| Abstract [eng] |
We present the ab-initio algebraic approach to the nuclear problem. To calculate the observables of the nucleus, one must ensure that the state vectors are antisymmetric and translationally invariant. These two requirements create tremendous difficulties. In this thesis, we approach this problem by using the Jacobi coordinate system to eliminate the center of mass coordinate. This complicates the antisymmetrization process, so we explore the symmetric group to obtain the antisymmetric irreducible representation of the state vectors. This is done by using the Lambda operators to construct the model space. This approach is explored for the p-shell nuclei, particularly the bound six nucleon system. The model space is built by calculating the coefficients of fractional parentage for three-particle subclusters of the six nucleon system and constructing these coefficients for the whole system. The general cases for calculating the representations of the permutation operators using the harmonic oscillator basis is explored in the last chapter of the thesis. |
