Abstract
A method is given for calculating the SU( mn)⊃SU( m)×SU( n) many-particle coefficients of fractional parentage (CFP) in terms of the single-particle CFP without using the SU( m) and SU( n) Racah coefficients. Some remarkable symmetries of the SU( mn) ⊃ SU( m) × SU( n) CFP are obtained on the grounds that they are at the same time the isoscalar factor for the permutation group chain S( f 1+ f 2)⊃S( f 1)⊗S( f 2). The application of the SU( mn)⊃SU( m)×SU( n) CFP to the quark model of nuclei is illustrated. It is shown that the transformation coefficients between the symmetry basis and the physical basis of two nuclear clusters are simply products of two SU( mn)⊃ SU( m)×SU( n) CFP.
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