Investigation of quantum phase transitions in the spdf interacting boson model based on dual algebraic structures for the four-level pairing model

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 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.

[1]  A. Zilges,et al.  Origin of low-lying enhanced E1 strength in rare-Earth nuclei. , 2015, Physical review letters.

[2]  J. Draayer,et al.  Alternative solvable description of the E(5) critical point symmetry in the interacting boson model , 2015 .

[3]  J. Draayer,et al.  Emergent dynamical symmetry at the triple point of nuclear deformations , 2014, 1412.8557.

[4]  D. Vretenar,et al.  Microscopic description of octupole shape-phase transitions in light actinide and rare-earth nuclei , 2014, 1402.6102.

[5]  D. Rowe,et al.  Dual pairing of symmetry and dynamical groups in physics , 2012, 1207.0148.

[6]  F. Kondev,et al.  NUCLEAR DATA SHEETS FOR A=110 , 2012 .

[7]  F. Iachello,et al.  Effect of a fermion on quantum phase transitions in bosonic systems , 2011, 1111.0781.

[8]  H. Ganev.  Phase Structure of the Interacting Vector Boson Model , 2011, 1103.2464.

[9]  M. Caprio,et al.  Dual algebraic structures for the two-level pairing model , 2011, 1102.1482.

[10]  P. Cejnar,et al.  Quantum phase transitions in the shapes of atomic nuclei , 2010 .

[11]  T. Otsuka,et al.  Formulating the interacting boson model by mean-field methods , 2010 .

[12]  J. M. Arias,et al.  Search for critical-point nuclei in terms of the sextic oscillator , 2010 .

[13]  J. Draayer,et al.  New exact solutions of the standard pairing model for well-deformed nuclei , 2009, 0904.2830.

[14]  R. Casten.  Shape phase transitions and critical-point phenomena in atomic nuclei , 2006 .

[15]  A. Faessler,et al.  Remarks on the shape transition from spherical to deformed gamma unstable nuclei , 2004, nucl-th/0407013.

[16]  M. Caprio,et al.  Phase structure of the two-fluid proton-neutron system. , 2004, Physical review letters.

[17]  P. Quentin,et al.  A self-consistent approach to the quadrupole dynamics of medium heavy nuclei , 2004 .

[18]  J. Suhonen,et al.  Low-lying collective states inRu98–106isotopes studied using a microscopic anharmonic vibrator approach , 2003 .

[19]  D. Meyer,et al.  Signature for vibrational to rotational evolution along the yrast line. , 2003, Physical review letters.

[20]  J. Draayer,et al.  Algebraic solutions of an sl-boson system in the U(2l + 1) ↔ O(2l + 2) transitional region , 2002 .

[21]  F. Iachello.  Analytic description of critical point nuclei in a spherical-axially deformed shape phase transition. , 2001, Physical review letters.

[22]  D. Kusnezov,et al.  Octupole correlations in the transitional actinides and the spdf interacting boson model , 2001 .

[23]  C. E. Alonso,et al.  Coupling of dipole mode to γ-unstable quadrupole oscillations , 2000, nucl-th/0007052.

[24]  J. Draayer,et al.  New algebraic solutions for SO(6) ↔ U(5) transitional nuclei in the interacting boson model , 1998 .

[25]  J. Blachot.  Nuclear Data Sheets for A = 108☆ , 1997 .

[26]  L. Morss,et al.  The role of triaxiality in the ground states of even-even neutron-rich Ru isotopes , 1994 .

[27]  Balraj Singh.  Nuclear data sheets for A = 100* , 1990 .

[28]  Frank.  Shape transition and dynamical symmetries in the interacting boson model. , 1989, Physical review. C, Nuclear physics.

[29]  A. Negret,et al.  Nuclear Data Sheets for A = 106 , 1988 .

[30]  F. Iachello,et al.  INTERACTING BOSON MODEL OF COLLECTIVE OCTUPOLE STATES (I). The rotational limit , 1987 .

[31]  G. Maino,et al.  Properties of giant resonances in the interacting boson model , 1984 .

[32]  J. Blachot.  Nuclear Data Sheets for A = 104 , 1984 .

[33]  D. Frenne.  Nuclear data sheets for A = 102 , 1982 .

[34]  Joseph N. Ginocchio,et al.  Relationship between the Bohr collective Hamiltonian and the interacting-boson model , 1980 .

[35]  O. Scholten,et al.  Classical Limit of the Interacting-Boson Model , 1980 .

[36]  A. Arima,et al.  BOSON SYMMETRIES IN VIBRATIONAL NUCLEI , 1974 .

[37]  H. Ui.  SU(1,1) quasi-spin formalism of the many-boson system in a spherical field , 1968 .

[38]  Ernest M. Loebl,et al.  Group theory and its applications , 1968 .