The paper explores the shadow of the repulsive Rutherford scattering - the portion of space entirely shielded from admitting any particle trajectory. The geometric properties of the projectile shadow are analyzed in detail in the fixed-target frame as well as in the center-of-mass frame, where both the charged projectile and the charged target cast their own respective shadows. In both frames the shadow is found to take an extremely simple, paraboloidal shape. In the fixed-target frame the target is precisely at the focus of this paraboloidal shape, while the focal points of the projectile and target shadows in the center-of-mass frame coincide. In the fixed-target frame the shadow takes on a universal form, independent of the underlying physical parameters, when expressed in properly scaled coordinates, thus revealing a natural length scale to the Rutherford scattering.

中文翻译：

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固定目标和质心坐标系中排斥性卢瑟福散射的阴影

该论文探讨了排斥性卢瑟福散射的阴影——空间的一部分完全被屏蔽，不允许任何粒子轨迹进入。在固定目标框架和质心框架中详细分析了弹丸阴影的几何特性，其中带电弹丸和带电目标投射了各自的阴影。在这两个帧中，发现阴影呈现出极其简单的抛物线形状。在固定目标坐标系中，目标恰好位于该抛物面形状的焦点上，而质心坐标系中弹丸和目标阴影的焦点重合。在固定目标框架中，当以适当缩放的坐标表示时，阴影呈现出一种通用形式，独立于潜在的物理参数，