#### Bulg. J. Phys. vol.44 no.4 (2017), pp. 478-488

#### Introduction of Fermion Degrees of Freedom in IVBM for the Description of Spectra of Odd Nuclei

V.P. Garistov

go back^{1}, A.I. Georgieva^{2}^{1}*Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria*^{2}*Institute of Electronics, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria*Abstract.A very accurate results for the energy spectra of the even-even nuclei have been obtained in a new more physical application of the dynamical symmetry:Sp(12,R) ⊃U(6) ⊃U(3) ⊗U(2) ⊃O(3) ⊗ (U(1) ⊗U(1)) of the Interacting Vector Boson Model (IVBM). The description of odd-mass nuclei requires the introduction of fermion degrees of freedom, that we make through the total momentI=l+_{n}sfor a single fermion_{n}ncoupled to the angular momentumLof the states of the ground and octupole bands of the even-even coreJ=L+I. From an algebraic point of view, this can be presented as an extension of the dynamical symmetry groupSp(12,R) of the IVBM to the orthosymplectic groupOSp(2Ω/12,R), which contains the direct product ofSO^{F}(2Ω) of the fermion degrees of freedom and the boson partSp^{B}(12,R) describing the even-even system. The approach can be extended for the description of the spectra of odd-odd nuclei as well. The results are illustrated by the comparison of the theory with the experimental spectra of the ground and octupole bands ot the even-even nuclei^{236}U and^{238}Pu and the long collective bands build on them in the odd^{237}U and^{239}Pu.