Boson-fermion mappings for odd systems from supercoherent states

We extend the formalism whereby boson mappings can be derived from generalized coherent states to boson-fermion mappings for systems with an odd number of fermions. This is accomplished by constructing supercoherent states in terms of both complex and Grassmann variables. In addition to a known mapping for the full so(2$N$+1) algebra, we also uncover some other formal mappings, together with mappings relevant to collective subspaces.Comment: 40 pages, REVTE

Interaction strengths in the interacting boson-fermion model

Although a number of different types of boson-fermion interactions are possible in the interacting boson-fermion model, empirical results have shown that the exchange term is of cardinal importance. A recently constructed similarity transformation which reexpresses the Dyson boson images of the single-j shell fermion operators in terms of seniority bosons is used to confirm that the origin of the exchange term in spherical nuclei is linked to the quadrupole pairing interaction between identical nucleons. The relative importance of the exchange and direct boson-fermion interactions is also discussed and it is indicated that the direct term is essential for a complete description of that excited state which carries the j value of the shell. © 1988 The American Physical Society.Articl

Collective boson realization for the nuclear Sp(6) model

We demonstrate the construction of an exact sd-boson realization of the Sp(6) fermion dynamical symmetry model (Ginocchio model) from an application of the generalized Dyson mapping and subsequent truncation. This realization is an illustration of the validity of the procedure initiated by Geyer and Hahne and analyzed in full generality by Kim and Vincent. We discuss the connection of the Sp(6) model with the SU(3) limit of the interacting-boson model and the implications for the interpretation of its parameters. © 1991 The American Physical Society.Articl