Patrick Ennis

This dissertation reports a series of measurements of an intermediate mass N = Z nucleus which constrain generalized models of nuclear structure. In particular, in $\sbsp{32}{64} \rm{Ge}\sb{32}$, the triaxial and octupole shape degrees of freedom are investigated, along with the possible isospin impurity of wave functions. This neutron-deficient isotope was produced in the reaction $\rm\sp{12}C(\sp{54}Fe, 2n\gamma )\sp{64}$Ge at a beam energy of 165 MeV. The production cross section for $\sp{64}$Ge was measured to be 640 $\pm$ 70 $\mu$barns, which represents only $\approx$0.15% of the total fusion cross section. “In-beam” $\gamma$-ray spectroscopy of nuclei produced at the sub-millibarn level has not previously been achieved. Recoil-$\gamma$-$\gamma$ correlations and recoil-$\gamma$ angular distributions were measured using the Daresbury Recoil Separator operated in conjunction with a large array of Compton suppressed $\gamma$-ray detectors. Absolute cross section measurements and Monte Carlo studies were performed at Yale University’s A.W. Wright Nuclear Structure Laboratory. A level scheme for $\sp{64}$Ge was constructed which contains 19 states. The nucleus appears to have a structure consistent with a $\gamma$-soft shape and shows little evidence for the predicted susceptibility to octupole deformation. Evidence for forbidden E1 transitions was found which may be indicative of considerable isospin mixing.

Future directions for the continued study of exotic nuclei are discussed in the context of the new $\gamma$-ray detector arrays and recoil mass separators being constructed around the world. In particular, we have compared our data which were triggered by recoiling nuclei and two detected gamma rays, to events triggered by detecting three gamma-rays. After proper analysis, it was found that for the strongly produced $\sp{64}$Zn ($\sigma$ = 160 $\pm$ 7 mbarns, $\approx$40% of the total fusion cross section), the two triggering methods produced spectra of comparable quality. However, for the much weaker reaction channel leading to $\sp{64}$Ge, a recoil gate was found to be essential in order to identify any $\sp{64}$Ge transitions. The implications of these measurements are generalized to the next generation of $\gamma$-ray spectrometers and recoil separators. The feasibility of performing more extensive spectroscopic measurements using these new devices is presented.