Relationship between X(5) models and the interacting boson model

Journal Article · Sun Aug 15 00:00:00 EDT 2010 · Physical Review. C, Nuclear Physics

DOI:https://doi.org/10.1103/PHYSREVC.82.024316· OSTI ID:21419429

Barea, Jose ^[1]; Arias, Jose M ^[2]; Garcia-Ramos, Jose Enrique ^[3]

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1. Instituto de Estructura de la Materia, CSIC, Serrano 123, E-28006 Madrid (Spain)
2. Departamento de Fisica Atomica, Molecular y Nuclear, Facultad de Fisica, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla (Spain)
3. Departamento de Fisica Aplicada, Universidad de Huelva, E-21071 Huelva (Spain)

The connections between the X(5) models [the original X(5) using an infinite square well, X(5)-{beta}{sup 8}, X(5)-{beta}{sup 6}, X(5)-{beta}{sup 4}, and X(5)-{beta}{sup 2}], based on particular solutions of the geometrical Bohr Hamiltonian with harmonic potential in the {gamma} degree of freedom, and the interacting boson model (IBM) are explored. This work is the natural extension of the work presented in Garcia-Ramos and Arias, Phys. Rev. C 77, 054307 (2008) for the E(5) models. For that purpose, a quite general one- and two-body IBM Hamiltonian is used and a numerical fit to the different X(5) model energies is performed; then the obtained wave functions are used to calculate B(E2) transition rates. It is shown that within the IBM one can reproduce well the results for energies and B(E2) transition rates obtained with all these X(5) models, although the agreement is not so impressive as for the E(5) models. From the fitted IBM parameters the corresponding energy surface can be extracted and, surprisingly, only the X(5) case corresponds in the moderately large N limit to an energy surface very close to the one expected for a critical point, whereas the rest of models are situated a little further away.

• OSTI ID: 21419429
• Journal Information: Physical Review. C, Nuclear Physics, Vol. 82, Issue 2; Other Information: DOI: 10.1103/PhysRevC.82.024316; (c) 2010 The American Physical Society; ISSN 0556-2813
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
DEGREES OF FREEDOM
E2-TRANSITIONS
HAMILTONIANS
HARMONIC POTENTIAL
INTERACTING BOSON MODEL
MATHEMATICAL SOLUTIONS
TWO-BODY PROBLEM
WAVE FUNCTIONS
ENERGY-LEVEL TRANSITIONS
FUNCTIONS
MANY-BODY PROBLEM
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MULTIPOLE TRANSITIONS
NUCLEAR MODELS
NUCLEAR POTENTIAL
POTENTIALS
QUANTUM OPERATORS
SHELL MODELS