Effects of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>β</mml:mi><mml:mtext>−</mml:mtext><mml:mi>γ</mml:mi></mml:mrow></mml:math>coupling in transitional nuclei and the validity of the approximate separation of variables

Caprio, M. A.

doi:10.1103/physrevc.72.054323

Cited by 93 publications

(98 citation statements)

References 42 publications

(115 reference statements)

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“…The presence of a bump might be related to the success of the confined β-soft (CBS) rotor model [43,44], the relevance of Davidson potentials in the description of X (5) propetries [47,48], as well as to the existence of a significant five-dimensional centrifugal effect found recently [49].…”

Section: Discussionmentioning

confidence: 99%

“…However, the existence of a bump in the PES corresponding to good experimental examples of X(5) might be related to the success of the confined β-soft (CBS) rotor model [43,44], employing an infinite square well potential displaced from zero, as well as to the relevance of Davidson potentials [45,46] is the minimum of the potential) in the description of X(5) properties [47,48]. It can also be related to the significant five-dimensional centrifugal effect [49] The prediction that the nucleus 186 Pt is critical is supported by several pieces of evidence.…”

Section: The X(5) Shape Phase Transitionmentioning

confidence: 99%

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E(5), X(5), and prolate to oblate shape phase transitions in relativistic Hartree-Bogoliubov theory

2006

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Relativistic mean field theory with the NL3 force is used for producing potential energy surfaces (PES) for series of isotopes suggested as exhibiting critical point symmetries.Relatively flat PES are obtained for nuclei showing the E(5) symmetry, while in nuclei corresponding to the X(5) case, PES with a bump are obtained. The PES corresponding to the Pt chain of isotopes suggest a transition from prolate to oblate shapes at 186 Pt.

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Section: Discussionmentioning

confidence: 99%

Section: The X(5) Shape Phase Transitionmentioning

confidence: 99%

E(5), X(5), and prolate to oblate shape phase transitions in relativistic Hartree-Bogoliubov theory

2006

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“…This is a limit in which the β 2 and γ degrees of freedom are weakly coupled and can be adiabatically separated, which is implied in the framework of the present work. The involvement of the K = 2 configurations in the collective motion implies the consideration of a strong β 2 -γ coupling [32].…”

Section: Electric Transition Probabilitiesmentioning

confidence: 99%

Nuclear collective motion with a coherent coupling interaction between quadrupole and octupole modes

et al. 2006

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A collective Hamiltonian for the rotation-vibration motion of nuclei is considered, in which the axial quadrupole and octupole degrees of freedom are coupled through the centrifugal interaction. The potential of the system depends on the two deformation variables β 2 and β 3 . The system is considered to oscillate between positive and negative β 3 -values, by rounding an infinite potential core in the (β 2 , β 3 )-plane with β 2 > 0. By assuming a coherent contribution of the quadrupole and octupole oscillation modes in the collective motion, the energy spectrum is derived in an explicit analytic form, providing specific parity shift effects. On this basis several possible ways in the evolution of quadrupole-octupole collectivity are outlined. A particular application of the model to the energy levels and electric transition probabilities in alternating parity spectra of the nuclei 150 Nd, 152 Sm, 154 Gd and 156 Dy is presented.

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“…However, an exact diagonalization of the X(5) Hamiltonian carried out in Ref. [8], has shown that many properties of the solution are dominated by β − γ coupling induced by the kinetic energy operator. The importance of the explicit treatment of the triaxial degree of freedom, i.e.…”

Section: Introductionmentioning

confidence: 99%

Beyond the relativistic mean-field approximation. III. Collective Hamiltonian in five dimensions

et al. 2009

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The framework of relativistic energy density functionals is extended to include correlations related to restoration of broken symmetries and fluctuations of collective variables. A new implementation is developed for the solution of the eigenvalue problem of a five-dimensional collective Hamiltonian for quadrupole vibrational and rotational degrees of freedom, with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The model is tested in a series of illustrative calculations of potential energy surfaces and the resulting collective excitation spectra and transition probabilities of the chain of even-even gadolinium isotopes.

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Effects ofβ−γcoupling in transitional nuclei and the validity of the approximate separation of variables

Cited by 93 publications

References 42 publications

E(5), X(5), and prolate to oblate shape phase transitions in relativistic Hartree-Bogoliubov theory

E(5), X(5), and prolate to oblate shape phase transitions in relativistic Hartree-Bogoliubov theory

Nuclear collective motion with a coherent coupling interaction between quadrupole and octupole modes

Beyond the relativistic mean-field approximation. III. Collective Hamiltonian in five dimensions

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