The destruction of 7 Be with neutrons represents the last possible standard avenue to reduce the predicted abundance of the primordial 7 Li and in this way to attempt to solve the Cosmological 7 Li problem. We discuss the results of an experiment performed at the Soreq Applied Research Accelerator Facility (SARAF) in Israel where we measured the Maxwellian Averaged Cross Sections (MACS) of the 7 Be(n,p), 7 Be(n,α), and 7 Be(n,γα) reactions. Our MACS measured at 49.5 keV in the window of the Big Bang Nucleosynthesis (BBN), indicate the lack of standard nuclear physics solution to the "Primordial 7 Li Problem".