The X-ray cascade from antiprotonic atoms was studied for 208Pb and 209Bi. Widths and shifts of the levels due to the strong interaction were determined. Using modern antiproton-nucleus optical potentials the neutron densities in the nuclear periphery were deduced. Assuming two parameter Fermi distributions (2pF) describing the proton and neutron densities the neutron rms radii were deduced for both nuclei. The difference of neutron and proton rms radii /r_np equal to 0.16 +-(0.02)_{stat} +- (0.04)_{syst} fm for 208Pb and 0.14 +- (0.04)_{stat} +- (0.04)_{syst} fm for 209Bi were determined and the assigned systematic errors are discussed. The /r_np values and the deduced shapes of the neutron distributions are compared with mean field model calculations.
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