Collective states of the odd-mass nuclei within the framework of the Interacting Vector Boson Model

A supersymmetric extension of the dynamical symmetry group $Sp^{B}(12,R)$ of the Interacting Vector Boson Model (IVBM), to the orthosymplectic group $OSp(2\Omega/12,R)$ is developed in order to incorporate fermion degrees of freedom into the nuclear dynamics and to encompass the treatment of odd mass nuclei. The bosonic sector of the supergroup is used to describe the complex collective spectra of the neighboring even-even nuclei and is considered as a core structure of the odd nucleus. The fermionic sector is represented by the fermion spin group $SO^{F}(2\Omega)\supset SU^{F}(2)$. The so obtained, new exactly solvable limiting case is applied for the description of the nuclear collective spectra of odd mass nuclei. The theoretical predictions for different collective bands in three odd mass nuclei, namely $^{157}Gd$, $^{173}Yb$ and $^{163}Dy$ from rare earth region are compared with the experiment. The $B(E2)$ transition probabilities for the $^{157}Gd$ and $^{163}Dy$ between the states of the ground band are also studied. The important role of the symplectic structure of the model for the proper reproduction of the $B(E2)$ behavior is revealed. The obtained results reveal the applicability of the models extension.Comment: 18 pages, 8 figure

Deformations of the Boson sp(4,R)sp(4,R) Representation and its Subalgebras

The boson representation of the sp(4,R) algebra and two distinct deformations of it, are considered, as well as the compact and noncompact subalgebras of each. The initial as well as the deformed representations act in the same Fock space. One of the deformed representation is based on the standard q-deformation of the boson creation and annihilation operators. The subalgebras of sp(4,R) (compact u(2) and three representations of the noncompact u(1,1) are also deformed and are contained in this deformed algebra. They are reducible in the action spaces of sp(4,R) and decompose into irreducible representations. The other deformed representation, is realized by means of a transformation of the q-deformed bosons into q-tensors (spinor-like) with respect to the standard deformed su(2). All of its generators are deformed and have expressions in terms of tensor products of spinor-like operators. In this case, an other deformation of su(2) appears in a natural way as a subalgebra and can be interpreted as a deformation of the angular momentum algebra so(3). Its representation is reducible and decomposes into irreducible ones that yields a complete description of the same

Simultaneous Description of Even-Even, Odd-Mass and Odd-Odd Nuclear Spectra

The orthosymplectic extension of the Interacting Vector Boson Model (IVBM) is used for the simultaneous description of the spectra of different families of neighboring heavy nuclei. The structure of even-even nuclei is used as a core on which the collective excitations of the neighboring odd-mass and odd-odd nuclei are built on. Hence, the spectra of the odd-mass and odd-odd nuclei arise as a result of the consequent and self-consistent coupling of the fermion degrees of freedom of the odd particles, specified by the fermion sector $SO^{F}(2\Omega)\subset OSp(2\Omega/12,R)$, to the boson core which states belong to an $Sp^{B}(12,R)$ irreducible representation. The theoretical predictions for different low-lying collective bands with positive and negative parity for two sets of neighboring nuclei with distinct collective properties are compared with experiment and IBM/IBFM/IBFFM predictions. The obtained results reveal the applicability of the used dynamical symmetry of the model.Comment: 6 pages, 1 figure, A talk given at the 7th International Conference of the Balkan Physical Union, September 9-13, 2009, Alexandropoulos, Greec