An Algorithm For Calculating Fundamental Isoscalar Factors Of O(5)(?) O(3) In D-boson Systems

In this thesis,an algorithm for calculating fundamental isoscalar factors of O?5????O?3?useful in calculating matrix elements of d-boson operators in an identical d-boson sys-tem are studied.Based on the expansion of O?5????O?3?basis vectors in terms of those of O?5????O₁?3??U?1?,the fundamental equation in determining the expansion coefficients,called the algebraic angular momentum projection equation,is derived by using the highest weight state of the angular momentum.Thus,components of an independent null space vector of the algebraic angular momentum projection matrix are the corresponding expansion coef-ficients of the basis vector of O?5????O?3?in terms of those of O?5????O₁?3??U?1?.In general,linearly independent null space vectors of a matrix are not mutually orthogonal,the Schmidt orthogonalization process is needed in order to get the orthonormalized independent null space vectors,of which the components are the corresponding expansion coefficients of the orthogonal basis vectors of O?5????O?3?in terms of those of O?5????O₁?3??U?1?.By us-ing these expansion coefficients and the available analytical expressions of the matrix elements of the d-boson creation operators in the O?5????O₁?3??U?1?basis,formulae for evaluating the fundamental Isoscalar Factors?ISF?of O?5????O?3?,i.e.those for the O?5?coupling??0???1 0?,with the angular momentum quantum number L=2?-k and the branching multiplicity,are derived,for which a Mathematica code is compiled accordingly.It is shown that the algorithm and the corresponding code based on the new algebraic angular momen-tum projection are comparatively simpler and CPU time-saving,which thus provide a new and effective tool for various calculations in the related nuclear structural models.