  A harmonically trapped ultracold 1D spinor Fermi gas with a strongly
attractive 1D even-wave interaction induced by a 3D Feshbach resonance is
studied. It is shown that it has two different super Tonks-Girardeau (sTG)
energy eigenstates which are metastable against collapse in spite of the strong
attraction, due to their close connection with 1D hard sphere Bose gases which
are highly excited gas-like states. One of these sTG states is a hybrid between
an sTG gas with strong $(\uparrow\downarrow$ attractions and an ideal Fermi gas
with no $(\uparrow\uparrow)$ or $(\downarrow\downarrow)$ interactions, the sTG
component being an exact analog of the recently observed sTG state of a 1D
ultracold Bose gas. It should be possible to create it experimentally by a
sudden switch of the $(\uparrow\downarrow)$ interaction from strongly repulsive
to strongly attractive, as in the recent Innsbruck experiment on the bosonic
sTG gas. The other is a trapped analog of a recently predicted sTG state which
is an ultracold gas of strongly bound $(\uparrow\downarrow)$ fermion dimers
which behave as bosons with a strongly attractive boson-boson interaction
leading to sTG behavior. It is proved that the probability of a transition from
the ground state for strongly repulsive interaction to this dimer state under a
sudden switch from strongly repulsive to strongly attractive interaction is
$\ll 1$, contrary to a previous suggestion.
