Microscopic collective nuclear models with horizontal mixture

By accounting for the difference in the spin and isospin projection among nucleons, the Sp(6,R) dynamical symmetry of the nuclear collective model is amplified in parallel with a horizontal extension of the instrinic shell structure. The generating kernels for the extended symplectic model basis functions are constructed in the form of a shortened coherent state. Analytical expressions for the microscopic Hamiltonian matrix elements, including central and tensor interactions, are obtained between the coherent states indicated.