## LSU Historical Dissertations and Theses

1994

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

J. P. Draayer

#### Abstract

Pseudo-SU(3) symmetry along with its simple symmetry-preserving and symmetry-breaking interactions is presented. This symmetry is a direct consequence of pseudo-spin symmetry which can be clearly seen in a single-particle shell model picture of heavy (A $\sbsp{\sim}{>}$ 100) atomic nuclei. Good pseudo-spin symmetry is shown to have its origin at a more fundamental level by considering relativistic mean field results for the strength parameters of the spin-orbit and the orbit-orbit interactions. As long as the residual interaction is a pseudo-spin scalar interaction, the many-particle extension of the single-particle picture is also expected to have,good total pseudo-spin symmetry. The quadrupole-quadrupole interaction Q${\cdot}Q$ can be approximated by its pseudo spin/space counterpart, $\tilde{Q}{\cdot}\tilde{Q},$ since it is approximately a good pseudo-spin scalar. Within a single major oscillator shell, this interaction possesses SU(3) (to be more precise pseudo-SU(3)) symmetry. As a caveat, the notion of identical bands in normal deformed and superdeformed nuclei can be viewed a consequence of pseudo-SU(3) dynamical symmetry. The pairing interaction, on the other hand, is an exact pseudo-spin scalar; however, it severely breaks SU(3) symmetry. To perform SU(3) shell-model calculations which include a symmetry-breaking interaction like pairing requires SU(3) technologies that consist of two parts: the SU3 and SU3RME packages. Contrary to the traditionally held view that the pairing interaction washes away the deformation, our current results show that the interaction induces triaxial deformed configurations. The combined interaction (known as the pairing-plus-quadrupole model) is systematically studied for even numbers of identical particles (either protons or neutrons) by varying the strength of each term in the interaction. Introducing a quadrupole-quadrupole interaction to a paired system pushes the ground state of the system away from a triaxiai geometry to a more prolate (oblate) one if the number of particles is below (above) the mid-shell. Further studies on the pairing and SU(3) show that the pairing interaction breaks the SU(3) symmetry in a very special way.

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