Boson representations of fermion systems: Proton-neutron systems.

Abstract

Applications of a procedure recently proposed to construct boson images of fermion Hamiltonians are shown for proton-neutron systems. First the mapping from SD fermion onto sd boson spaces is discussed and a ${Q}_{\ensuremath{\pi}}$\ensuremath{\cdot}${Q}_{\ensuremath{\nu}}$ interaction investigated. A Hermitian one-body Q boson operator is derived and analytical expressions for its coefficients are obtained. A (${Q}_{\ensuremath{\pi}}$+${Q}_{\ensuremath{\nu}}$)\ensuremath{\cdot}(${Q}_{\ensuremath{\pi}}$+${Q}_{\ensuremath{\nu}}$) interaction is, then, studied for particle-hole systems and the connections with the ${\mathrm{SU}}^{\mathrm{*}}$(3) dynamical symmetry of the neutron-proton interacting boson model are discussed. Finally, an example of mapping from SDG onto sdg spaces is analyzed. Fermion spectra and E2 matrix elements are well reproduced in the boson spaces.