EDF. Illustration is made on the fission of $^{258}$Fm. The collective mass and collective momentum associated to quadrupole deformation including non-adiabatic effects is estimated along the TD-EDF path. With these information, the onset of dissipation during fission is discussed.
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