Influence of differential elastic nucleon-nucleon cross section on stopping and collective flow in heavy-ion collisions at intermediate energies

Abstract

By considering three different Nucleon-Nucleon (NN) elastic differential cross sections: the Cugnon \emph{et al.} parameterized differential cross section [Nucl. Instrum. Methods Phys. Res., Sect. \textbf{B111}, 215 (1996)], and the differential cross section derived from the collision term of the self-consistent relativistic Boltzmann-Uehling-Uhlenbeck equation proposed by Mao \emph{et al.} [Z.\ Phys.\ A {\bf 347}, 173 (1994)], as well as the isotropic differential cross section, within the newly updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model, the influence of the differential elastic NN cross section on various observables (e.g., nuclear stopping, both the rapidity and transverse-velocity dependence of the directed and elliptic flows) in Au+Au collisions at beam energies 150, 250, 400, and 800 MeV$/$nucleon is investigated. By comparing calculations with those three differential cross sections, it is found that the nuclear stopping power, the directed and elliptic flows are affected to some extent by the differential cross sections, and the impact of differential cross section on those observables becomes more visible as the beam energy increases. The effect on the elliptic flow difference $v_{2}^{n}$-$v_{2}^{H}$ and ratio $v_{2}^{n}$/$v_{2}^{H}$ of neutrons versus hydrogen isotopes ($Z=1$), which have been used as sensitive observables for probing nuclear symmetry energy at high densities, is weak.