A new approximate projection method is proposed to treat the spurious state problem in the Dyson boson description of nuclear collective motion. In this method, successive orders of approximate projection are used to construct the various physical states in the Dyson boson representation of the shell model. Even in the lowest orders of approximation, the approximately projected boson states obtained turn out to be quite accurate in producing physical quantities. Furthermore, this approximate projection method is applicable not only to vibrational or transitional nuclei but also to rotational nuclei.
The interacting boson model introduced in Section 33 has been described from the point of view of the collective model of the nucleus. The 5 components of a d -boson have been related to the 5 degrees of freedom of a shape, with constant volume, which may have quadrupole deformations. The s -boson has been added to simplify the construction of eigenstates which belong to irreducible representations of the U (6) group, the fully symmetric ones being characterized by an integer N . We saw how simple Hamiltonians including single boson energies and boson boson interactions give very good description of various kinds of collective motion.