Antiprotonic X rays were used to investigate the nuclear matter densities. Neutron densities in 26 isotopes were determined using this method. The information on the nuclear matter density at relatively large radii was then converted to rms radii by the use of a two-parameter Fermi-function profile. The obtained systematics of differences of the neutron and proton rms radii is in a fair agreement with theoretical calculations and results of other experimental methods.