Study of Phase Transitions and Critical Points in the Rare-Earth Region in the Framework of the Interacting Boson Model (IBM-1)

خالد صالح جاسم الجميلي

J. E. García-Ramos, J. M. Arias, José Barea +1 more

Wen-Ting Dong, Yu Zhang, B. C. He +4 more

Abstract The spectral fluctuations and transition intensity fluctuations in the excited-state quantum phase transitions (ESQPTs) have been investigated within the framework of the interacting boson model (IBM) by adopting three statistical measures, including the nearest neighbor level spacing distribution P ( S ) measuring the chaoticity (regularity) in energy spectra, the Δ 3 ( L ) statistics of Dyson and Mehta measuring the spectral rigidity and the intensity distribution P ( y ) measuring the chaoticity (regularity) in B ( E 0) transitions. The results indicate that that the ESQPT as a function of the excitation energy may occur as a transition from regular (or semiregular) to highly chaotic if only the associated whole spectrum is chaotic, which fits most of the deformed situations in the IBM including those in the U(5)–SU(3) and SU(3)–O(6) transitional regions. Otherwise, the ESQPT will appear as a transition from regular (or semiregular) to regular such as the cases in the U(5)–O(6) transitional region or those on the ‘Alhassid–Whelan arc’, which represents a nearly regular parameter region connecting the U(5) and SU(3) limits in the IBM.

M. A. Jafarizadeh, Amir Jalili, N. Fouladi +1 more

Abstract The building blocks of the interacting boson model (IBM) are associated with both s and d bosons for positive parity states. An extension of sd −IBM along these models to spdf −IBM can provide the appropriate framework to describe negative parity states. In this paper, a solvable extended transitional Hamiltonian based on the affine SU ( 1 , 1 ) ^ Lie algebra is proposed to describe low lying positive and negative parity states between the spherical and deformed gamma-unstable shape. Quantum phase transitions (QPTs) are investigated based on dual algebraic structures for the four-level pairing model. Numerical extraction to low-lying energy levels and transition rates within the control parameters of this evaluated Hamiltonian are presented for various N values. By reproducing the experimental results, the method based on the signatures of the phase transition, such as the expectation value of the boson number operators in the lowest excited states, are used to provide a better description of Ru isotopes in this transitional region.

J. M. Arias

N. V. Zamfir, Gustavo E. Fernandes