Constructing formula for total reaction cross sections without adjustable energy-dependent parameters

We review our formula for a proton-nucleus total reaction cross section, $\sigma_{\rm R}$, constructed in the black-sphere approximation, in which a nucleus is viewed as a ``black'' sphere of radius ``$a$''. In this formula, the cross section, $\pi a^2$, is expressed as a function of the mass and neutron excess of the target nucleus and the kinetic energy of incident proton, $T_p$, in a way free from any adjustable $T_p$-dependent parameter. We deduce the dependence of $\sigma_{\rm R}$ on $T_p$ from a simple argument involving the proton ``optical'' depth within the framework of the black-sphere approximation of nuclei. We find that, for stable nuclei, this formula remarkably well reproduces the empirical $T_p$ dependence of $\sigma_{\rm R}$ at $T_p=100$--1000 MeV without introducing any adjustable energy-dependent parameter. We show that, in this formula, the energy dependence of $a$ is determined by that of nucleon-nucleon total cross sections, while the target-mass-number dependence of $a$ is sensitive to the surface thickness of the target. In the future experiments of neutron-rich unstable nuclei, we could expect that the neutron-excess dependence of $a$ would play an important role in deducing the density dependence of nuclear symmetry energy.