The Ginocchio Model and the Interacting Boson Approximation

Abstract

Various approaches to nuclear collective motions have been made since Bohr and Mottelson published their classic works.¹⁾ Among these, the Interacting Boson Approximation²⁾ (IBA) and the boson expansion theory³⁾ have been successful in explaining properties of vibrational, transitional and rotational nuclei. The interacting boson approximation assumes that the collective low-lying states of heavy nuclei are composed primarily of monopole and quadrupole pairs of fermions that are approximated as monopole and quadrupole bosons.⁴⁾ The boson expansion method⁵⁾ determines an expansion for the fermion operators by demanding that the commutation relations are preserved in the boson space. In general this leads to an infinite expansion for the fermion pair operators in powers of bosons. Furthermore all the fermion pairs, not just the collective pairs, are mapped onto bosons. This theory is implemented in practice by first making a BCS transformation from particles to quasiparticles.³⁾ The boson expansions are then made in the quasiparticle basis. Ultimately only a collective quadrupole boson in this quasiparticle space is retained and an effective boson Hamiltonian for this collective quadrupole boson is derived.³⁾