In-medium nucleon-nucleon cross sections from characteristics of nuclear giant resonances and nuclear stopping power

Based on the Boltzmann-Uehling-Uhlenbeck (BUU) transport equation, a medium correction to the elastic nucleon-nucleon ($NN$) cross sections is given by comparing the width of the isovector giant dipole resonance in $^{208}\mathrm{Pb}$ and the nuclear stopping obtained from the BUU equation with those from experimental measurements. For the nuclear stopping, we choose the scaled rapidity distributions and the nuclear stopping power $vartl$, denoted as the ratio of the variances of the transverse to that of the longitudinal rapidity distributions, of central $^{197}\mathrm{Au}+^{197}\mathrm{Au}$ collisions at the energy of $150A\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}$ measured by the INDRA and the FOPI collaborations. This enables us to provide a unified medium correction of elastic $NN$ cross sections for distinct energy regimes. A reliable in-medium $NN$ cross section, as given here, will reduce the uncertainties of the BUU equation when applying it to nuclear collective motion and heavy-ion collisions to extract the information of the nuclear equation of state.