AN APPLICATION OF THE DEMOCRATIC MAPPING IN REALISTIC SYSTEMS

Abstract

The democratic mapping is used for the calculation of low lying states of nuclei in the sd and fp shells. In addition to demonstrating the applicability of the method in realistic cases where many non-degenerate levels are present, the method allows for the ranking of the various bosons according to their importance as building blocks of low lying states. It is proven that the s and d bosons are the most important building blocks, followed by the d' and g bosons. Thus one of the basic assumptions of the Interacting Boson Model (IBM) is proven to be correct. Very good agreement between the boson calculation and the shell model results is obtained for A = 20 nuclei when 12 bosons are taken into account, while an even larger number of bosons is required to reproduce the low-lying states of the A = 44 nuclei. In order to obtain equally good results with a smaller number of bosons one needs to introduce effective boson hamiltonians which correspond to truncated fermion spaces.