Show that when the motion of nucleons within the nucleus is taken into account, the threshold energy E' for producing anti protons in the collision of protons with a nuclear target is given approximately by

E'_min ≈ (1 − p/m_Pc)E_min ≈ 5.2 GeV,

where E_min ≈ 6.6 GeV is the threshold energy for producing anti protons on a proton target, and p = |p|, the magnitude of the internal momenta of the nucleons, is taken to be typically of order 0.2 GeV/c.