Simple description of odd-Anuclei around the critical point of the spherical to axially deformed shape phase transition

Abstract

An analytically solvable model, X(3/ 2j + 1), is proposed to describe odd-A nuclei near the X(3) critical point. The model is constructed based on a collective core described by the X(3) critical point symmetry coupled to a spin-j particle. A detailed analysis of the spectral patterns for j = 1/2, 3/2 cases is provided to illustrate dynamical features of the model. Through comparing the theory with experimental data and results of other models, it is found that the X(3/ 2j + 1) model can be taken as a simple yet very effective scheme to describe those odd-A nuclei with an even-even core at the critical point of the spherical to axially deformed shape phase transition. I. IntroductionRecently, critical point symmetries [1][2][3][4][5] have attracted considerable attention, since they provide benchmark results for the study of even-even nuclei as they undergo a transition between two different phases (shapes) [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. In particular, the critical point of the spherical to γ-unstable shape transition [1], called E(5), and the critical point from the spherical to axially deformed shape [2], called X(5), have been confirmed by experiment [23][24][25][26]. In view of their successful application in helping to understand even-even systems, it seems critical point symmetries in odd-A systems warrant further investigation. And since the low-lying structures of two adjacent nuclei with more or less than one neutron or proton should be driven by similar collective considerations, the critical point symmetries observed in even-even systems should also be evident in the adjacent odd-A nuclei. The first case of a critical point Bose-Fermi symmetry, called E(5/4) [27], was developed by Iachello to describe, analytically, the γ-soft critical point E(5) configuration coupled to a j = 3/2 particle.135 Ba was suggested as an empirical example of E(5/4) symmetry, with a report of a detailed analysis given in [28]. While these results show significant agreement between theory and experiment, there are also some differences. Another critical point Bose-Fermi symmetry, called E(5/12) [29], was developed by Alonso, Arias, and Vitturi, who extended the case of the E(5/4) symmetry with a spin-j particle into the multi-j case with j = 1/2, 3/2, 5/2. Both the E(5/4) and E(5/12) models were developed to describe odd-A nuclei near even-even nuclei that display the E(5) critical point symmetry [1]; that is, nuclei in the spherical to γ-unstable transitional region. As the X(5) symmetry seems well confirmed in experiment [2], it provides a better test for exploring effects of the X(5) critical point symmetry in odd-A nuclei near the even-even partners at the X(5) critical point. Very recently, in the same spirit as the E(5/4) and E(5/12) examples, an X(5/ 2j+1) model that coupled a spin-j particle to the X(5) symmetry core was advanced [30].In this article, we propose an exactly solvable model, called X(3/ 2j+1), based on the X(3) critical point symmetry [5]. Although the original X(5/ ...

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