where the operator ϖ ij (ϖ iso ij ) interchanges the spins (isospins) of fermions i and j provided that these spins (isospins) are dierent; N α (N ζ ) and N β (N η ) denote the number of spin-up (isospin-up) and spin-down (isospindown) fermions, respectively. Formula (17) for the square of the isospin is introduced here in complete analogy with the familiar expression for the square of the regular spin.