Calculating the initial energy density in heavy ion collisions by including the finite nuclear thickness
Calculating the initial energy density in heavy ion collisions by including the finite nuclear thickness
复制标题
DOI：
10.1103/physrevc.103.024907
复制
发表时间：
2020-12
影响因子：
3.1
通讯作者：
T. Mendenhall;Zi-Wei Lin
中科院分区：
文献类型：
--
作者：
T. Mendenhall;Zi-Wei Lin
在选择合适的形成时间后，可以用Bjorken能量密度公式估计重离子碰撞产生的初始能量密度$\ensuremath{\tau}{}_{\mathrm{F}}$。然而，由于忽略了有限的核厚度，Bjorken公式在低能量下失效。这里我们同时考虑了初始能量产生的有限持续时间和有限纵向扩展。当$\ensuremath{\tau}{}_{\mathrm{F}}$不比两个原子核的穿越时间小太多时，我们的结果与之前只考虑有限时间持续时间的研究结果相似。特别是，我们发现在低能量下，初始能量密度的最大值要低得多，但演化时间比比约肯公式长得多，而在足够大$\ensuremath{\tau}{}_{\mathrm{F}}$和/或足够高的能量下，我们的结果接近比约肯公式。我们还发现一个质的区别，我们的最大能量密度${\ensuremath{\epsilon}}^{\mathrm{max}}$在$\ensuremath{\tau}{}_{\mathrm{F}}=0$是有限的，而Bjorken公式发散为$1/\ensuremath{\tau}{}_{\mathrm{F}}$，之前的结果在低能发散为$ln(1/\ensuremath{\tau}{}_{\mathrm{F}})$，而在高能发散为$1/\ensuremath{\tau}{}_{\mathrm{F}}$。此外，我们的能量密度解近似满足标度关系。因此，${\ensuremath{\epsilon}}^{\mathrm{max}}$的$\ensuremath{\tau}{}_{\mathrm{F}}$依赖性决定了$A$依赖性，在我们的结果中，低能量时${\ensuremath{\epsilon}}^{\mathrm{max}}$的较弱的$\ensuremath{\tau}{}_{\mathrm{F}}$依赖性意味着$A$对${\ensuremath{\epsilon}}^{\mathrm{max}}$的增加较慢。
The initial energy density produced in heavy ion collisions can be estimated with the Bjorken energy density formula after choosing a proper formation time $\ensuremath{\tau}{}_{\mathrm{F}}$. However, the Bjorken formula breaks down at low energies because it neglects the finite nuclear thickness. Here we include both the finite time duration and finite longitudinal extension of the initial energy production. When $\ensuremath{\tau}{}_{\mathrm{F}}$ is not too much smaller than the crossing time of the two nuclei, our results are similar to those from a previous study that only considers the finite time duration. In particular, we find that at low energies the initial energy density has a much lower maximum value but evolves much longer than the Bjorken formula, while at large-enough $\ensuremath{\tau}{}_{\mathrm{F}}$ and/or high-enough energies our result approaches the Bjorken formula. We also find a qualitative difference in that our maximum energy density ${\ensuremath{\epsilon}}^{\mathrm{max}}$ at $\ensuremath{\tau}{}_{\mathrm{F}}=0$ is finite, while the Bjorken formula diverges as $1/\ensuremath{\tau}{}_{\mathrm{F}}$ and the previous result diverges as $ln(1/\ensuremath{\tau}{}_{\mathrm{F}})$ at low energies but as $1/\ensuremath{\tau}{}_{\mathrm{F}}$ at high energies. Furthermore, our solution of the energy density approximately satisfies a scaling relation. As a result, the $\ensuremath{\tau}{}_{\mathrm{F}}$ dependence of ${\ensuremath{\epsilon}}^{\mathrm{max}}$ determines the $A$ dependence, and the weaker $\ensuremath{\tau}{}_{\mathrm{F}}$ dependence of ${\ensuremath{\epsilon}}^{\mathrm{max}}$ in our results at low energies means a slower increase of ${\ensuremath{\epsilon}}^{\mathrm{max}}$ with $A$.