Shape phase mixing in critical point nuclei

Abstract

Spectral properties of nuclei near the critical point of the quantum phase transition between spherical and axially symmetric shapes are studied in a hybrid collective model which combines the $\gamma$-stable and $\gamma$-rigid collective conditions through a rigidity parameter. The model in the lower and upper limits of the rigidity parameter recovers the X(5) and X(3) solutions respectively, while in the equally mixed case it corresponds to the X(4) critical point symmetry. Numerical applications of the model on nuclei from regions known for critical behavior reveal a sizable shape phase mixing and its evolution with neutron or proton numbers. The model also enables a better description of energy spectra and electromagnetic transitions for these nuclei.Comment: 12 pages, 5 figures, 3 table

Collective motion in prolate γ-rigid nuclei within minimal length concept via a quantum perturbation method

“…[4,14]. Other efforts have also been directed to special realizations in the framework of the Bohr-Mottelson model and its extensions [15,16,17,18,19,20,21,22,23,24,25] where the collective shape variables or inertial parameters are imposed by some constraints. From a structural point of view, the collective Bohr Hamiltonian induces, however, a coupling of the β, γ, and rotational degrees of freedom, thereby yielding a rich set of physical phenomena.…”

A unified description of nuclear structures in shape phase transitions

“…Similarly, one can find from figures 2 and 3 that the consistency between the two models also appears for the case of γ=20°. In fact, the T(4) dynamics in all cases with γä[6°, 30°] can be well fitted by the IBM Hamiltonian (13)…”

“…Although the T(4) model is built from the γ-rigid solutions of the Bohr Hamiltonian, it is reasonable to expect that the T(4) model and the IBM may yield similar dynamical features when the two models are applied to the same physical situations. To justify this, we have worked out the parameter locus of the T(4) model in the triangle phase diagram through fitting the typical energy ratios obtained from the T(4) model at given γ by using the IBM Hamiltonian (13). The related energy ratios include…”

“…Critical point symmetries (CPSs) [1][2][3][4][5][6][7][8][9][10][11][12][13][14] provide benchmarks for nuclear structures in different types of shape phase transitions (SPTs) [15][16][17]. The concept of CPS has been proved to be rooted in the Euclidean dynamical symmetry [1,[18][19][20] (or the partial Euclidean dynamical symmetry [12,21]).…”

Critical point symmetry for odd-odd nuclei and collective multiple chiral doublet bands

“…Critical point symmetries (CPSs) in nuclear structure have attracted considerable attention [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20], as these models may provide parameter-free (up to an overall scale) predictions about nuclear properties in the shape phase transitional region [21,22]. The typical examples include the E(5) CPS for the spherical to γ-unstable shape phase transition (SPT) [1], the X(5) CPS for the spherical to axially deformed SPT [2], the Y(5) CPS for the axial to triaxial SPT [6], and the Z(5) CPS for the prolate to oblate SPT [7].…”