arXiv 2301.035482023-01nucl-th

核物质临界点附近的粒子数涨落

Particle-number fluctuations near the critical point of nuclear matter

A. G. Magner, S. N. Fedotkin, U. V. Grygoriev

备注：: 22 pages, 10 figures, 2 tables
DOI：: 10.1103/PhysRevC.107.024610

摘要：

本文用带量子统计修正的状态方程计算了具有粒子间范德瓦耳斯和Skyrme局域密度相互作用的同位素对称核物质的粒子数涨落$ω$。波动，$ω\propto 1/\mathcal{K}$，解析推导出通过等温不可压缩性$\mathcal{K}$在一阶以上的一个小的量子统计参数。我们的近似分析结果似乎与精确的数值计算结果吻合得很好。这些结果也接近于在临界点附近用更精确的不可压缩性$\mathcal{K}$的Tolman和Rowlinson展开式所得到的结果。通过忽略小的量子统计效应，对有限粒子数平均$\langle N \rangle$得到了一个更一般的涨落公式$ω$，在临界点得到了改进.它示出，对于一个大的无量纲参数，$α\propto \mathcal{K}^2\langle N \rangle/\mathcal{K}^{\prime\prime} $，其中$\mathcal{K}^{\prime\prime}$是不可压缩的$\mathcal{K}$作为平均粒子密度$n$的函数的二阶导数，远离临界点（$α\gg 1$），人们发现传统的渐近线，$ω\propto 1/\mathcal{K}$，波动$ω$。对于小参数$α\ll 1$，在临界点附近，其中$\mathcal{K}=0$和$α=0$，得到$ω$的另一渐近线。这些波动，在临界点附近具有作为平均密度$n$的函数的最大值，对于$\langle N \rangle$的有限值是有限的并且相对较小，与传统计算的结果相反。

英文摘要：

The equation of state with quantum statistics corrections is used for particle number fluctuations $ω$ of isotopically symmetric nuclear matter with interparticle van der Waals and Skyrme local density interactions. The fluctuations, $ω\propto 1/\mathcal{K}$, are analytically derived through the isothermal incompressibility $\mathcal{K}$ at first order over a small quantum-statistics parameter. Our approximate analytical results appear to be in good agreement with the results of accurate numerical calculations. These results are also close to those obtained by using more accurate Tolman and Rowlinson expansions of the incompressibility $\mathcal{K}$ near the critical point. A more general formula for fluctuations $ω$, improved at the critical point, was obtained for a finite particle-number average $\langle N \rangle$ by neglecting, for simplicity, small quantum statistics effects. It is shown that for a large dimensionless parameter, $α\propto \mathcal{K}^2\langle N \rangle/\mathcal{K}^{\prime\prime} $, where $\mathcal{K}^{\prime\prime}$ is the second derivative of the incompressibility $\mathcal{K}$ as function of the average particle density $n$, far from the critical point ($α\gg 1$), one finds the traditional asymptote, $ω\propto 1/\mathcal{K}$, for the fluctuations $ω$. For a small parameter, $α\ll 1$, near the critical point, where $\mathcal{K}=0$ and $α=0$, one obtains another asymptote of $ω$. These fluctuations, having a maximum near the critical point as function of the average density $n$, for finite values of $\langle N \rangle$ are finite and relatively small, in contrast to the results of the traditional calculations.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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