Many Body Theory for Quartets, Trions, and Pairs in Low Density Multi-component Fermi-systems *

Cluster formation in strongly interacting Fermi-systems is one of the most interesting subjects in many body physics. So far, in condensed matter, only the study of formation of two body clusters has been studied in a wide perspective in the context of pairing, that is superfluidity and superconductivity (see e.g.1 in the context of cold atoms). However, in nuclear physics, due to the existence of four different fermions, all attracting one another, the scenario of cluster formation is much richer. Of course, there also exist Cooper pairs of neutrons and protons, and to a lesser degree proton-neutron pairs, but in addition there exist tritons, helions (trions) and α-particles (quartets), to cite only the lightest ones. For instance, the formation and condensation of α-particles is presently in the focus of our studies. However, adding to a gas of α-particles two neutrons per α-particle, at some higher excitation energy, this system may be transformed into a gas of tritons. For example, one may imagine that Be is composed out of four tritons at sufficiently high energies. Also nucleons themselves are trions when seen as bound states formed out of three quarks. Then