  This report concerns the energy of a zero-temperature many-body system of
spin 1/2 fermions interacting via a two-body potential with a free space
infinite scattering length and zero effective range; the Unitary limit. Given
the corresponding phase-shift $\delta(k)=\pi/2$ a one-term separable potential
is obtained by inverse scattering assuming a momentum cut-off $\Lambda$ such
that $\delta(k)=0$ for $k>\Lambda$. The \it effective \rm interaction in the
many-body system is calculated in a pp-ladder approximation with Pauli-blocking
but neglecting mean-field (dispersion) corrections; effective mass $m^{*}=1$.
Using only the zero relative momentum component of this interaction the total
energy is $\xi=4/9$ (in units of the fermigas), a result reported by several
previous authors. Integrating the momentum dependent interaction over the Fermi
sea this energy is revised to $\xi=0.24.$ This result is independent of density
and of the cut-off $\Lambda$ if $\Lambda > \sim 3k_{f}$.
  With $m^{*}\neq 1$ there is however a strong dependence on this cut-off.
  Including hh-ladders estimates give $\xi=0.4\leftrightarrow 0.6$, but a
reliable result would in this case require a Green's function calculation.
