  The total reaction cross section of high-energy nucleus-nucleus collision
refects the nuclear density profiles of the colliding nuclei and has been a
standard tool to investigate the size properties of short-lived unstable
nuclei. This basis relies on the assumption that the nucleus-nucleus collision
is strongly absorptive in the sense of an optical model. However, this property
does not hold completely, while incomplete absorption occurs when an overlap
density of two colliding nuclei is low enough. In this paper, we propose a way
to quantify this incompleteness, that is, the "blackness" of the total reaction
cross section. A significance of this quantification is drawn by taking an
example of the total reaction cross sections of proton-rich C isotopes.
