THE GRAPHICAL SPIN ALGEBRA METHOD APPLIED TO U(2N) GENERATORS

An efficient method for the evaluation of the matrix elements of U(2n) spin-dependent generators in a fully spin adapted Gelfand-Tsetlin bas is is given. This is done by evaluating the matric elements of the U(2 n) generators in a Yamanouchi-Kotani basis whose orbital part is equiv alent, up to phase factors, to the Gelfand-Tsetlin basis. This allows the expression for the matrix elements to be separated into products o f creation and annihilation operators, which are evaluated using Wick' s theorem, and products of SU(2) Clebsch-Gordan coefficients, whose sp in graphs are factorized into easily evaluated segment diagrams. The m atrix elements of a single U(2n) generator reduce to a sum of products of segment values. These values are given in formula form involving 3 -j and 6-j symbols and in table form, where the formulas have been eva luated for all the nonvanishing segments. (C) 1995 American Institute of Physics.