Fermion degrees of freedom in ortosymplectic extension of interacting vector boson model

We introduce fermion degrees of freedom to the symplectic extension of the Interacting Vector Boson Model /IVBM/, which describes very accurately the energy spectra of the even-even nuclei, obtained in a new more physical application of the dynamical symmetry: S p (12 ,R ) ⊃U (6 ) ⊃U (3 ) ⊗U (2 ) ⊃O (3 ) ⊗(U (1 ) ⊗U (1 ) ) . In this way we obtain the super symmetric ortosymplectic upgrade OS p(2Ω/12, R), which contains the direct product of S O^F (2Ω) of the fermion degrees of freedom and the boson part S p^B(12, R) describing the even-even system. This allows the description of odd and odd-odd nuclei, which can be done simultaneously by coupling to the angular momentum L of the collective states of the low laying excited bands of the even-even core the total moment j_n = l_n + s_n for a single fermion n, or the coupled momenta of the two odd particles J = L+j_n. The respective Hamiltonians containing the terms reflecting these couplings are constructed and their eigenvalues are obtained analytically. The results are illustrated by the comparison of the theory with the experimental spectra of some neighboring even-even and odd heavy nuclei.