SYMMETRY ADAPTATION OF MANY-PARTICLE STATES WITH RESPECT TO BOTH O(4)AND THE SYMMETRICAL GROUP

We present an algorithm for the efficient construction of many-particl e wave functions that belong to a given O(4) irreducible representatio n and are at the same time characterized by a well-defined permutation al symmetry. The construction proceeds recursively, generating and the n using sets of O(4) coefficients of fractional parentage (cfps) that correspond to an increasing number of particles. The N-1 to N O(4)-cfp s are obtained as the eigenvectors of the transposition class-sum of t he symmetric group, in a basis consisting of N-particle O(4)-coupled f unctions. The evaluation of the corresponding matrix elements requires the use of the N-2 to N-1 O(4)-cfps, calculated in the preceding iter ation, as well as of the O(4) recoupling coefficients. The results are applicable to many-electron systems, where they are particularly rele vant to the study of multiply ionized atoms and to the description of the vibration-rotation spectra of polyatomic molecules within the alge braic framework of the vibron model. (C) 1996 Academic Press, Inc.