  A two orbital model for the new Fe-based superconductors is studied using the
Lanczos method as well as pairing mean-field approximations. Our main goals are
(i) to provide a comprehensive analysis of this model using numerical
techniques with focus on half-filling and on the state with two more electrons
than half-filling and (ii) to investigate the nodal structure of the mean-field
superconducting state and compare the results with angle-resolved photoemission
data. In particular, we provide evidence that at half-filling spin 'stripes',
as observed experimentally, dominate over competing states.
  Depending on parameters, the state with two more electrons added to half
filling is either triplet or singlet. Since experiments suggest spin singlet
pairs, our focus is on this state. Under rotation, it transforms as the B_2g
representation of the D_4h group. We also show that the s+/- pairing operator
transforms as A_1g and becomes dominant only in an unphysical regime of the
model where the undoped state is an insulator. For robust values of the
effective electronic attraction producing the Cooper pairs, assumption
compatible with recent angle-resolved photoemission (ARPES) results that
suggesting small Cooper-pair size, the nodes of the two-orbital model are found
to be located only at the electron pockets. Since recent ARPES efforts have
searched for nodes at the hole pockets or only in a few directions at the
electron pockets, our results for the nodal distribution may help to guide
future experiments. More in general, the investigations reported here aim to
establish several of the properties of the two orbital model. Only a detailed
comparison with experiments will clarify how far this simple model present a
valid description of the Fe pnictides.
