Microscopic foundation of the interacting boson model in thes d-shell nuclei

Abstract

Starting from an isospin invariant shell-model hamiltonian, we describe a method for deriving microscopically the IBM-hamiltonian appropriate to light sd-shell nuclei. The key ingredients of our approach are: a) the Belyaev-Zelevinsky-Marshalek (BZM) bosonization procedure; b) two successive unitary transformations that extract the "maximally (s~, s~) and J decoupled" collective bosons with angular momenta J=0 + s~+, + + + d+~(T= 0), d+~(T= 1)).The method is applied to obtain the low-energy spec-= 2(d,~,,, d~, tra and the electron scattering form factors for the 0~-~2~-transitions in g~ and 24Mg. Good agreement with the exact shell-model results is achieved. The inclusion of proton-neutron bosons (s~+~, d~+~ (T= 1), d~+~(T=0)), as well as the renormalization of boson parameters due to the non-collective degrees of freedom, are shown to play a crucial role.