  We consider a fully polarized ultracold Fermi gas interacting through a
p-wave Feshbach resonance. Using a two-channel model, we find the effective
potential at the point where the p-wave scattering length goes to zero. Here
the effective interaction provides attraction and one can therefore ask about
the stability of the system. We calculate the energy density of the system in
the Thomas-Fermi approximation, determine the profile of the gas, and the
critical number of particle in the system as function of the relevant
interaction parameters. The instability can be deduced from a simple breathing
mode argument which explains the scaling found numerically. The critical
particle number turns out to be extremely large unless the external confinement
is very tight. We therefore conclude that the effect is insignificant for
standard trapping potentials and that the magnetic dipole interaction is the
important term at zero scattering length. However, for tight confinement as in
an optical lattice higher-order corrections can become important.
