  A significant feature of the one-dimensional super Tonks-Girardeau gas is its
metastable gas-like state with a stronger Fermi-like pressure than for free
fermions which prevents a collapse of atoms. This naturally suggests a way to
search for such strongly correlated behaviour in systems of interacting
fermions in one dimension. We thus show that the strongly attractive Fermi gas
without polarization can be effectively described by a super Tonks-Girardeau
gas composed of bosonic Fermi pairs with attractive pair-pair interaction. A
natural description of such super Tonks-Girardeau gases is provided by Haldane
generalized exclusion statistics. In particular, we find that they are
equivalent to ideal particles obeying more exclusive statistics than
Fermi-Dirac statistics.
