The Antiproton Ion Collider at FAIR L. Fabbietti a , P. Beller b , F. Bosch b , M. Cargnelli c , T. Faestermann a , B. Frankze b , H. Fuhrmann c , R.S. Hayano d , A. Hirtl c , J. Homolka a , P. Kienle a , Ch. Kozhuharov b , R. Kr¨ ucken a , H. Lenske e , Y. Litvinov f , J. Marton c , F. Nolden b , P. Ring a , Y. Shatunov f , A.N. Skrinsky f , K. Suzuki a , V.A. Vostrikov f , T. Yamaguchi d , E. Widmann c , S. Wycech g ,J. Zmeskal c a Technische Universit¨at M¨ unchen, Munich, Germany b Gesellschaft fr Schwerionenforschung, Darmstadt, Germany c Stefan Meyer Institut, Vienna, Austria d University of Tokyo, Tokyo, Japan e Justus-Liebig Universit¨ at Giessen, Giessen, Germany f Budker Institute of Nuclear Physics, Novosibirsk, Russia g Andrzej Soltan Institute for Nuclear Studies (IPJ), Warsaw, Poland A novel method [1] is proposed to determine the charge and the matter radii instable and short lived nuclei using an pBar-A collider. The experiment makes use of the appropriately modified electron-ion collider Elise, to collide 30 MeV anti-protons with 740 AMeV ions. The anti-protons are first collected in the CR ring with 3 GeV energy and then cooled in the RESR ring to 30 MeV. The heavy ions produced in the SFRS are precooled in the CR ring, cooled in the RESR ring to 740 AMeV and fed to the NESR ring. The total pBar-nucleon annihilation cross-section is measured detecting the loss of stored ions and the pBar-n, pBar-p cross-sections detecting the A - 1(Z - 1 or N - 1) nuclei left over after the annihilation, using the Schottcky method. Theoretical predictions show that the annihilation cross-section is proportional to the mean squared radius. 451