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On the correspondence between fermion and boson states and operators

1980; Elsevier BV; Volume: 337; Issue: 3 Linguagem: Inglês

10.1016/0375-9474(80)90152-9

1873-1554

Joseph N. Ginocchio, Igal Talmi,

Cold Atom Physics and Bose-Einstein Condensates

Mapping of shell-model (fermion) Hamiltonians onto boson Hamiltonians which underly the interaction boson model 1–5) is investigated. A simple correspondence is defined and a sufficient condition given for shell-model Hamiltonians to simply correspond to finite hermitian boson Hamiltonians. A special case is discussed where diagonalization of a shell-model Hamiltonian for valence protons and neutrons can be exactly carried out in an equivalent (but different) boson space. If, however, the proton Hamiltonian and neutron Hamiltonian are diagonal in the seniority scheme, mapping of fermion states onto orthogonal boson states cannot be a simple correspondence. In that case the boson quadrupole operators equivalent to fermion guadrupole operators cannot be single-boson operators but must be more complicated, ones.