Analytical expressions for some outer product isoscalar factors

Abstract EN

Abstract coupling coe¢ cients (OPCCs) for the symmetric group.

The classiÖcation of the interaction operators with respect to the permutation symmetry of the n particle system is given with the relation of the OPCCs of the symmetric group Sn : We derived all the required outer product isoscalar factors (OPISFs) for one, two and three body interaction operators.

As examples, we have calculated the OPISFs of [1] [n 1], [2] [n 2], 1 2 [n 2], [3] [n 3], [21] [n 3], and 1 3 [n 3] :The general method of Önding the modiÖed ground representation (MGR) of the generators of the symmetric groups is discussed.

AMS ClassiÖcations: 20C35, 20B30, 20B35,