## LSU Historical Dissertations and Theses

1997

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Physics and Astronomy

Jerry P. Draayer

#### Abstract

Electron scattering offers numerous advantages for studying nuclear structure: the weakness of the electromagnetic interaction, the precise knowledge of the reaction mechanism, the ability to vary independently the transferred momentum and energy, as well as the excellent spatial resolution that can be obtained with the point-like probing particles, have made this approach a valuable tool in nuclear physics. Scattering experiments provide crucial tests for the applicability and limitations of modern nuclear models and further our understanding of the nucleon-nucleon interaction and its modifications in nuclear matter. A microscopic theory for deformed nuclei, which takes proper account of the Exclusion Principle and of inter-shell couplings, is given by the symplectic shell model. In the context of electron scattering it provides a multi-shell realization of the nuclear shell model and allows for a careful study of the relevance of multi-shell correlations. A detailed overview of the Elliott SU(3) model and its multi-$\hbar\omega$ extension, the symplectic shell model, is given. The expansion of electron scattering charge and current multipole operators in a second quantized fermion representation is reviewed. A fermion realization of the symplectic shell model, which complements the traditional bosonic representation, is developed. A recursive process is presented in which symplectic matrix elements of arbitrary one-body fermion operators between states of excitation $N\hbar\omega$ and $N\sp\prime\hbar\omega$ in the same or in different symplectic bands are related back to valence shell matrix elements, which can be evaluated by standard shell model techniques. The formalism is employed to calculate electron scattering form factors for the deformed light nucleus $\sp{24}$Mg in the symplectic shell model, and to discuss the significance of multi-shell corrections.

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