Nuclear symmetry energy $E_{ \rm{ sym}}(\rho)$ at density $\rho$ is normally expanded or simply parameterized as a function of $\chi=(\rho-\rho_0)/3\rho_0$ in the form of $E_{ \rm{ sym}}(\rho)\approx S+L\chi+2^{ -1}K_{ \rm{ sym}}\chi^2+6^{ -1}J_{ \rm{ sym}}\chi^3+\cdots$ using its magnitude $S$, slope $L $, curvature $K_{ \rm{ sym}}$ and skewness $J_{ \rm{ sym}}$ at the saturation density $\rho_0$ of nuclear matter. Much progress has been made in recent years in constraining especially the $S$ and $L$ parameters using various terrestrial experiments and astrophysical observations. However, such kind of expansions/parameterizations do not converge at supra-saturation densities where $\chi$ is not small enough, hindering an accurate determination of high-density $E_{ \rm{ sym}}(\rho)$ even if its characteristic parameters at $\rho_0$ are all well determined by experiments/observations. By expanding the $E_{ \rm{ sym}}(\rho)$ in terms of a properly chosen auxiliary function $\Pi_{ \rm{ sym}}(\chi,\Theta_{ \rm{ sym}})$ with a parameter $\Theta_{ \rm{ sym}}$ fixed accurately by an experimental $E_{ \rm{ sym}}(\rho_{ \rm{ r}})$ value at a reference density $\rho_{ \rm{ r}}$, we show that the shortcomings of the $\chi$-expansion can be completely removed or significantly reduced in determining the high-density behavior of $E_{ \rm{ sym}}(\rho)$. In particular, using two significantly different auxiliary functions, we show that the new approach effectively incorporates higher $\chi$-order contributions and converges to the same $E_{ \rm{ sym}}(\rho)$ much faster than the conventional $\chi$-expansion at densities $\lesssim3\rho_0$. Several quantitative demonstrations using Monte Carlo simulations are given.
Categories: nucl-th astro-ph.HE nucl-ex