Extensive calculations based on the approximation of single particle wave functions (the Hartree method) have been made for the nuclei between ${\mathrm{He}}^{6}$ and ${\mathrm{O}}^{16}$ using the general symmetrical interaction operator given by Eq. (1). The Coulomb interaction is treated as a small perturbation. Secular equations are avoided by the construction of space wave functions in the normal state configuration belonging to irreducible representations of the symmetric group. These functions yield an energy matrix which is diagonal in the ordinary and Majorana interaction energies. The contributions of the spin exchange and Coulomb operators to the energy terms are found by a first-order perturbation calculation. Although the general symmetrical operator contains several parameters as yet undetermined, only those parameters which have been fixed by consideration of the two, three and four particle problems are involved in the energy differences within the group of low lying terms belonging to the normal state configuration. These term differences are identical with those recently computed for unsymmetrical interaction operators of the saturation type. New results for mass defects, excitation energies and energy relations between isobars are compared with experimental values.