2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/82569It is shown that the nuclear Hamiltonian can be separated rigorously as ${\cal H}={\cal H}_m+{\cal H}_M.$ For sufficiently smooth forces the monopole part ${\cal H}_m $is entirely responsible for Hartree-Fock selfconsistency and hence saturation properties. The multipole part ${\cal H}_M$ contains the ``residual'' terms - pairing, quadrupole, etc. - that will be analyzed in a companion paper. We include a review of the basic results often needed when working with multipole decompositions and average monopole properties.20 Pages, RevTeX 3.0Nuclear Theorytext