Assuming a simple spherical relativistic mean field model of the nucleus, we estimate the width of the antiproton-neutron annihilation (Γ n ) and the width of antiproton-proton (Γ p ) annihilation, in an antiprotonic atom system. This allows us to determine the halo factor f , which is then discussed in the context of experimental data obtained in measurements recently done on LEAR utility at CERN. Another quantity which characterizes the deviation of the average nuclear densities ratio from the corresponding ratio of the homogeneous densities is introduced too. It was shown that it is also a good indicator of the neutron halo. The results are compared to experimental data as well as to the data of the simple liquid droplet model of the nuclear densities. The single particle structure of the nuclear density tail is discusssed also.