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)-β2\beta^2, X(5)-β4\beta^4, 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)-$\beta^2$, X(5)-$\beta^4$, 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)-$\beta^2$, and X(5)-$\beta^4$ 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

Alternative Interpretation of Sharply Rising E0 Strengths in Transitional Regions

It is shown that strong 0+2 -> 0+1 E0 transitions provide a clear signature of phase transitional behavior in finite nuclei. Calculations using the IBA show that these transition strengths exhibit a dramatic and robust increase in spherical-deformed shape transition regions, that this rise matches well the existing data, that the predictions of these E0 transitions remain large in deformed nuclei, and that these properties are intrinsic to the way that collectivity and deformation develop through the phase transitional region in the model, arising from the specific d-boson coherence in the wave functions, and that they do not necessarily require the explicit mixing of normal and intruder configurations from different IBA spaces.Comment: 6 pages, 3 figure

Exactly separable version of the Bohr Hamiltonian with the Davidson potential

An exactly separable version of the Bohr Hamiltonian is developed using a potential of the form u(beta)+u(gamma)/beta^2, with the Davidson potential u(beta)= beta^2 + beta_0^4/beta^2 (where beta_0 is the position of the minimum) and a stiff harmonic oscillator for u(gamma) centered at gamma=0. In the resulting solution, called exactly separable Davidson (ES-D), the ground state band, gamma band and 0_2^+ band are all treated on an equal footing. The bandheads, energy spacings within bands, and a number of interband and intraband B(E2) transition rates are well reproduced for almost all well-deformed rare earth and actinide nuclei using two parameters (beta_0, gamma stiffness). Insights regarding the recently found correlation between gamma stiffness and the gamma-bandhead energy, as well as the long standing problem of producing a level scheme with Interacting Boson Approximation SU(3) degeneracies from the Bohr Hamiltonian, are also obtained.Comment: 35 pages, 11 postscript figures, LaTe