  In order to clear up the sensitivity of the nucleus--nucleus reaction cross
sections $\sigma_R$ to the nuclear matter distributions in exotic halo nuclei,
we have calculated the values of $\sigma_R$ for scattering of $^6$He,
$^{11}$Li, and $^{19}$C nuclei on several nuclear targets at the energy of 0.8
GeV/nucleon. The calculations were performed in the "rigid target"
approximation to the Glauber theory, different shapes of the nuclear density
distributions in $^6$He, $^{11}$Li, and $^{19}$C being assumed.
