**Principal Investigator**
Serdar Kuyucak **Project** r53

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 of the topics to be consired 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.

**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 harder to investigate experimentally because it is masked by the strong quadrupole interaction. Signatures for the hexadecapole degree of freedom have recently appeared from various spectroscopic studies, necessitating theoretical approaches which treat the quadrupole and hexadecapole degrees of freedom on an equal footing. In low-spin region, double-phonon quadrupole versus single-phonon hexadecapole bands is one such controversial topic that requires sdg-IBM calculations. In high-spin and superdeformed region, the use of the sdg-IBM is essential for a correct description of band structures. In addition, because the 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 occurence.

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

Our investigations of double-phonon bands indicates that unharmonicities claimed to be observed in some nuclei cannot be accommodated in collective models. These results suggest that the origin of unharmonicity is likely to be elsewhere, for example, mixing with quasiparticle states. Recent experiments on complimentary electric quadrupole transitions seem to confirm this interpretation.

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 were obtained. Currently, we are working on the identical band problem and the staggering effects in superdeformed nuclei.

**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, **B349** 189 (1995)

*High-spin States in the sdg Boson Model with Applications
to Actinide Nuclei,* S Kuyucak, S. C. Li,
Phys. Lett. B, **B354** 189 (1995)

*Description of high-spin states in deformed and
superdeformed Nuclei* S. Kuyucak, V Int.
Spring Seminar on Nuclear Structure, Ravello, Italy, 1995, ed.
A. Covello (World Scientific, Singapore)

*Desciption of deformed nuclei in the sdg boson
model* S.C. Li and S. Kuyucak, Nucl. Phys.
A, (Submitted).