Coupling coefficients of SUsub(n) contains S0sub(n) for 0sub(n)-scalar microscopic theory of collective states

Boson realisations of all 0sub(n)-scalar states which span a subspace of the Hilbert space for the collective degrees of freedom of the nucleus and are labelled by irreducible representations of the chain of subgroups U3 contains U2 contains U1 of the complementary group Sp(6,R) are given. Two general expressions for isoscalar factors of SUsub(n) contains S0sub(n) needed for constructing 0sub(n)-scalar basis functions depending on the microscopic collective variables in the oscillator basis are derived. These isoscalar factors couple three symmetric representations of SUsub(n)(Usub(n)) [p10]x[p20]x[p30] to the representation [h1h2h3] of SUsub(n) subduced to the S0sub(n)(0sub(n))-scalar representation and, more generally, to the S0sub(n) irreducible representation [fff], which appears in the case of the closed shells. (author)