Introduction

In addition to low-lying collective modes extensively discussed in Volume 1 and in this book in terms of bosonic degrees of freedom, nuclei also display high-lying collective modes. The microscopic description of these modes is different from that of the low-lying modes, as shown schematically in Fig. 12.1. The latter are built from correlated pairs of nucleons in the valence shell, while the former are built from correlated particle-hole pairs, with one or more particles outside the valence shell. A description of high-lying modes in terms of bosons is also possible, although not particularly useful in itself since only one vibrational state of each mode is observed. It becomes useful only when coupling low-lying and high-lying modes. This coupling leads to the splitting and mixing of the high-lying modes which is often observed.

High-lying collective modes have been introduced in the interacting boson model by Morrison and Weise (1982) and, independently, by Scholtz and Hahne (1983). They proposed a description of the giant dipole resonance via a p boson coupled to a system of interacting s and d bosons and solved the resulting Hamiltonian numerically. Subsequently, Rowe and Iachello (1983) showed that, for deformed nuclei, a class of Hamiltonians exists that correspond to dynamic symmetries and that for such Hamiltonians analytic results can be obtained for energies and transition matrix elements. Since then the model has been applied to several (series of) isotopes (Maino et al., 1984; 1985; Scholtz, 1985; Maino et al., 1986a; Scholtz and Hahne, 1987; Nathan, 1988) and has been extended to include monopole and quadrupole giant reso-nances (Maino et al., 1986b) and dipole resonances in light (Maino et al., 1988) and odd-even nuclei (Maino, 1989).