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Register a new userRestoring Broken Symmetries for Nuclei and Reaction Fragments
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Authors
Aurel Bulgac
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In typical microscopic approaches, particularly when pairing correlations are present, nuclei and nuclear fragments do not have well defined quantum numbers and symmetries should be restored. I present here a formalism for the simultaneous projection of total particle numbers of a nucleus, particle number of reaction fragments, and of the reaction fragment intrinsic spins and of their correlation, and also for their symmetry restored densities and total energies. These new formulas for the symmetry restored quantities, are free of any singularities, unlike those in the previously introduced prescriptions.
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In reactions the wave packets of the emerging products typically are not eigenstates of particle number operators or any other conserved quantities and their properties are entangled. I describe a particle projection technique in parts of space, whic
h eschews the need to evaluate Pfaffians in the case of overlap of generalized Slater determinants or Hartree-Fock-Bogoliubov type of vacua. The extension of these formulas for calculating either angular momentum or particle projected energy distributions of the reaction fragments are presented as well. The generalization to simultaneous particle and angular momentum projection of various reaction fragment observables is straightforward.
It is shown that the rotational band structure of the cluster states in 12C and 16O can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the alpha-particles, i.e. an equilateral triangle for 12C, and a regular tetrahedron for 16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of alpha-particles. Finally, some first results are presented for odd-cluster nuclei.
Magnetic and chiral bands have been a hot subject for more than twenty years. Therefore, quite large volumes of experimental data as well as theoretical descriptions have been accumulated. Although some of the formalisms are not so easy to handle, the results agree impressively well with the data. The objective of this paper is to review the actual status of both experimental and theoretical investigations. Aiming at making this material accessible to a large variety of readers, including young students and researchers, I gave some details on the schematic models which are able to unveil the main features of chirality in nuclei. Also, since most formalisms use a rigid triaxial rotor for the nuclear systems core, I devoted some space to the semi-classical description of the rigid triaxial as well as of the tilted triaxial rotor. In order to answer the question whether the chiral phenomenon is spread over the whole nuclear chart and whether it is specific only to a certain type of nuclei, odd-odd, odd-even or even-even, the current results in the mass regions of $Asim 60,80,100,130,180,200$ are briefly described for all kinds of odd/even-odd/even systems. The chiral geometry is a sufficient condition for a system of proton-particle, neutron-hole and a triaxial rotor to have the electromagnetic properties of chiral bands. In order to prove that such geometry is not unique for generating magnetic bands with chiral features, I presented a mechanism for a new type of chiral bands. One tries to underline the fact that this rapidly developing field is very successful in pushing forward nuclear structure studies.
Background: Quasi dynamical symmetries (QDS) and partial dynamical symmetries (PDS) play an important role in the understanding of complex systems. Up to now these symmetry concepts have been considered to be unrelated. Purpose: Establish a link between PDS and QDS and find an emperical manifestation. Methods: Quantum number fluctuations and the intrinsic state formalism are used within the framework of the interacting boson model of nuclei. Results: A previously unrecognized region of the parameter space of the interacting boson model that has both O(6) PDS (purity) and SU(3) QDS (coherence) in the ground band is established. Many rare-earth nuclei approximately satisfying both symmetry requirements are identified. Conclusions: PDS are more abundant than previously recognized and can lead to a QDS of an incompatible symmetry.
We consider holographic theories at finite temperature in which a continuous global symmetry in the bulk is spontaneously broken. We study the linear response of operators in a regime which is dual to time dependent, long wavelength deformations of solutions generated by the symmetry. By computing the boundary theory retarded Greens function we show the existence of a gapless mode with a diffusive dispersion relation. The diffusive character of the mode is compatible with the absence of a conserved charge from the field theory point of view. We give an analytic expression for the corresponding diffusion constant in terms of thermodynamic data and a new transport coefficient $sigma_{b}$ which is fixed by the black hole horizon data. After adding a perturbative source on the boundary, we compute the resulting gap $deltaomega_{g}$ as a simple function of $sigma_{b}$ and of data of the thermal state.
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