The Construction Of Angular Momentum Eigenstates In The Shell Model For Single-j Shell With J=11/2, 13/2, 15/2

By using the angular momentum projection technique, a single-j shell multi-particle states are projected into states with definite total angular momentum. Orthogonal basis of the U(2j+ 1)(?)O(3) is thus obtained in resolving the multiplicity problem. In this thesis, single-j shell states with total angular momentum J=11/2,13/2 and 15/2 are constructed. The results should be useful in calculating the Sp(2j+1)(?)O(3) coupling coefficients. The method can also be extended to multi-j cases, which provides a new procedure for various shell model calculations.