4/30/2002

Student Name: Kristina Sviratcheva

Committee:
Dr. Jerry P. Draayer (chair)
Dr. J Bush Jones
Dr. Aiichiro Nakano

Place: 222 Nicholson Hall
Date: Friday, May 3, 2002, 9:30 A.M.

Title:Algebraic and numerical computations for non-deformed and q-deformed fermion realizations of sp(4)

Abstract:
A description of the nuclear many-body problem involves high-performance computing methods for shell-model calculations or when symmetries in nuclear structure are considered. The latter approach yields a simple picture for nuclear phenomena, but in the same time it requires an intensive calculations for corresponding non-commutative algebras, especially when approximately good symmetries and non-linearities are involved.

A computational package is developed to provide for algebraic computations for non-commutative multiplications of the generators of the non-deformed and deformed symplecitc Sp(4) groups. They calculate the action of the generators and invariants on the basis states, as well as the normalization and overlapping functions for the basis vectors.The results are used for applications of the theoretical concept to the nuclear structure and are involved in finding the eigenvalues and eigenvectors of a general pairing Hamiltonian.

A numerical optimization procedure uses the computed matrix elements of the interaction to estimate the pairing strength parameters and the nuclear energies in the deformed and non-deformed cases. A graphical user interface is implemented to help visualizing the nuclei according to the sp(4) classification scheme and to retrieve theoretically predicted and available experimental nuclear data.

All are welcome.