MICROSCOPIC FOUNDATIONS OF THE INTERACTING BOSON MODEL FROM THE SHELL-MODEL POINT-OF-VIEW

The validity of the essential ingredients of the microscopic formulati on of the interacting boson model: (i) truncation of the shell-model o r fermion space and (ii) the procedures for mapping the truncated ferm ion space on to the boson space, is tested over various (spherical, de formed and transitional) regions both in the simplistic single j-shell , identical boson systems and the more realistic multi j-shell, proton -neutron systems depending on the feasibility of such calculations. In the situations where the truncation and mapping procedures fail to re produce the exact shell-model results, it is demonstrated that renorma lization and higher order mapping procedures cure the associated probl ems, respectively and provide excellent agreements. In addition, a Ham iltonian of the interacting boson-fermion model which is relevant for a study of odd mass nuclei is derived for a single j-shell case in the shell-model framework, which yields results identical to those in the shell-model for the monopole pairing interaction.