Symmetry adaptation of many-particle states with respect to both O(4) and the symmetric group

Journal Article · Sun Feb 25 04:00:00 EST 1996 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1996.0024· OSTI ID:241205

Novoselsky, A ^[1]; Katriel, J ^[2]; Gilmore, R ^[3]

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1. Hebrew Univ., Jersulem (Israel)
2. Technion-Israel Institute of Technology, Haifa (Israel)
3. Drexel Univ., Philadelphia, PA (United States)

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 tile 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. 19 refs.

• OSTI ID: 241205
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 1 Vol. 246; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
IONIZATION
MANY-BODY PROBLEM
MOLECULES
O GROUPS
ROTATIONAL STATES
SYMMETRY
VIBRATIONAL STATES
WAVE FUNCTIONS