A. Novoselsky et al., SYMMETRY ADAPTATION OF MANY-PARTICLE STATES WITH RESPECT TO BOTH O(4)AND THE SYMMETRICAL GROUP, Annals of physics, 246(1), 1996, pp. 166-189
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.