Probing the isospin dependence of the in-medium nucleon-nucleon cross sections with radioactive beams

Within a transport model we search for potential probes of the isospin dependence of the in-medium nucleon-nucleon (NN ) cross sections. Traditional measures of the nuclear stopping power are found to be sensitive to the magnitude but they are ambiguous for determining the isospin dependence of the in-medium NN cross sections. It is shown that isospin tracers, such as the neutron/proton ratio of free nucleons, at backward rapidities and angles in nuclear reactions induced by radioactive beams in inverse kinematics are a sensitive probe of the isospin dependence of the in-medium NN cross sections. At forward rapidities and angles, in contrast, they are more sensitive to the density dependence of the symmetry energy. Measurements of the rapidity and angular dependence of the isospin transport in nuclear reactions will enable a better understanding of the isospin dependence of in-medium nuclear effective interactions.

Figure 1

(Color online) The ratio of np to pp scattering cross sections as a function of incident nucleon energy. The solid line is extracted from experimental data [17]; the dashed lines are extracted from calculations in symmetric matter using the Bonn A potential within the Dirac-Bruckner approach in Ref. 6.

Figure 2

(Color online) Quadruple moment as a function of beam energy in head-on collisions of ${}^{100}\mathrm{Zn}+{}^{40}\mathrm{Ca}$ with the three choices of nucleon-nucleon cross sections.

Figure 3

(Color online) Rapidity distributions (lower panel) of all nucleons and their isospin asymmetries (upper panel) in head-on collisions of ${}^{100}\mathrm{Zn}+{}^{40}\mathrm{Ca}$ at a beam energy of 200 MeV/A using a γ parameter of 1.

Figure 4

(Color online) The same as Fig. 3 but using a γ parameter of 2.

Figure 5

(Color online) Angular distributions of the free neutron to proton ratio $(n/p){}_{\mathrm{free}}$ in head-on collisions of ${}^{100}\mathrm{Zn}+{}^{40}\mathrm{Ca}$ at a beam energy of 200 MeV/nucleon.

Figure 6

(Color online) The $(n/p){}_{\mathrm{free}}$ ratio as a function of nucleon kinetic energy at backward (upper panel) and forward (lower panel) angles in head-on collisions of ${}^{100}\mathrm{Zn}+{}^{40}\mathrm{Ca}$ at a beam energy of 200 MeV/nucleon.

Figure 7

(Color online) Rapidity (upper panel) and angular (lower panel) dependences of isospin asymmetries of all nucleons in the reaction of ${}^{100}\mathrm{Zn}+{}^{40}\mathrm{Ca}$ at a beam energy of 200 MeV/nucleon and impact parameter of 4 fm using a γ parameter of 1.