  We consider strong interactions at finite density in mean field theory,
through an effective lagrangian that can describe both nuclear matter and quark
matter. This lagrangian has three couplings that are all fixed by experiment
and no other parameters. With increasing baryon density we then find the
following hierarchy. At nuclear density and above we have nuclear matter with
chiral spontaneous symmetry breaking (SSB), followed by the pion condensed
quark matter, again with chiral SSB, albeit with a different realization and
finally a transition to the diquark CFL state which also has chiral SSB (and
colour SSB), with yet another realization. To one's surprise at zero
temperature (in mean field theory), at any finite density chiral symmetry is
never restored!
  We find another remarkable feature and this is that the tree level mass of
the sigma particle, that is set by experiment to about 800 MeV, has a crucial
and unexpected influence on the physics. Strange quark matter and strange stars
are ruled out for a sigma mass above 700 MeV and neutron stars with magnetic
pion condensed cores, that could provide magnetic fields of neutron stars,
exist only for a small interval, between 750-850 MeV, for the sigma mass.
