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The dissertation is based on the investigation of the spontaneous fission of 252Cf experiment with the Gammasphere array. Prompt triple gamma coincidence data were analyzed to identify new transitions and states in neutron-rich fission fragments produced in the 252Cf spontaneous fission. A new technique was developed to measure gamma-ray angular correlations and g-factors of excited states in neutron-rich nuclei. The angular properties of the detectors in the Gammasphere array were analyzed. Their response functions and relative efficiencies were measured as well. By scanning the prompt experimental gamma-ray coincidence data event by event, gamma-ray angular correlation matrices were created. Angular correlations of several cascades were studied for spin/parity assignments. In the fission experiment, the 252Cf source was sandwiched between two Fe foils to stop fission fragments. For states with lifetimes of the order of a few nanoseconds, the angular correlation of successive gamma-rays will be perturbed by the randomly-oriented impurity hyperfine fields in Fe foils. By measuring perturbed angular correlations, the 2+-state g-factors of several neutron-rich nuclei were measured, which were found to be in agreement with reported values. The level schemes of neutron-rich 88-92Kr isotopes were expanded, with spin/parity assigned by following regional systematics and angular correlation measurements. In the neutron-rich 102Zr, three new collective bands were identified, with spins and parities assigned by angular correlation measurements. For the 114Ru nucleus, the ground-state band and gamma-band were extended. Cranked shell model calculations indicate that the band-crossing of the ground-state band is from alignment of two g9/2 protons, instead of h11/2 neutrons as in the case of 108,110,112Ru. Several new transitions and states were identified in 137Cs. The level scheme of 138Cs was constructed for the first time, with thirteen states and fifteen gamma-transitions identified. Shell model calculations were performed for 137,138Cs, which were in agreement with the experimental data.