Theoretical Physics, **Machine** VP

Research School of Physical Sciences and Engineering

**Co-Investigator** Siu Cheung Li

Theoretical Physics,

Research School of Physical Sciences and Engineering

**Investigation of Collective Nuclei in the SDG Interacting Boson Model**

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 topical questions that we intend to address are (i) signatures for double-phonon bands that will help to distinguish them from single-phonon hexadecapole bands and (ii) description of identical bands in superdeformed nuclei.

**What are the basic questions addressed? **

In the liquid drop model of collective nuclei, one expands the nuclear surface in terms of spherical harmonics. For positive parity states, the dominance of the quadrupole degree of freedom has been well established. The hexadecapole degree of freedom, which is the next order correction, is much harder to investigate experimentally because it is masked by the strong quadrupole interaction. After 40 years of developments in detector technology, clear signatures for the hexadecapole degree of freedom have finally appeared from various spectroscopic studies, necessitating theoretical approaches which treat the quadrupole and hexadecapole degrees of freedom on an equal footing. In the low-spin region, double-phonon quadrupole versus single-phonon hexadecapole bands is one such controversial topic that requires sdg-IBM calculations. In the high-spin and superdeformed region, the use of the sdg-IBM is essential for a correct description of band structures. In addition, because IBM is based on symmetries, it is well placed to address the recent phenomenon of identical bands and the role played by symmetries in their occurrence.

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

Our initial investigations on unharmonicities in double-phonon bands showed that this was not possible using the standard parameter sets available in the literature. We have therefore expanded our search and started using triaxiality as a guide in inducing unharmonicity. So far, we haven't found a realistic set of parameters that could describe unharmonic excitations.

On the high-spin side, we have developed a 1/N expansion method and used the exact diagonalization results to test its accuracy. The analytic results proved to be very accurate, and were used in a systematic study of high-spin states in actinide nuclei. The hybrid approach, namely numerical diagonalization for low-spin and analytic 1/N expansion for high-spin states, appears to be the most promising way for complete analysis of nuclear spectra within the sdg-IBM framework.

**What computational techniques are used and why is a supercomputer required?
**

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.

**Publications**

*1/N Expansion Formalism for High-spin States*, S Kuyucak and S C
Li, Phys. Lett. B, submitted.

*High-spin States in the sdg Boson Model with Applications to Actinide
Nuclei,* S Kuyucak, S C Li and P von Brentano, Phys. Lett. B, submitted.

*Vibrational Bands in Deformed Nuclei; An sdg Boson Model Perspective*, S
Kuyucak, Proc. IV Int. Conf. on Selected Topics in Nuclear Structure, V
Soloviev (ed.), Dubna, Russia (1994).