Description of heavy deformed nuclei within the pseudo-SU(3) shell model (original) (raw)
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Pseudo + Quasi SU(3): Towards a Shell-Model Description of Heavy Deformed Nuclei
Computational and Group-Theoretical Methods in Nuclear Physics - Proceedings of the Symposium in Honor of Jerry P Draayer's 60th Birthday, 2004
The pseudo-SU(3) model has been extensively used to study normal parity bands in even-even and odd-mass heavy deformed nuclei. The use of a realistic Hamiltonian that mixes many SU(3) irreps has allowed for a successful description of energy spectra and electromagnetic transition strengths. While this model is powerful, there are situations in which the intruder states must be taken into account explicitly. The quasi-SU(3) symmetry is expected to complement the model, allowing for a description of nucleons occupying normal and intruder parity orbitals using a unified formalism.
Shell model scheme for quadrupole phenomena in heavy deformed nuclei
Nuclear Physics A, 1990
The microscopic collective model, which extends the seminal work of Elliott on the SU(3) model for describing the structure of light deformed nuclei to include multiple 2hm shell-model excitations of the monopole (l=0) and quadrupole (l=2) type, is shown to be a logical extension of the pseudo SU(3) scheme for heavy deformed nuclei. The main advantage of this extended theory is that E2 transition strengths, intraband as well as interband, can be reproduced without introducing effective charges. Results for both 24Mg and 168Er are presented. The symmetry algebra of this extended theory is that of the symplectic group Sp(3,R) which contains SU(3) as a subgroup. It is therefore also called the symplectic model and in the case of the pseudo SU(3) extension, the pseudo-symplectic model. Basic premises of the theory are reviewed.
Dipole and quadrupole collectivity in atomic nuclei
Journal of Physics: Conference Series, 2012
The interrelation of the dipole, i.e. cluster and quadrupole collectivity of atomic nuclei is studied in the examples of the superdeformed and hyperdeformed sates of N = Z nuclei. Our method is largely based on symmetry-considerations.
It is argued that there exist natural shell model spaces optimally adapted to the operation of two variants of Elliott's SU3 symmetry that provide accurate predictions of quadrupole moments of deformed states. A selfconsistent Nilsson-like calculation describes the competition between the realistic quadrupole force and the central field, indicating a remarkable stability of the quadruplole moments-which remain close to their quasi and pseudo SU3 values-as the single particle splittings increase. A detailed study of the N = Z even nuclei from 56 Ni to 96 Cd reveals that the region of prolate deformation is bounded by a pair of transitional nuclei 72 Kr and 84 Mo in which prolate ground state bands are predicted to dominate, though coexisting with oblate ones.
Nuclear Physics A, 1995
A model system which mimics the shell-model dynamics of strongly deformed nuclei is constructed in order to study the role of particles in the unique parity orbitals of heavy deformed nuclei and to test the validity and applicability of some commonly used truncation procedures. Working in a truncation-free environment and including quadrupole-quadrupole, spin-orbit, orbit-orbit, and pairing forces, we find that for standard nuclear systems the correlations generated among particles in the unique parity space and by the interaction of nucleons in the normal parity orbitals with those in the unique parity orbitals play an important role in driving the many-particle system towards its maximum allowed deformation. The results suggest that nucleons in the unique parity levels contribute significantly to the overall collectivity of a nuclear system and should be taken into account explicitly whenever possible, or at least through renormalization procedures that can be justified in special cases, like for collective states below the backbending region.
Pseudo-symplectic model for strongly deformed heavy nuclei
Nuclear Physics A, 1991
An extension of the strong-coupled pseudo SU(3) model, which is a scheme that has found application in the study of superdeformed bands in heavy nuclei, is introduced. The theory includes multiple inter-shell excitations of the monopole and quadrupole type. It is an extension to heavy (A> 100) nuclei of the microscopic collective model which applies for light (A6 28) systems. Because the scheme has a Sp(3,R) 3 W(3) group theoretical structure, it is called the pseudosymplectic modeI. A boson expansion for the model hamiltonian is given and results for an application of the theory to *38U presented.
Physical Review Letters, 2000
A superdeformed rotational band has been identified in 36 Ar, linked to known low-spin states, and observed to its high-spin termination at I p 16 1 . Cranked Nilsson-Strutinsky and spherical shell model calculations assign the band to a configuration in which four pf-shell orbitals are occupied, leading to a low-spin deformation b 2 ഠ 0.45. Two major shells are active for both protons and neutrons, yet the valence space remains small enough to be confronted with the shell model. This band thus provides an ideal case to study the microscopic structure of collective rotational motion. PACS numbers: 21.10.Re, 21.60.Cs, 23.20.Lv, 27.30. + t The microscopic description of collective motion is a fundamental challenge in quantum many-body physics. A classic example in the field of nuclear structure is the desire to understand, within a spherical shell model framework, the origins of nuclear deformation and collective rotation. For deformed nuclei in the first half of the sd shell, this is accomplished in Elliott's SU(3) model . For heavier nuclei, SU(3) symmetry is destroyed by the strong spin-orbit interaction and the relevant coupling scheme is less clear. The microscopic degrees of freedom contributing to the rotational motion can be determined by comparing experimental data, the intuitive results of deformed mean field calculations, and rigorous shell model (SM) diagonalizations. However, the contradictory requirements of having a sufficiently large number of active particles for collective rotation to develop, and a sufficiently small number to permit SM calculations, severely limit the opportunities for such direct comparisons. Considerable effort has recently been focused on 48 Cr [2-9], in large part because it is one of a few nuclei where these criteria are satisfied. Rotors like 48 Cr are, however, the exception rather than the rule, in that particles from only a single major shell are active, whereas rotational motion in heavier nuclei quite generally involves two major shells for both protons and neutrons.
Shell model description of normal parity bands in even-even heavy deformed nuclei
Physical Review C, 2000
The pseudo-SU͑3͒ model is used to describe the low-energy spectra and electromagnetic transition strengths in 156 Gd, 158 Gd, and 160 Gd. The Hamiltonian includes spherical single-particle energies, the quadrupolequadrupole interaction, proton and neutron pairing interactions, plus four rotorlike terms. The quadrupolequadrupole and pairing interaction strengths are assigned the values ϭ23A Ϫ5/3 and G ϭ21/A, G ϭ17/A, respectively. The single-particle energies were taken from experiment but scaled to yield an overall best fit. For the other four rotorlike terms, which do not mix SU͑3͒ representations and induce only small changes in the spectra, a consistent set of parameters is given. The basis states are built as linear combinations of SU͑3͒ states which are the direct product of SU͑3͒ proton and neutron states with pseudospin zero. The results are in good agreement with experimental data, demonstrating the suitability of the model to describe heavy deformed nuclei.