Search for critical-point nuclei in terms of the sextic oscillator

Journal Article · Thu Apr 15 00:00:00 EDT 2010 · Physical Review. C, Nuclear Physics

DOI:https://doi.org/10.1103/PHYSREVC.81.044304· OSTI ID:21388913

Levai, G; Arias, J M ^[1]

---

1. Institute of Nuclear Research of the Hungarian Academy of Sciences (ATOMKI), Post Office Box 51, H-4001 Debrecen (Hungary)

The spherical to deformed gamma-unstable shape transition in nuclei is discussed in terms of the sextic oscillator as a gamma-independent potential in the Bohr Hamiltonian. The wave functions, energy eigenvalues, and electric quadrupole and monopole transition rates are calculated in closed analytical form for the lowest-lying energy levels. It is shown that the locus of critical points for the spherical to deformed gamma-unstable shape phase transition corresponds to a parabola in the parameter space of the model. The ratios of energy eigenvalues and electromagnetic transition probabilities are constant along this parabola. It is thus possible to associate parameter-free benchmark values to the ratios of relevant observables at the critical point of the transition that can be compared to experimental data. In addition, systematic studies of the shape evolution in isotope chains can be performed within the model. As an application, the model parameters are fitted to the energy spectra of the chains of even-even Ru, Pd, and Cd isotopes and the electric quadrupole transition probabilities are calculated. It is found that {sup 104}Ru, {sup 102}Pd, and {sup 106,108}Cd nuclei, which are usually considered to be good candidates for the E(5) symmetry, lie rather close to the critical parabola that separates the spherical and deformed gamma-unstable domains. The isotope {sup 116}Cd is proposed as a new candidate for a similar critical-point nucleus.

• OSTI ID: 21388913
• Journal Information: Physical Review. C, Nuclear Physics, Vol. 81, Issue 4; Other Information: DOI: 10.1103/PhysRevC.81.044304; (c) 2010 The American Physical Society; ISSN 0556-2813
• Country of Publication: United States
• Language: English

Related Subjects

73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BENCHMARKS
CADMIUM 106
CADMIUM 108
CADMIUM 116
CHAINS
E2-TRANSITIONS
EIGENVALUES
ENERGY LEVELS
ENERGY SPECTRA
EVEN-EVEN NUCLEI
HAMILTONIANS
OSCILLATORS
PALLADIUM 102
PARABOLAS
PHASE TRANSFORMATIONS
RUTHENIUM 104
SIMULATION
SPHERICAL CONFIGURATION
SYMMETRY
WAVE FUNCTIONS
CADMIUM ISOTOPES
CONFIGURATION
ELECTRONIC EQUIPMENT
ENERGY-LEVEL TRANSITIONS
EQUIPMENT
FUNCTIONS
INTERMEDIATE MASS NUCLEI
ISOTOPES
MATHEMATICAL OPERATORS
MULTIPOLE TRANSITIONS
NUCLEI
PALLADIUM ISOTOPES
QUANTUM OPERATORS
RUTHENIUM ISOTOPES
SHAPE
SPECTRA
STABLE ISOTOPES