Аннотация:A proposal for an experiment to measure the cross section of antiprotonproduction in a proton-nuclear collision in a kinematically forbidden regionfor nucleon-nucleon interaction on a fixed LHC target is considered. It isshown that this process can be separated from the kinematically allowedproduction process using the existing detectors of the ALICE facility at aproton energy of 7 TeV with a fixed nuclear target. Assuming the scale de-pendence of the cross section, the data obtained can be used to estimate thesubthreshold cross section for the production of superheavy particles with amass of several tens of TeV in the LHC lead nucleus beam.