Quantum phase transitions in odd-A nuclei: The effect of the odd particle from spherical to oblate shapes

Quantum shape-phase transitions in odd-nuclei are investigated within the framework of the interacting boson-fermion model (IBFM). We consider the case of a single-j fermion coupled to an even-even boson core that performs a transition from spherical to oblate shapes varying a control parameter in the boson Hamiltonian. The aim of this work is to see the effect of the coupling of the unpaired fermion on the transition, to understand how the coupled single particle modifies the geometric shape of the system and how each of the odd states behaves when the boson core shifts along the transitional path.Scientific and Technical Research Council of Turkey BIDEB-2224AMinisterio de Economía y Competitividad FIS2011-28738- c02-01, CSD2007-00042Junta de Andalucía FQM160, P11-FQM-763

The one nucleon transfer operator in the microscopic IBM without NOA

The mapping of the single fermion creation operator (ci†) onto the Interacting Boson-Fermion space (IBFM) is revisited within the Generalized Seniority scheme. In the original work the Number Operator Approximation (NOA) was used. Here the exact evaluation of the relevant terms using exact values for the fermion matrix elements in the Generalized Seniority scheme is worked out. This provides a new, improved, single particle transfer operator to be used in IBFM.Ministerio de Economía y Competitividad FIS2011-28738-c02-01Junta de Andalucía FQM-160 y Project P11-FQM-7632Consolider-Ingenio 2010 Programme CPAN CSD2007-0004

Odd-even 147–153Pm isotopes within the neutron-proton interacting boson-fermion model

Low-lying energy states of the 147 -153Pm isotopic chain are studied within the framework of the neutron-proton interacting boson-fermion model (IBFM-2). The spectra of these isotopes show a transition from a particle coupled to a vibrational core to a particle coupled to a deformed one. The calculation reproduces this behavior. In addition, reduced transition probabilities B(E2) and B(M1) and quadrupole and magnetic moments, as well as spectroscopic factors corresponding to stripping and pickup transfer reactions, are calculated. Obtained results compare well with the available experimental data, which reinforces the reliability of the wave functions obtained within the IBFM-2 model.Ministerio de Ciencia e Innovación (España) FIS2009-07277 FIS2008-04189CPAN-Ingenio CSPD-2007-00042Junta de Andalucía FQM160 P07-FQM-0296

Shape phase transition in odd nuclei in a multi- j model: The UB(6) ⊗ UF(12) case

The phase transition in odd nuclei when the underlying even-even core nuclei experience a transition from spherical to deformed γ-unstable shapes is investigated. The odd particle is assumed to be moving in the three single-particle orbitals j=1/2,3/2, and 5/2. At the critical point in the phase transition, an analytic solution to the corresponding Bohr Hamiltonian, called E(5/12), is worked out. Energy spectra and electromagnetic transitions and moments are presented. The same problem is also attacked in the framework of the interacting boson-fermion model (IBFM). Two different Hamiltonians are used. The first one is constructed ad hoc so as to mimic the situation in the E(5/12) model. The second one leads to the occurrence of the OB(6) ⊗ UF(12) symmetry when the boson part approaches the O(6) condition. The entire transition line is studied with this Hamiltonian and, in particular, the critical point. Both IBFM calculations at the critical point are consistent with the E(5/12) results.Ministerio de Educación y Ciencia (España)FEDER FIS2005-0110

One-particle spectroscopic intensities as a signature of shape phase transition: The γ -unstable case

We investigate the evolution of one-particle spectroscopic intensities as a possible signature of shape phase transitions. The study describes the odd systems in terms of the interacting boson–fermion model. We consider the particular case of an odd j=3/2 particle coupled to an even-even boson core that undergoes a phase transition from spherical U(5) to γ-unstable O(6) situation. At the critical point, our findings are compared with the one-particle spectroscopic intensities that can be obtained within the E(5/4) model proposed by [F. Iachello, Phys. Rev. Lett. 95, 052503 (2005); F. Iachello, in Symmetries and Low-Energy Phase Transitions in Nuclear Structure Physics, edited by G. Lo Bianco (University of Camerino Press, Camerino, Italy, in press)].Ministerio de Educación y Ciencia y FEDER FIS2005-0110

Search for E(5) symmetry in nuclei: The Ru isotopes

We carry out an interacting boson model study of the Ru isotopes using a U(5)-SO(6) transitional Hamiltonian with fixed parameters, where the variation is due only to the change in boson number N. Transitional behavior in 104Ru is compared with recent predictions of an E(5) critical symmetry, including a modified version with an alternative b dependence for the T(E2) operator.Ministerio de Ciencia y Tegnología PB98- 111

Importance of the single-particle continuum in BCS pairing with a pseudostate basis

In a recent work [arXiv:1510.03185] the use of the Transformed Harmonic Oscillator (THO) basis for the discretization of the singleparticle continuum into a Generalized Bardeen-Cooper-Schrieffer (BCS) formalism was proposed for the description of weakly bound nuclei. We make use of the flexibility of this formalism to study the evolution of the pairing when the nucleus becomes more and more weakly bound. Specifically we focus on the evolution of the occupation of the different partial waves in 22O when the Fermi level approaches zer

β-decay rates of 121–131Cs in the microscopic interacting boson-fermion model

β -decay rates of 121–131 Cs have been calculated in the framework of the neutron-proton interacting boson- fermion model (IBFM-2). For odd- A nuclei, the decay operator can be written in a relatively simple form in terms of the one-nucleon transfer operator. Previous studies of β decay in IBFM-2 were based on a transfer operator obtained by using the number operator approximation (NOA). In this work a new form of the one-nucleon transfer operator, derived microscopically without the NOA approximation, is used. The results from both approaches are compared and show that the deviation from experimental data is reduced without using the NOA approximation. Indications about the renormalization of the Fermi and Gamow-Teller matrix elements are discussed. This is a further step toward a more complete description of low-lying states in medium and heavy nuclei which is necessary to compute reliable matrix elements in studies of current active interest such as double- β decay or neutrino absorption experimentsMinisterio de Economía y Competitividad (España) FIS2014-53448-C2-1-PConsejería de Economía, Innovación, Ciencia y Empleo de la Junta de Andalucía FQM-160 P11-FQM-763

Review of critical point symmetries and shape phasetransitions within algebraic and collective models

Several aspect of shape phase transitions and critical point symmstries are reviewed inthis contribution within the frameworks of the Interacting Boson Model(IBM) and theInteracting Boson Fermion Model(IBFM) for even and odd sysstems respectively andcompared with collective geometric models. We discuss in particular the case of an oddj= 3/2 particle coupled to an even-even boson core that undergoes a transition from thespherical limitU(5) to theγ-unstable limitO(6). The spectrum and transition rates atthe critical point are similar to those of the even core and they agree qualitatively with theE(5/4) boson-fermion symmetry. We discuss also theUBF(5) toSUBF(3) shape phasetransition in which the allowed fermionic orbitals arej= 1/2,3/2,5/2. The formalismof the intrinsic or coherent states is used to describe in details the ground state as wellas the excitedβ−andγ−bands. This formalism is also used to calculate the PotentialEnergy Surface of the cubic quadrupole operator that leads to traixial

Backbending of Dy isotopes described with the neutron-photon IBA plus two-quasiparticle model

The formalism of the neutron-photon interacting boson model, extended to include two-quasiparticle excitations, is used in a study of the high spin states of 154,156,158Dy isotropes. Good agreement is obtained between the calculated energies and transition rates and the experimental results