102Pd:An E(5) nucleus?

Evolution of nuclear shapes in medium mass isotopes from a microscopic perspective

“…The chains shown in Figs. 1 and 2, as well as the one corresponding to the Ba chain, contain E(5) candidates found from systematic studies on available data on energy levels, E2, E1, and M1 strengths [7,8,10,28,29]. In Figs.…”

“…Along with each contour plot we have also plotted a two-dimensional cut corresponding to axially symmetric shapes that is used as a reference to identify maxima and minima. The first two isotopes have been chosen because there are experimental indications [8,9] that point them as possible examples of the E(5) symmetry. The remaining isotopes are usually considered as γ soft and in principle should not be considered as candidates of E(5) but their axial PECs pointed to a E(5)-like Q 0 -γ potential energy surface.…”

“…Several candidates have already been proposed experimentally for both E(5) and X(5) symmetries. For example, the nuclei 134 Ba [7], 102 Pd [8], 108 Pd [9], and 128−130 Xe [10] have been identified as candidates for E(5), whereas 152 Sm [11], 150 Nd [12], 154 Gd [13], and 156 Dy [14] provide examples of X(5) symmetry.…”

Alternative solvable description of the E(5) critical point symmetry in the interacting boson model

“…It is expected that a suitable IBM Hamiltonian, like the U(5), O (6), and SU(3) limiting cases, may fit the E(5) critical point nuclei better, especially when relatively higher excited levels are taken into consideration, though it is commonly believed that the BMM may be regarded as the large-N limit of the IBM [16][17][18]. The purpose of this work is to establish an extended Hamiltonian near the critical point of the U(5)-O(6) transitional region of the IBM, of which the solution should be closer to that of the E(5) model with finite N. Namely, the model is suitable to describe the E(5) critical symmetry nuclei as reported in [5][6][7][8][9], while the model in the large-N cases may be close to those of the E(5)-β 2n type models similar to the results reported in [15].…”

“…The potential used in the E(5) model only depends on the β degree of freedom with an infinite square well. It has been shown that there are many nuclei with the E(5) critical point symmetry, such as 134 Ba [5], 104 Ru [6], 102 Pd [7], 108 Pd [8], and 116 Cd [9]. Inspired by the E(5) model, Lévai and Arias studied the Bohr Hamiltonian with a sextic potential and a centrifugal barrier, of which quasi-exact solutions can be derived [10], while Bonatsos et al explored numerical solutions for the γ-independent Bohr Hamiltonian with β 2n potentials for n ≥ 1 called the confined γ-soft rotor model [11], in which the spectra and transition rates for the β 2n potentials for 2 ≤ n ≤ 4 are given explicitly and compared with the original E(5) model.…”