Investigation of Collective Nuclei in the sdg Interacting Boson Model


Principal Investigator

Serdar Kuyucak

Theoretical Physics,

Research School of Physical Sciences and Engineering

This project investigates collective excitation modes in deformed nuclei. The initial goal of describing
low-lying, low-spin excitation modes has been extended to include high-spin states and, in particular, superdeformed states which have become one of the frontier areas. We use the interacting boson model (IBM) with s, d, and g bosons where d and g represent the quadrupole and hexadecapole degrees of freedom. The basis space in sdg-IBM is very large, therefore, use of a supercomputer is necessary for an exact diagonalization of model Hamiltonians. Our aim is to provide a consistent picture for both low and high-spin collective spectra. Some of the topics considered in this project are i) nature of double-phonon bands, ii) high-spin states in deformed nuclei, iii) description of identical bands in superdeformed nuclei.



Shin-Ho Chung

Department of Chemistry,

The Faculties



r53 - VPP




What are the results to date and the future of this work?

The hybrid approach to the sdg-IBM calculations, namely, numerical diagonalization for low-spin and analytic 1/N expansion for high-spin states, has been used in a systematic study of deformed rare-earth and actinide nuclei. Long standing problems associated with the description of moment of inertia and E2 transitions in the IBM were resolved by including the d-boson energy in the Hamiltonian. A uniformly successful description of both low-lying band structures and high-spin states was obtained.

Applications of the model to superdeformed nuclei also yielded encouraging results for descripton of dynamical moment of inertia, especially in the Hg-Pb region. The staggering effect, claimed to be observed in some superdeformed nuclei, could not be explained consistently invoking a hexadecapole deformation as suggested earlier. This effect disappeared in subsequent experiments. Currently, we are working on introducing octupole bosons in the model so as to be able to describe the excited superdeformed bands which have an octupole nature.

What computational techniques are used?

The program uses the Lanczos method for diagonalization of large Hamiltonian matrices. The basis space for problems of interest is typically around 10,000 to 100,000 (after truncation) which requires large computer memory and fast processing time. Practical execution of the project, therefore, hinges on availability of a supercomputer.


S. Kuyucak, Collective Model Description of High-spin States, Prog. Part. Nucl. Phys. 38, 127-136 (1997).

- Appendix A