Symmetry Adaptation of Many-Particle States with Respect to BothO(4) and the Symmetric Group
✍ Scribed by Akiva Novoselsky; Jacob Katriel; Robert Gilmore
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 667 KB
- Volume
- 246
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
We present an algorithm for the efficient construction of many-particle wave functions that belong to a given O(4) irreducible representation and are at the same time characterized by a well-defined permutational symmetry. The construction proceeds recursively, generating and then 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)-cfps are obtained as the eigenvectors of the transposition class-sum of the symmetric group, in a basis consisting of N-particle O(4)-coupled functions. The evaluation of the corresponding matrix elements requires the use of the N&2 to N&1 O(4)-cfps, calculated in the preceding iteration, as well as of the O(4) recoupling coefficients. The results are applicable to many-electron systems, where they are particularly relevant to the study of multiply ionized atoms and to the description of the vibration rotation spectra of polyatomic molecules within the algebraic framework of the vibron model.