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Register a new userUnderlying structure of collective bands and self-organization in quantum systems
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The underlying structure of low-lying collective bands of atomic nuclei is discussed from a novel perspective on the interplay between single-particle and collective degrees of freedom, by utilizing state-of-the-art configuration interaction calculations on heavy nuclei. Besides the multipole components of the nucleon-nucleon interaction that drive collective modes forming those bands, the monopole component is shown to control the resistance against such modes. The calculated structure of 154Sm corresponds to coexistence between prolate and triaxial shapes, while that of 166Er exhibits a deformed shape with a strong triaxial instability. Both findings differ from traditional views based on beta/gamma vibrations. The formation of collective bands is shown to be facilitated from a self-organization mechanism.
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The quantum self-organization is introduced as one of the major underlying mechanisms of the quantum many-body systems, for instance, atomic nuclei. It is shown that atomic nuclei are not necessarily like simple rigid vases containing almost free nucleons, in contrast to the naive Fermi liquid picture. Nuclear forces are demonstrated to be rich enough to change single-particle energies for each eigenstate, so as to enhance the relevant collective mode. When the quantum self-organization occurs, single-particle energies can be self-organized (or self-optimized), being enhanced by (i) two quantum liquids, e.g., protons and neutrons, (ii) two major force components, e.g., quadrupole interaction (to drive collective mode) and monopole interaction (to control resistance). Type II shell evolution is considered to be a simple visible case involving excitations across a (sub)magic gap. Actual cases such as shape coexistence, quantum phase transition, octupole vibration/deformation, super deformation, etc. can be studied with this scope. The quantum self-organization becomes more important in heavier nuclei where the number of active orbits and the number of active nucleons are larger. With larger numbers of them, the effects of the organization can be more significant. The quantum self-organization is a general phenomenon, and is expected to be found in other quantum systems.
A systematic investigation of the nuclear observables related to the triaxial degree of freedom is presented using the multi-quasiparticle triaxial projected shell model (TPSM) approach. These properties correspond to the observation of $gamma$-bands, chiral doublet bands and the wobbling mode. In the TPSM approach, $gamma$-bands are built on each quasiparticle configuration and it is demonstrated that some observations in high-spin spectroscopy that have remained unresolved for quite some time could be explained by considering $gamma$-bands based on two-quasiparticle configurations. It is shown in some Ce-, Nd- and Ge-isotopes that the two observed aligned or s-bands originate from the same intrinsic configuration with one of them as the $gamma$-band based on a two-quasiparticle configuration. In the present work, we have also performed a detailed study of $gamma$-bands observed up to the highest spin in Dysposium, Hafnium, Mercury and Uranium isotopes. Furthermore, several measurements related to chiral symmetry breaking and wobbling motion have been reported recently. These phenomena, which are possible only for triaxial nuclei, have been investigated using the TPSM approach. It is shown that doublet bands observed in lighter odd-odd Cs-isotopes can be considered as candidates for chiral symmetry breaking. Transverse wobbling motion recently observed in $^{135}$Pr has also been investigated and it is shown that TPSM approach provides a reasonable description of the measured properties.
In this paper, we begin by reviewing a certain number of mathematical challenges posed by the modelling of collective dynamics and self-organization. Then, we focus on two specific problems, first, the derivation of fluid equations from particle dynamics of collective motion and second, the study of phase transitions and the stability of the associated equilibria.
Experimentally observed superdeformed (SD) rotational bands in $^{36}$Ar and $^{40}$Ar are studied by the cranked shell model (CSM) with the paring correlations treated by a particle-number-conserving (PNC) method. This is the first time the PNC-CSM calculations are performed on the light nuclear mass region around $A=40$. The experimental kinematic moments of inertia $J^{(1)}$ versus rotational frequency are reproduced well. The backbending of the SD band at frequency around $hbaromega=1.5$ MeV in $^{36}$Ar is attributed to the sharp rise of the simultaneous alignments of the neutron and proton $1d_{5/2}[202]5/2$ pairs and $1f_{7/2}[321]3/2$ pairs, which is the consequence of the band crossing between the $1d_{5/2}[202]5/2$ and $1f_{7/2}[321]3/2$ configuration states. The gentle upbending at the low frequency of the SD band in $^{40}$Ar is mainly effected by the alignments of the neutron $1f_{7/2}[321]3/2$ pairs and proton $1d_{5/2}[202]5/2$ pairs. The PNC-CSM calculations show that besides the diagonal parts, the off-diagonal parts of the alignments play an important role in the rotational behavior of the SD bands.
It is argued that the experimental criteria recently used to assign wobbling nature to low-spin bands in several nuclei are insufficient and risky. New experimental data involving angular distribution and linear polarization measurements on an excited band in 187Au, previously interpreted as longitudinal wobbling, are presented. The new data show that the linking transitions have dominant magnetic nature and exclude the wobbling interpretation.
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