Alternative characterization of the spherical to axially deformed shape-phase transition in the interacting boson model

Abstract

The quantum phase transitional behavior of an alternative characterization of the spherical to axially deformed shape-phase transition in the interacting boson model is explored. Specifically, the usual SU (3) quadrupole-quadrupole interaction is replaced by an O(6) cubic interaction, and the transitional behavior of the low-lying energy levels, eigenstates, isomer shifts, E2 transition rates, and expectation values of shape variables across the entire transitional region are all examined within this context. A comparison with outcomes of the usual U (5)-SU (3) transitional description shows that the spherical to axially deformed shape-phase transition can also be described within this alternative context, especially near the critical point. However, with the O(6) cubic interaction the transition is considerably smoother than for the U (5)-SU (3) case, but with the nuclear shape less well defined, even in the axially deformed limit. It is also shown that the new scheme seems better than the usual U (5)-SU (3) scheme in describing low-lying spectrum of 152 Sm with the X(5) critical point symmetry.

Description of 150 Nd nucleus by a new alternative scheme

“…In order to demonstrate that the UQ scheme indeed serves as an alternative description of the spherical to axially deformed phase transition, recently we have systematically investigated the possible X(5) candidate of 152 Sm for N =90, and shown that the new scheme can indeed reasonably describe the low-lying spectrum of 152 Sm and E2 transition rates with the X(5) critical point symmetry [25] . Now in this subsection, another possible X(5) symmetry candidate, 150 Nd nucleus, will be further investigated by the new UQ scheme, of which the results are compared with the experimental data [31][32][33][34] and those obtained from the U (5)-SU (3) scheme.…”

“…The critical point y c will be different for different choices of the function f 2 (N ), and we adopt f 2 (N )=0.8N 2 as used in Ref. [25] which puts the critical point y c of the UQ scheme close to x c of the U (5)-SU (3) scheme.…”

“…From these investigations one understands that similar results may be realized when the quadratic scalar formed with the U (5)-SU (3) quadrupole operator is replaced by the cubic scalar formed with the quadrupole interaction of the O( 6) limit. Inspired by this new idea, in our very recent work [25], a systematic investigation of this alternative scheme was dynamically investigated, in which the transitional behaviors of the low-lying energy levels, eigenstates, isomer shifts, E2 transition rates, and expectation values of shape variables across the entire transitional region are all examined. A comparison with outcomes of the usual U (5)-SU (3) transitional description shows that the spherical to axially deformed shapephase transition can also be described within this alternative context, especially near the critical point.…”

New γ-soft rotation in the interacting boson model with SU(3) higher-order interactions *

“…Isacker demonstrated that higher-order interactions can be individually used to present a rotational spectrum [17], where is the quadrupole operator in the limit. This interesting result was further studied by [18,19].…”

Prolate-oblate asymmetric shape phase transition in the interacting boson model with SU (3) higher-order interactions

“…Higher-order terms can induce such effects [31,32,[85][86][87][88]. Third-order interaction ( Q0 × Q0 × Q0 ) (0) can show a rotational spectrum [97], where Q0 is the quadrupole operator in the O(6) limit, which was further studied by [98,99]. Especially in the new developments [19-21, 26, 27, 29], SU (3) higher-order interactions can be used to describe some realistic anomalies in nuclear structure, and provide a new description for the oblate shape and the rigid triaxial shape, thus these interactions are of practical significance.…”