  Neutron matter at low density is studied within the hole-line expansion.
Calculations are performed in the range of Fermi momentum $k_F$ between 0.4 and
0.8 fm$^{-1}$. It is found that the Equation of State is determined by the
$^1S_0$ channel only, the three-body forces contribution is quite small, the
effect of the single particle potential is negligible and the three hole-line
contribution is below 5% of the total energy and indeed vanishing small at the
lowest densities. Despite the unitary limit is actually never reached, the
total energy stays very close to one half of the free gas value throughout the
considered density range. A rank one separable representation of the bare NN
interaction, which reproduces the physical scattering length and effective
range, gives results almost indistinguishable from the full Brueckner G-matrix
calculations with a realistic force. The extension of the calculations below
$k_F = 0.4$ fm$^{-1}$ does not indicate any pathological behavior of the
neutron Equation of State.
