A New Algorithm For The Evaluation Of Elementary Wigner Coefficients Of Su(3)(?) So(3)

In this thesis,Mathematica codes for evaluating the expansion coefficients of SU?3????SO?3????SO?2?basis vectors in terms of those of the canonical U?3????U?2????U?1?and the elementary Wigner coefficients of SU?3????SO?3?,i.e.,for the SU?3?coupling[n₁₃,n₂₃]?[1,0],are complied according to the new algebraic angular momentum projection procedure.As concrete examples,numerical results of some elementary Wigner coefficients of SU?3????SO?3?are demonstrated and verified by using the orthonormal conditions.The elementary Wigner coefficients of SU?3????SO?3?can be used to construct more complicated non-elementary Wigner coefficients,which are useful tools in the SU?3?-shell model calcula-tions.The new algebraic angular momentum projection procedure in determining expansion coefficients for the expansion of basis vectors of SU?3????SO?3????SO?2?in terms of those of the U?3????U?2????U?1?,is outlined.The expansion coefficients are nothing but compo-nents of a linearly independent null space vector of the angular momentum projection matrix,of which a Mathematica code is complied according to the algorithm.The procedure can be used to evaluate these expansion coefficients and to determine the branching multiplicity of SU?3??SO?3?simultaneously.The Gram-Schmidt orthogonalization method is adopted due to the fact that the expansion coefficients are not mutually orthogonal with respect the branching multiplicity labels for cases with branching multiplicity greater than one.Formulae of the ele-mentary Wigner coefficients of SU?3????SO?3?are derived via the Racah factorization lemma,which are expressed in terms of the orthonormalized expansion coefficients and the analytical expressions of the matrix elements of SU?3?generators in the canonical basis.A Mathematica code is complied for numerical computations accordingly.The Hill-Wheeler integrals necessary in the original Elliott-Harvey projection operator method for the same problem are avoided in the algebraic angular momentum projection procedure outlined in this thesis,which,therefore,is simpler and CPU time-saving.