arXiv 2106.087682021-06nucl-thhep-phnucl-ex

重离子碰撞中原子核的形状

Shape of atomic nuclei in heavy ion collisions

Jiangyong Jia

备注：: 18 pages, 9 figures plus two appendixes, published version
DOI：: 10.1103/PhysRevC.105.014905

摘要：

在重离子碰撞的流体动力学模型描述中，末态各向异性流$v_n$与核子在横平面$\varepsilon_n$上的多极形状分布的强度，$v_n\propto \varepsilon_n$成线性关系。对于$n=1,2,3,4$，$\varepsilon_n$对碰撞离子的形状敏感，其特征在于四极$β_2$、八极$β_3$和十六极$β_4$变形。这种灵敏度的研究分析，也在蒙特卡洛Glauber模型。人们观察到一个强大的线性关系，$\langle\varepsilon_n^2\rangle = a_n'+b_n'β_n^2$，在一个固定的中心事件。$\langle\varepsilon_1^2\rangle$有$β_3$和$β_4$的贡献，$\langle\varepsilon_3^2\rangle$有$β_4$的贡献。在超中心碰撞中，$β_2$和$\varepsilon_3$之间以及$β_3$和$\varepsilon_2$之间的交叉贡献很小，而在非中心碰撞中则有明显的交叉贡献.此外，$\langle\varepsilon_n^2\rangle$对非轴向形状参数（如三轴度）不敏感。这是一个好消息，因为$v_2$、$v_3$和$v_4$的测量值可用于同时约束$β_2$、$β_3$和$β_4$值。最好是通过比较两个质量数相似的碰撞离子，从而获得几乎相同的$a_n'$，以获得与两种物质的$β_n$相关的简单方程。这开辟了在比低能核结构物理（$<10^{-21}$）探测的时间尺度（$<10^{-24}$ s）短得多的时间尺度上绘制原子核形状的可能性，这最终可能提供与核结构实验中获得的信息互补的信息。

英文摘要：

In the hydrodynamic model description of heavy ion collisions, the final-state anisotropic flow $v_n$ are linearly related to the strength of the multi-pole shape of the distribution of nucleons in the transverse plane $\varepsilon_n$, $v_n\propto \varepsilon_n$. The $\varepsilon_n$, for $n=1,2,3,4$, are sensitive to the shape of the colliding ions, characterized by the quadrupole $β_2$, octupole $β_3$ and hexadecapole $β_4$ deformations. This sensitivity is investigated analytically and also in a Monte Carlo Glauber model. One observes a robust linear relation, $\langle\varepsilon_n^2\rangle = a_n'+b_n'β_n^2$, for events in a fixed centrality. The $\langle\varepsilon_1^2\rangle$ has a contribution from $β_3$ and $β_4$, and $\langle\varepsilon_3^2\rangle$ from $β_4$. In the ultra-central collisions, there are little cross contributions between $β_2$ and $\varepsilon_3$ and between $β_3$ and $\varepsilon_2$, but clear cross contributions are present in non-central collisions. Additionally, $\langle\varepsilon_n^2\rangle$ are insensitive to non-axial shape parameters such as the triaxiality. This is good news because the measurements of $v_2$, $v_3$ and $v_4$ can be used to constrain simultaneously the $β_2$, $β_3$, and $β_4$ values. This is best done by comparing two colliding ions with similar mass numbers and therefore nearly identical $a_n'$, to obtain simple equation that relates the $β_n$ of the two species. This opens up the possibility to map the shape of the atomic nuclei at a timescale ($<10^{-24}$s) much shorter than probed by low-energy nuclear structure physics ($<10^{-21}$s), which ultimately may provide information complementary to those obtained in the nuclear structure experiments.

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