Orthosymplectic supersymmetry and its application to nuclear physics.

Abstract

Phenomenological models have long been employed by nuclear physicists to explain systematic trends in data. The Geometrical Model of Bohr, Mottelson and Rainwater (GM) and the Interacting Boson Model (IBM) are two such models that have been used to study the spectra of even-even nuclei. The IBM differs from previous boson models in that the total number of bosons is conserved and finite. In the GM the bosons of lowest angular momentum have ℓ = 2 and are taken to represent quadrupole shape vibrations, whereas in the IBM the bosons are generally taken to have ℓ = 0, 2 and can be interpreted as correlated pairs of fermions. These models have been extended to handle the neighboring odd-even nuclei by considering the interaction of a fermion with the bosonic space. If the fermionic space consists of the single-particle angular momenta j₁, j₂, ..., then the largest group describing this mixed system of bosons and fermions is the product group Uᴮ(5) x Uᶠ(m(j)) (GM) or Uᴮ(6) x Uᶠ(m(j)) (IBM), where m(j) = Σ(2jᵢ + 1). If one of the subgroups of Uᴮ(5) or Uᴮ(6) is isomorphic to one of the subgroups of Uᶠ(m(j)), then we can combine the two group chains into a common bose-fermi group chain. These combined bose-fermi groups have been used extensively in the Interacting Boson-Fermion Model (IBFM) to study odd-even nuclei and have been claimed as evidence for the existence of supersymmetries; however, the superalgebras associated with these supersymmetries were never identified. We have identified, for the first time, the superalgebras that are associated with some of these combined bose-fermi symmetries. This superalgebra, the non-compact orthosymplectic superalgebra Osp(4s+2/2,R), is fundamentally different than those previously used in the IBFM, where the product algebra was simply embedded into the superalgebra U(6/m(j)). The U(6/m(j)) superalgebras do not imply any particular coupling scheme, and hence cannot be associated with any particular one of the combined bose-fermi algebras. The last few chapters are devoted to a study of coherent states for the non-compact orthosymplectic supergroups Osp(1/2N,R) and Osp(2/2N,R), although the results generalize rather easily to the compact versions of these supergroups. These coherent states, besides being of mathematical interest, form the basis for a study of Osp(M/2N,R) coherent states. (Abstract shortened with permission of author.)