This report concerns the energy of a zero-temperature many-body system of spin \frac { 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 effective 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 3 k _ { 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 .