Robert J. Casperson

An investigation into the role of the hexadecapole degree of freedom in weakly-collective vibrational nuclei is described. The interacting boson model-2 is used to attempt to describe the structure of ⁹⁴Mo, but certain key features of a low-lying mixed-symmetry state seem to lie outside the model space. Shell model calculations indicated that the hexadecapole degree of freedom plays a role, and calculations using g-bosons were performed to attempt to describe the anomalous features. These calculations produced an excellent fit for ⁹⁴Mo, and showed that the hexadecapole degree of freedom plays a role in the low-lying 4⁺ mixed-symmetry state of that nucleus.

To continue the experimental search for the hexadecapole degree of freedom in other weakly-collective nuclei, an experiment was performed at WNSL at Yale University. The nucleus ¹⁴⁰Nd was produced using a proton beam, in order to populate 4⁺ states of interest, and many new states were identified during the analysis. Several new multipole mixing ratios are found for transitions that were observed, and candidates for the 4⁺ mixed-symmetry states are identified. Future calculations using the shell model should provide insight into whether the hexadecapole degree of freedom plays a role in ¹⁴⁰Nd.

The interacting boson model is used to study quantum phase transitional behavior in collective nuclei. The software ibar is developed for the purpose of understanding the effects of finite system size on the characteristics of quantum phase transitions in nuclei. The behavior of electric monopole (E0) transition strengths in transitional nuclei is introduced, and an investigation into the theoretical behavior of this transition for large system sizes is described. The features of the E0 transition strength curves are identified and understood using wavefunction analysis. Finally, the details of those wavefunctions provide an interesting opportunity for relating the algebraic quantum numbers to the geometric variables β and γ.