Nucleon-nucleon cross sections in neutron-rich matter and isospin transport in heavy-ion reactions at intermediate energies

Nucleon-nucleon (NN) cross sections are evaluated in neutron-rich matter using a scaling model according to density, momentum, and isospin dependent nucleon effective masses. It is found that the in-medium NN cross sections are not only reduced but also have a different isospin dependence compared with the free-space ones. Because of the neutron-proton effective mass splitting the difference between nn and pp scattering cross sections increases with the increasing isospin asymmetry of the medium. Within the transport model IBUU04, the in-medium NN cross sections are found to influence significantly the isospin transport in heavy-ion reactions. With the in-medium NN cross sections, a symmetry energy of ${E}_{\mathrm{sym}}(\ensuremath{\rho})\ensuremath{\approx}31.6(\ensuremath{\rho}/{\ensuremath{\rho}}_{0}){}^{0.69}$ was found most acceptable compared with both the MSU isospin diffusion data and the presently acceptable neutron-skin thickness in $^{208}\mathrm{Pb}$. The isospin dependent part ${K}_{\mathrm{asy}}({\ensuremath{\rho}}_{0})$ of isobaric nuclear incompressibility was further narrowed down to $\ensuremath{-}500\ifmmode\pm\else\textpm\fi{}50$ MeV. The possibility of determining simultaneously the in-medium NN cross sections and the symmetry energy was also studied. The proton transverse flow, or even better the combined transverse flow of neutrons and protons, can be used as a probe of the in-medium NN cross sections without much hindrance from the uncertainties of the symmetry energy.