Study of Spinor Symmetries in Nuclear Structure

One of the possible spinor symmetries of the interacting boson-fermion model is studied. The interacting boson -fermion model is a direct extension of the interacting boson model of nuclear collective states, where the fermion degrees of freedom of the odd nucleon are coupled to the boson core. Since in this model nuclei are treated as a mixed system of bosons and fermions, in order to discuss its symmetries the ordinary concept of symmetry is extended to spinor symmetries. In this work, we discuss the spinor symmetry, Spin(6), which arises when the bosons have SO(6) symmetry and the fermions occupy a single particle orbital with j = 3/2 which is described by an SU(4) symmetry. The states are classified according to the irreducible representations of the group chain Spin(6)(R-HOOK)Spin(5)(R-HOOK)Spin(3)(R -HOOK)Spin(2). An energy formula is derived assuming that the Hamiltonian can be written in terms of the Casimir operators of this group chain. The Spin(6) wave functions are constructed by expanding them into product of the boson SO(6) and fermion SU(4) wave functions. Using these wave functions we obtain closed expressions for electromagnetic (E0, M1, E2) transition rates, static moments and (one and two) nucleon transfer reaction intensities. Comparison of the calculations with the experimental data on iridium and gold isotopes shows that the Spin(6) symmetry scheme forms a reasonable zeroth order approximation in describing properties of these nuclei. Improvements over the results is possible by (i) incorporating other single particle orbitals (j = 1/2, 5/2, 7/2) to the dominant j = 3/2 orbital, (ii) mixing the boson SU(3) limit to the SO(6) limit. Although, in general, these effects must be dealt with numerical computations, the cases of mixing of the j = 1/2 orbital and the boson SU(3) limit can be studied in perturbation theory. We also report the results of the perturbation calculations of the above effects.