arXiv 2104.021852021-04nucl-thastro-ph.HEnucl-ex

确定超饱和密度对称能的辅助函数法

Auxiliary Function Approach for Determining Symmetry Energy at Supra-saturation Densities

Bao-Jun Cai, Bao-An Li

备注：: Discussions and references added. Phys. Rev. C in press
发表信息：: Phys. Rev. C 103, 054611 (2021)
DOI：: 10.1103/PhysRevC.103.054611

摘要：

在密度$ρ$下的核对称能$E_{\rm{sym}}(ρ)$通常被展开或简单地参数化为在核物质的饱和密度$ρ_0$下的$χ=(ρ-ρ_0)/3ρ_0$的函数，其形式为使用其量值$S$、斜率$L $、曲率$K_{\rm{sym}}$和偏斜度$J_{\rm{sym}}$的$E_{\rm{sym}}(ρ)\approx S+Lχ+2^{-1}K_{\rm{sym}}χ^2+6^{-1}J_{\rm{sym}}χ^3+\cdots$。近年来，利用各种地面实验和天体物理观测，特别是在约束$S$和$L$参数方面取得了很大进展。然而，这种扩展/参数化在$χ$不够小的超饱和密度下不收敛，从而阻碍了高密度$E_{\rm{sym}}(ρ)$的准确确定，即使其在$ρ_0$的特征参数都通过实验/观察很好地确定。通过扩展$E_{\rm{sym}}(ρ)$在一个适当选择的辅助功能$Π_{\rm{sym}}(χ,Θ_{\rm{sym}})$与参数$Θ_{\rm{sym}}$固定准确的实验$E_{\rm{sym}}(ρ_{\rm{r}})$值在参考密度$ρ_{\rm{r}}$方面，我们表明，$χ$ -扩展的缺点可以完全删除或显着减少在确定的高密度行为的$E_{\rm{sym}}(ρ)$。特别是，使用两个显着不同的辅助功能，我们表明，新的方法有效地结合了更高的$χ$阶的贡献，并收敛到相同的$E_{\rm{sym}}(ρ)$比传统的$χ$膨胀密度$\lesssim3ρ_0$快得多。几个定量演示使用Monte Carlo模拟。

英文摘要：

Nuclear symmetry energy $E_{\rm{sym}}(ρ)$ at density $ρ$ is normally expanded or simply parameterized as a function of $χ=(ρ-ρ_0)/3ρ_0$ in the form of $E_{\rm{sym}}(ρ)\approx S+Lχ+2^{-1}K_{\rm{sym}}χ^2+6^{-1}J_{\rm{sym}}χ^3+\cdots$ using its magnitude $S$, slope $L $, curvature $K_{\rm{sym}}$ and skewness $J_{\rm{sym}}$ at the saturation density $ρ_0$ 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 $χ$ is not small enough, hindering an accurate determination of high-density $E_{\rm{sym}}(ρ)$ even if its characteristic parameters at $ρ_0$ are all well determined by experiments/observations. By expanding the $E_{\rm{sym}}(ρ)$ in terms of a properly chosen auxiliary function $Π_{\rm{sym}}(χ,Θ_{\rm{sym}})$ with a parameter $Θ_{\rm{sym}}$ fixed accurately by an experimental $E_{\rm{sym}}(ρ_{\rm{r}})$ value at a reference density $ρ_{\rm{r}}$, we show that the shortcomings of the $χ$-expansion can be completely removed or significantly reduced in determining the high-density behavior of $E_{\rm{sym}}(ρ)$. In particular, using two significantly different auxiliary functions, we show that the new approach effectively incorporates higher $χ$-order contributions and converges to the same $E_{\rm{sym}}(ρ)$ much faster than the conventional $χ$-expansion at densities $\lesssim3ρ_0$. Several quantitative demonstrations using Monte Carlo simulations are given.

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