#### Bulg. J. Phys. vol.44 no.4 (2017), pp. 454-465

#### Multiple Multi-Orbit Fermionic and Bosonic Pairing and Rotational SU(3) Algebras

V.K.B. Kota

go back^{}*Physical Research Laboratory, Ahmedabad 380 009, India*Abstract.In nuclei with valence nucleons that are identical nucleons and occupyrnumber ofj-orbits, there will be 2^{r-1}number of multiple pairing (quasi-spin) SU(2) algebras with the generalized pair creation operatorS_{+}being a sum of single-jpair creation operators with arbitrary phases. Also, for each set of phases there will be a corresponding Sp(2Ω) algebra in U(2Ω) ⊃ Sp(2Ω); Ω = ∑ (2j+1)/2. Using this correspondence, derived is the condition for a general one-body operator of angular momentum rankkto be a quasi-spin scalar or a vector vis-a-vis the phases inS_{+}. These will give special seniority selection rules for electromagnetic transitions. We found that the phase choice advocated by Arvieu and Moszkowski gives pairing Hamiltonians having maximum correlation with well known effective interactions. All the results derived for identical fermion systems are shown to extend to identical boson systems such assd, sp, sdgandsdpfinteracting boson models (IBM's) with SU(2) → SU(1,1) and Sp(2\Omega) → SO(2Ω). Going beyond pairing, for a given set of oscillator orbits, there are multiple rotational SU(3) algebras both in shell model and IBM's. Different SU(3) algebras in IBM's are shown, usingsdgIBM as an example, to give different geometric shapes.