EQUATIONS FOR THE SU(3)-IRREDUCIBLE DENSITY-MATRIX OF EXCITED-STATES

A derivation of algebraic equations for the SU(3)-irreducible density matrix is given for the basis of the unitary scheme defined by the chain of subgroups U[3(A - 1)] superset-of SU(3) X U(A - 1) and U(A - 1) superset-of O (A - 1) superset-of S(A), allowing states with a large number of excitation quanta to be considered. A method of solution of these equations is considered with the help of the well-known density matrix of the canonical SU(3) basis of this chain. An explicit expression for the density matrix is given for states with the SU(3) quantum numbers E123 = [omega1 + 2m,omega1,omega3] in terms of the density matrix of the states with E123 = [omega1,omega2,omega3], where (omega1,omega2,omega3) are the quantum numbers of the group O(A - 1).