| Nuclear Level Densities are crucial inputs in the study of many physical processes spanning from Astrophysics to Nuclear Medicine. The knowledge of Nuclear Level Densities provides information about the internal structure of any nucleus, which determines the manner in which the nucleus participates in a physical process. This dissertation is a theoretical study of Nuclear Level Densities for nuclei that exist away from the valley of stability. As such, these nuclei are not naturally occurring and are usually very difficult to synthesize in a laboratory. Not only are these nuclei difficult to study in a laboratory, theoretical efforts to study them have been limited so far. Thus, the purpose of this dissertation has been to develop the methodology and procedure to enable the study of such nuclei.;These efforts to make these nuclei theoretically accessible involve a variety of theoretical and computational tools. Effective potentials and regular Quantum mechanical methods have been used to compute the single particle excitation energies of a neutron or a proton inside a nucleus. These single particle energy levels are then used as inputs in rigorous many-body calculations that formulate the nucleus as a gas of fermions. Since exact many-body calculations are not possible, matrix formulations or spectral distribution methods are used. Also, these analyses have been done using the second-quantization formulation of Quantum Mechanics. A computational tool such as the Lanczos tri-diagonalization procedure has been used in the many-body codes to calculate the Nuclear Level Densities.;The results reported in this dissertation shows that nuclei near the drip lines can indeed be studied using the methods described here at least for 40 ≤ A ≤ 100. Due to the lack of experimental data for such nuclei, a comparison of these results with experimental extractions was not possible at this time. In the near future, however, such comparisons will be made possible due to ongoing efforts at Ohio University and Yale University. |
