A simple geometrical model with event-by-event fluctuations is suggested to study elliptical and triangular eccentricities in the initial state of relativistic heavy-ion collisions. This model describes rather well the ALICE and ATLAS data for Pb + Pb collisions at center-of-mass energy TeV per nucleon pair, assuming that the second, v ₂, and third, v ₃, harmonics of the anisotropic flow are simply linearly proportional to the eccentricities ɛ ₂ and ɛ ₃, respectively. We show that the eccentricity ɛ ₃ has a pure fluctuation origin and is substantially dependent on the size of the overlap area only, while the eccentricity ɛ ₂ is mainly related to the average collision geometry. Elliptic flow, therefore, is weakly dependent on the event-by-event fluctuations everywhere except of the very central collisions 0%–2%, whereas triangular flow is mostly determined by the fluctuations. The scaling dependence of the magnitude of the flow harmonics on atomic number, v _n ∝ A ^−1/3, is predicted for this centrality interval.

建议使用具有逐事件波动的简单几何模型来研究相对论重离子碰撞初始状态下的椭圆和三角形偏心率。该模型很好地描述了 Pb + Pb 碰撞的 ALICE 和 ATLAS 数据，每个核子对的质心能量为TeV，假设各向异性流的二次谐波v ₂和三次谐波v ₃简单地成线性比例分别为ɛ ₂和ɛ ₃。我们表明，偏心率ɛ ₃具有纯波动起源，并且基本上仅取决于重叠区域的大小，而偏心率ɛ 3 ₂主要与平均碰撞几何有关。因此，除了非常中心的碰撞 0%–2% 之外，椭圆流微弱地依赖于随事件的波动，而三角流主要由波动决定。对于该中心性区间，预测了流动谐波幅度对原子序数v _n ∝ A ^-1/3的缩放依赖性。