Generalized interacting boson model and the collective behaviour in nuclei

The effect of including the high spin bosons on the manifestation of collective behaviour in nuclei is examined by plotting theB(E2; 2⁺→0⁺) rates as a function of neutron number for various values ofη, whereη is the highest angular momentum of the bosons included in the calculation.B(E2; 2⁺→0⁺) values of a large number of nuclei in various regions of the nuclear periodic table are calculated with a single value for the effective charge in the generalized scheme. Irreducible representations of SU(3) contained in the symmetric partition [N] of U(15) are worked out for integersN uptoN=15, to enable the explicit inclusion of theg boson into calculations. The experimentally observed odd-K bands in²³⁴U and¹⁸⁴W are described as a direct consequence of theg boson.     

T = 0 versusT = 1 pairing in 0(36) limit of IBM-4 for heavyN = Z nuclei

In theO(36) limit of the interacting boson model including spin-isospin degrees of freedom (IBM-4), starting with a group chain that preservess andd boson spins and isospins together with a simple mixing hamiltonian, it is shown that the model generates, for heavyN =Z nuclei, even-even to odd-odd staggering in the number ofT = 0 pairs in the ground states for moderate difference in the basicT = 0 andT = 1s-boson pair energies; the staggering disappears when the energy difference is large.     

Group theoretical aspects ofU B(6) ⊗U F(20) symmetry limits of IBFM related to theU B(5) andO B(6) limits of IBM

TheU ^B(6)⊗U ^F(20) Bose-Fermi dynamical symmetry of interacting boson-fermion model arises when the odd nucleon occupies single particle orbits withj=1/2, 3/2, 5/2, and 7/2. The subgroup structures ofU ^B(6)⊗U ^F(20) related to theU ^B(5) andO ^B(6) limits of sdIBM (U ^B(6)) are analysed. Broadly speaking,U ^B(6)⊗U ^F(20) admitsU ^BF(5)⊗U _s ^F (4), Spin^BF(5)⊗U _k ^F (5) andU ^BF(5)⊗U _s ^F (2) limits withU ^B(5) core and Spin^BF(6),O ^BF(5)⊗U _s ^F (4), Spin^BF(6)⊗U _k ^F (5) andO ^BF(6)⊗U _s ^F (2) limits withO ^B(6) core respectively. For each of these seven symmetry limits, group chains, quantum numbers labelling the basis states, generators and Casimir operators for the various subgroups and energy formulas are given. Recoupling coefficients (reduced Wigner coefficients) for constructing wavefunctions of low-lying states are tabulated and these will allow (together with sdIBMU ^B(5) andO ^B(6) limit results) one to calculateB(E2)’s,B(M1)’s, one and two nucleon transfer strengths etc. in the seven symmetry limits. Experimental examples for theU ^B(6)⊗U ^F(20) symmetry limits are briefly discussed.     

Microscopic insight in the study of yrast bands in selenium isotopes

The yrast bands of even-even selenium isotopes with A = 68–78 are studied in the framework of projected shell model, by employing quadrupole plus monopole and quadrupole pairing force in the Hamiltonian. The oblate and prolate structures of the bands have been investigated. The yrast energies, backbending plots and reduced E2 transition probabilities and g-factors are calculated and compared with the experimental data. The calculated results are in reasonably good agreement with the experiments.      

<Emphasis Type="Italic">O</Emphasis>(12) limit and complete classification of symmetry schemes in proton-neutron interacting boson model

It is shown that the proton-neutron interacting boson model (pnIBM) admits new symmetry limits withO(12) algebra which breakF spin but preserves theF _z quantum numberM _F. The generators ofO(12) are derived and the quantum numberU ofO(12) for a given boson numberN is determined by identifying the corresponding quasi-spin algebra. TheO(12) algebra generates two symmetry schemes and for both of them, complete classification of the basis states and typical spectra are given. With theO(12) algebra identified, complete classification of pnIBM symmetry limits with goodM _F is established.