\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."> Nucleon effective mass splitting and density-dependent symmetry energy effects on elliptic flow in heavy ion collisions at <i>E</i><sub>lab</sub>= 0.09 ~ 1.5 GeV/nucleon -
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