An effective Skyrme-type interaction for the calculation of nuclear structures of the whole mass table

The Hartree-Fock-Bogolyubov formalism is extended for 3 body interactions and applied to spherical nuclei. The structure of the proposed extension of the Skyrme-type interaction is given, together with the analytical expression of the corresponding Hartree-Fock differential equation. The Skyrme-force parameters are modified in order to be able to reproduce the ground state properties. The problem of the spin-stability of the proposed interaction is treated. The Skyrme-interaction is applied as particle-hole interaction and saturation properties are studied. Structure of the charge, neutron density distributions and changes introduced by adding protons or neutrons are treated. (MDC)