  An extension of the Semimicroscopic Algebraic Cluster Model (SACM) is
proposed, based on the pseudo-SU(3) model. The Hamiltonian and the
spectroscopic factor operator of the model are presented and a procedure of
constructing the model space. Because a huge number of SU(3) irreducible
representations (irrep) appear, one has to be careful in designing a practical,
consistent path to reduce the Hilbert space. The concept of forbiddenness,
taking into account excitations of the clusters, is introduced and applied. The
applications are to two systems with a low forbiddenness, namely to 236U ->
210Pb + 26Ne and 224Ra -> 210Pb + 14C, and to 236U -> 146Xe + 90Sr, which
appears in the fission of 236U, which requires a large forbiddenness. Energies,
electromagnetic transitions and spectroscopic factors are calculated.
