Orbital fractional parentage coefficients for the harmonic oscillator shell model
Abstract
The Hamiltonian of n particles moving in a common harmonic oscillator potential has as its symmetry group the unitary group U(3 n) in 3 n dimensions, n particle states of the harmonic oscillator shell model can be characterized as bases of irreducible representations (BIR) of the group U(3 n) and of certain subgroups of this group. Use is made of these subgroups for the factorization and calculation of 2, 3, and 4 particle fractional parentage coefficients (fpc) of the harmonic oscillator shell model. Recoupling coefficients for subgroup chains of the symmetric group S (n) appear as factors in the fpc. These coefficients are analyzed and calculated explicitly. The 2, 3 and 4 particle fpc of the 1 s 1 p shell configuration are obtained as products of these recoupling coefficients with known reduced Wigner coefficients of the unitary group U(3) in 3 dimensions. Possible applications are indicated.
- Publication:
-
Zeitschrift fur Physik
- Pub Date:
- April 1967
- DOI:
- 10.1007/BF01333370
- Bibcode:
- 1967ZPhy..205..181K