  The Gallagher-Moszkowski rule in the spectroscopy of odd-odd nuclei imposes a
new spin constraint on the energy functionals for self-consistent mean field
theory. The commonly used parameterization of the effective three-body
interaction in the Gogny and Skyrme families of energy functionals is
ill-suited to satisfy the spin constraint. In particular, the Gogny
parameterization of the three-body interaction has the opposite spin dependence
to that required by the observed spectra. The two-body part has a correct sign,
but in combination the rule is violated as often as not. We conclude that a new
functional form is needed for the effective three-body interaction that can
take into better account the different spin-isospin channels of the
interaction.
