669 research outputs found
0+ states in the large boson number limit of the Interacting Boson Approximation model
Studies of the Interacting Boson Approximation (IBA) model for large boson
numbers have been triggered by the discovery of shape/phase transitions between
different limiting symmetries of the model. These transitions become sharper in
the large boson number limit, revealing previously unnoticed regularities,
which also survive to a large extent for finite boson numbers, corresponding to
valence nucleon pairs in collective nuclei. It is shown that energies of 0_n^+
states grow linearly with their ordinal number n in all three limiting
symmetries of IBA [U(5), SU(3), and O(6)]. Furthermore, it is proved that the
narrow transition region separating the symmetry triangle of the IBA into a
spherical and a deformed region is described quite well by the degeneracies
E(0_2^+)=E(6_1^+), E(0_3^+)=E(10_1^+), E(0_4^+)=E(14_1^+), while the energy
ratio E(6_1^+) /E(0_2^+) turns out to be a simple, empirical, easy-to-measure
effective order parameter, distinguishing between first- and second-order
transitions. The energies of 0_n^+ states near the point of the first order
shape/phase transition between U(5) and SU(3) are shown to grow as n(n+3), in
agreement with the rule dictated by the relevant critical point symmetries
resulting in the framework of special solutions of the Bohr Hamiltonian. The
underlying partial dynamical symmetries and quasi-dynamical symmetries are also
discussed.Comment: 6 pages, 4 postscript figures, LaTeX. To appear in the Proceedings of
the International Conference on Nuclear Physics and Astrophysics: From Stable
Beams to Exotic Nuclei (Cappadocia, 2008
Unified description of 0+ states in a large class of nuclear collective models
A remarkably simple regularity in the energies of 0+ states in a broad class
of collective models is discussed. A single formula for all 0+ states in
flat-bottomed infinite potentials that depends only on the number of dimensions
and a simpler expression applicable to all three IBA symmetries in the large
boson number limit are presented. Finally, a connection between the energy
expression for 0+ states given by the X(5) model and the predictions of the IBA
near the critical point is explored.Comment: 4 pages, 3 postscript figures, uses revTe
Connecting the X(5)-, X(5)-, and X(3) models to the shape/phase transition region of the interacting boson model
The parameter independent (up to overall scale factors) predictions of the
X(5)-, X(5)-, and X(3) models, which are variants of the X(5)
critical point symmetry developed within the framework of the geometric
collective model, are compared to two-parameter calculations in the framework
of the interacting boson approximation (IBA) model. The results show that these
geometric models coincide with IBA parameters consistent with the phase/shape
transition region of the IBA for boson numbers of physical interest (close to
10). Nuclei within the rare-earth region and select Os and Pt isotopes are
identified as good examples of X(3), X(5)-, and X(5)-
behavior
SU(3) quasidynamical symmetry underlying the Alhassid--Whelan arc of regularity
The first example of an empirically manifested quasi dynamical symmetry
trajectory in the interior of the symmetry triangle of the Interacting Boson
Approximation model is identified for large boson numbers. Along this curve,
extending from SU(3) to near the critical line of the first order phase
transition, spectra exhibit nearly the same degeneracies that characterize the
low energy levels of SU(3). This trajectory also lies close to the
Alhassid-Whelan arc of regularity, the unique interior region of regular
behavior connecting the SU(3) and U(5) vertices, thus offering a possible
symmetry-based interpretation of that narrow zone of regularity amidst regions
of more chaotic spectra.Comment: 4 pages, LaTeX, 5 eps figure
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