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Symmetry Adaptation of Many-Particle States with Respect to BothO(4) and the Symmetric Group
Journal article   Peer reviewed

Symmetry Adaptation of Many-Particle States with Respect to BothO(4) and the Symmetric Group

Akiva Novoselsky, Jacob Katriel and Robert Gilmore
Annals of physics, v 246(1), pp 166-189
25 Feb 1996
DOI: https://doi.org/10.1006/aphy.1996.0024
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Abstract

We present an algorithm for the efficient construction of many-particle wave functions that belong to a givenO(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 ofO(4) coefficients of fractional parentage (cfps) that correspond to an increasing number of particles. TheN−1 toNO(4)-cfps are obtained as the eigenvectors of the transposition class-sum of the symmetric group, in a basis consisting ofN-particleO(4)-coupled functions. The evaluation of the corresponding matrix elements requires the use of theN−2 toN−1O(4)-cfps, calculated in the preceding iteration, as well as of theO(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.

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Collaboration types
Domestic collaboration
International collaboration
Web of Science research areas
Physics, Multidisciplinary
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