The existence of the anti-hyperons was proven by the discovery of an anti-lambda by M. Baldo-Ceolin and D. J. Prowse in 1958. A beam of negative pions with energy E_π = 4.6 GeV hit an emulsion stack. What is the final state containing a Λ̅ that can be produced in a π^- p collision at minimum energy? Find the threshold energy if the  target protons are free and, approximately, if they are bound inside nuclei with a Fermi momentum p_f = 150 MeV. Assuming that the pion beam was produced at a distance l = 8 m upstream of the emulsion and that the number of produced pions was N₀ = 106/cm², how many pions per cm² reached the emulsion?