论文标题
通过包括有限的核厚度来计算重离子碰撞中的初始能量密度
Calculating the initial energy density in heavy ion collisions by including the finite nuclear thickness
论文作者
论文摘要
重离子碰撞中产生的初始能量密度可以在选择适当的地层时间$τ{_ {\ rm f}} $之后使用Bjorken能量密度公式估算。但是，Bjorken公式在低能的情况下分解，因为它忽略了有限的核厚度。在这里，我们包括初始能源产生的有限持续时间和有限的纵向扩展。当$τ{_ {\ rm f}} $不比两个核的交叉时间小得多，我们的结果与以前研究的研究相似，后者仅考虑有限的时间。特别是，我们发现在低能的初始能量密度的最大值要低得多，但演变的时间比Bjorken公式长得多，而在$τ{_ {\ rm f}} $和/或高启动能量下，我们的结果方法是Bjorken公式。我们还发现一个质的差异是，我们的最大能量密度$ε^{\ rm max} $ at $τ{_ {_ {\ rm f}} = 0 $是有限的，而bjorken公式为$ 1/ττ{_ _ {\ rm f}} $ and $ \ ln（1/° f}}）$在低能量时，但为$ 1/τ{_ {\ rm f}} $在高能时。此外，我们对能量密度的解决方案大致满足缩放关系。结果，$τ{_ {\ rm f}} $ - $ε^{\ rm max} $的依赖性确定$ a $ a-依赖性，并且$ a $τ{_ {_ {\ rm f}} $ - $ε^{\ rm max max flos a $ rm max firiies in y y y y y rip a y的依赖性$ a $的max} $。
The initial energy density produced in heavy ion collisions can be estimated with the Bjorken energy density formula after choosing a proper formation time $τ{_{\rm F}}$. 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 $τ{_{\rm F}}$ 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 $τ{_{\rm F}}$ and/or high-enough energies our result approaches the Bjorken formula. We also find a qualitative difference in that our maximum energy density $ε^{\rm max}$ at $τ{_{\rm F}}=0$ is finite, while the Bjorken formula diverges as $1/τ{_{\rm F}}$ and the previous result diverges as $\ln (1/τ{_{\rm F}})$ at low energies but as $1/τ{_{\rm F}}$ at high energies. Furthermore, our solution of the energy density approximately satisfies a scaling relation. As a result, the $τ{_{\rm F}}$-dependence of $ε^{\rm max}$ determines the $A$-dependence, and the weaker $τ{_{\rm F}}$-dependence of $ε^{\rm max}$ in our results at low energies means a slower increase of $ε^{\rm max}$ with $A$.
