Nucleon effective mass splitting and density-dependent symmetry energy effects on elliptic flow in heavy ion collisions at E_(lab)= 0.09 ～ 1.5 GeV/nucleon

By incorporating an iso spin-dependent form of the momentum-dependent potential in the ultra-relativistic quantum molecular dynamics(UrQMD) model,we systematically investigate effects of the neutron-proton effective mass splitting m*_(n-p)=m*_n-m*_p/m and the density-dependent nuclear symmetry energy E_(sym)(ρ) on the elliptic flow v_2 in~(197)Au+~(197) Au collisions at beam energies from 0.09 to 1.5 GeV/nucleon.It is found that at higher beam energies(≥0.25 GeV/nucleon) with the approximately 75 MeV difference in slopes of the two different E_(sym)(ρ),and the variation of m*_(n-p) ranging from-0.03 to 0.03 at saturation density with isospin asymmetry δ=(ρ_n-ρ_p)/ρ-0.2,the E_(sym)(ρ) has a stronger influence on the difference in v_2 between neutrons and protons,i.e.,v_2~n-v_2~p,than m*_(n-p) has.Meanwhile,at lower beam energies(≤0.25 GeV/nucleon),v_2~n-v_2~p is sensitive to both the E_(sym)(ρ) and the m*_(n-p).Moreover,the influence of m*_(n-p) on v_2~n-v_2~p is more evident with the parameters of this study when using the soft,rather than stiff,symmetry energy.

Nucleon effective mass splitting and density-dependent symmetry energy effects on elliptic flow in heavy ion collisions at Elab= 0.09 ~ 1.5 GeV/nucleon

By incorporating an isospin-dependent form of the momentum-dependent potential in the ultra-relativistic quantum molecular dynamics (UrQMD) model, we systematically investigate effects of the neutron-proton effective mass splitting \begin{document}$m_{n-p}^{*}$\end{document}=\begin{document}$\frac{m_{n}^{*}-m_{p}^{*}}{m}$\end{document} and the density-dependent nuclear symmetry energy \begin{document}$E_{\rm{sym}}(\rho)$\end{document} on the elliptic flow \begin{document}$v_2$\end{document} in \begin{document}$^{197}{{\rm{Au}}}$\end{document} + \begin{document}$^{197}{{\rm{Au}}}$\end{document} collisions at beam energies from 0.09 to 1.5 GeV/nucleon. It is found that at higher beam energies (\begin{document}$\geqslant$\end{document} 0.25 GeV\begin{document}$/$\end{document}nucleon) with the approximately 75 MeV difference in slopes of the two different \begin{document}$E_{\rm{sym}}(\rho)$\end{document}, and the variation of \begin{document}$m_{n-p}^{*}$\end{document} ranging from –0.03 to 0.03 at saturation density with isospin asymmetry \begin{document}$\delta=(\rho_{n}-\rho_{p})/\rho=0.2$\end{document}, the \begin{document}$E_{\rm{sym}}(\rho)$\end{document} has a stronger influence on the difference in \begin{document}$v_{2}$\end{document} between neutrons and protons, i.e., \begin{document}$v_{2}^{n}-v_{2}^{p}$\end{document}, than \begin{document}$m_{n-p}^{*}$\end{document} has. Meanwhile, at lower beam energies (\begin{document}$\leqslant$\end{document} 0.25 GeV\begin{document}$/$\end{document}nucleon), \begin{document}$v_{2}^{n}-v_{2}^{p}$\end{document} is sensitive to both the \begin{document}$E_{\rm{sym}}(\rho)$\end{document} and the \begin{document}$m_{n-p}^{*}$\end{document}. Moreover, the influence of \begin{document}$m_{n-p}^{*}$\end{document} on \begin{document}$v_{2}^{n}-v_{2}^{p}$\end{document} is more evident with the parameters of this study when using the soft, rather than stiff, symmetry energy.