| The microscopic nuclear many-body problem has been studied for over half a century. Though its solution has been found at the few-body level, a rigorous solution for the many-body case still remains intractable. One particular aspect of the problem deals with formulating the effective, renormalized operators that are used within the truncated Hilbert space. This thesis addresses issues related to the formulation and calculation of the effective interaction. In particular, (1) it describes a procedure for correcting the boundary effect between the model space P and the excluded space Q when working within an oscillator basis, (2) it describes a method for setting up and calculating the effective interaction perturbatively within an oscillator model space, (3) it presents an alternative method for calculating the effective interaction non-perturbatively within an oscillator model space, (4) lastly, it gives a renormalization procedure for systematically softening the strong repulsive core. Such a procedure incorporates both non-perturbative renormalization group methods as well as perturbative methods.; Application of these methods is confined to the few-body cases (i.e. deuteron, 3He, and triton). |
