Abstract
A recent analysis of the correspondence between fermion and boson spaces is extended to systems with an odd number of fermions. A fermion space is now mapped onto a boson-fermion space. The case is discussed of the SD-j and sd-j spaces, i.e., spaces in which an odd particle moving in a j orbit is coupled to systems of S,D pairs and s,d bosons, respectively. The sd-j image of the quadrupole-quadrupole interaction is constructed both for systems of identical particles and for proton-neutron systems. Numerical comparisons are shown between spectra in the SD-j and sd-j spaces. The role of the exchange term in the sd-j Hamiltonian is analyzed. The comparison with other mapping techniques as well as with phenomenological Hamiltonians is discussed.
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