The shell structure of nuclei far from stability evolves from the standard shell model picture that accurately describes stable nuclei. Experimental evidence has been given by changes in structural properties of nuclei such as the shell closures. The evolution of shell structure is gradual and must be studied by looking systematically at isotopic or isotonic nuclear chains. Studies of these chains can deepen the understanding of shell structures, magic numbers and the collective natures of nuclei far from stability.The neutron rich silicon isotopes display evidence of shell evolution seen in the ratio of the low-lying excitation energies. 34Si has a closed shell nature with a proton bubble structure which evolves along the isotopic chain to the absence of the N=28 shell closure expected in 42Si. Another complementary way to probe these changes is by studying the reduced transition rates of the first 2+ and 4+ states. The ratio of the reduced transition rates has characteristic values for different collective modes. However, these values are not known for isotopes that are more neutron rich than 30Si. The reduced transition rates can be compared to various theoretical models to understand the changes taking place in this neutron-rich region.This work discusses an experiment that studied 36Si and 38Si to determine the lifetimes of their excited states and to determine the reduced transition rates of the first 2+ and 4+ states in both nuclei. From these B(E2) values, the ratio is calculated and compared to the collective models and shell model calculations. The recoil distance measurement was conducted at the National Superconducting Cyclotron Laboratory using the S800 Spectrograph, the GRETINA array, and the TRIPLEX plunger. The experiment successfully measured the lifetimes of the 2+1 and 4+1 states in 38Si and the 4+1 and 6+1 states in 36Si. Results from the measurement included the confirmation of the 2383-keV state in 38Si that had only been seen once before. The B(E2) values determined from the experiment indicate the reduced collectivity for the first 4+ states of 36,38Si indicating the persistence of the N=20 magic number through 36Si and 38Si.
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