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arXiv 2109.00604nucl-thhep-phnucl-ex
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高能重离子碰撞中原子核的三轴形变

Probing triaxial deformation of atomic nuclei in high-energy heavy ion collisions

Jiangyong Jia

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20 pages, 14 figures, plus 3 appendix, published version
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摘要：

大多数原子核的形变都具有四极形状，由其总强度$β_2$和三轴度$γ$描述。在高能重离子碰撞中，通过测量夸克-胶子等离子体对初始状态下偏心率$\varepsilon_2$和密度梯度$d_{\perp}$的集体流响应，可以获得这种形变.利用分析估计和Glauber模型，证明了方差$\langle\varepsilon_2^2\rangle$或$\langle(δd_{\perp}/d_{\perp})^2\rangle$和偏度$\langle\varepsilon_2^2δd_{\perp}/d_{\perp}\rangle$或$\langle(δd_{\perp}/d_{\perp})^3\rangle$分别具有$a'+b'β_2^2$和$a'+(b'+c'\cos(3γ))β_2^3$的简单解析形式。从这些，我构造了几个归一化偏度，以隔离$γ$的$β_2$的依赖，并表明任何归一化偏度和任何方差之间的相关性可以同时约束$β_2$和$γ$。假设椭圆流$v_2$和末态粒子的平均横动量$[p_{\mathrm{T}}]$之间存在线性关系，则对于$v_2$和$[p_{\mathrm{T}}]$的方差和偏度也可以得到类似的结论.我们的发现激发了一个专门的系统扫描的高能量重离子碰撞，以测量原子核的三轴性。这可以通过长核$\cos(3γ)=1$和扁核$\cos(3γ)=-1$与已知的$β_2$值的碰撞来更好地完成，以校准系数$b'$和$c'$，然后是感兴趣的物质的碰撞，特别是具有已知$β_2$但未知$γ$的物质的碰撞。结果表明，高能碰撞作为一种工具，进行跨学科的核物理研究提供了独特的机会。

英文摘要：

Most atomic nuclei are deformed with a quadrupole shape described by its overall strength $β_2$ and triaxiality $γ$. The deformation can be accessed in high-energy heavy-ion collisions by measuring the collective flow response of the produced quark-gluon plasma to the eccentricity $\varepsilon_2$ and the density gradient $d_{\perp}$ in the initial state. Using analytical estimate and a Glauber model, I show that the variances, $\langle\varepsilon_2^2\rangle$ or $\langle(δd_{\perp}/d_{\perp})^2\rangle$, and skewnesses, $\langle\varepsilon_2^2δd_{\perp}/d_{\perp}\rangle$ or $\langle(δd_{\perp}/d_{\perp})^3\rangle$, have a simple analytical form of $a'+b'β_2^2$ and $a'+(b'+c'\cos(3γ))β_2^3$, respectively. From these, I constructed several normalized skewnesses to isolate the $γ$ dependence from that of $β_2$, and show that the correlations between any normalized skewness and any variance can constrain simultaneously the $β_2$ and $γ$. Assuming a linear relation with elliptic flow $v_2$ and mean-transverse momentum $[p_{\mathrm{T}}]$ of final state particles, similar conclusions are also expected for the variances and skewnesses of $v_2$ and $[p_{\mathrm{T}}]$. Our findings motivate a dedicated system scan of high-energy heavy ion collisions to measure triaxiality of atomic nuclei. This is better done by collisions of prolate, $\cos(3γ)=1$, and oblate nuclei, $\cos(3γ)=-1$, with well known $β_2$ values to calibrate the coefficients $b'$ and $c'$, followed by collisions of species of interest especially those with known $β_2$ but unknown $γ$. The results demonstrate the unique opportunities offered by high-energy collisions as a tool to perform interdisciplinary nuclear physics studies.

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