The fact that repulsive Rutherford scattering casts a paraboloidal shadow is rarely exploited in introductory mechanics textbooks. Another rarely used construction in such textbooks is the Hamilton vector, a cousin of the more famous LaplaceRunge-Lenz vector. We will show how the latter (Hamilton’s vector) can be used to explain and clarify the former (paraboloidal shadow). ar X iv :2 10 1. 03 54 3v 1 [ ph ys ic s. cl as sph ] 1 0 Ja n 20 21

中文翻译：

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排斥性卢瑟福散射和汉密尔顿矢量的阴影

推力卢瑟福散射投射抛物面阴影这一事实在介绍力学教科书中很少被利用。此类教科书中另一个很少使用的构造是 Hamilton 向量，它是更著名的 LaplaceRunge-Lenz 向量的表亲。我们将展示如何使用后者（汉密尔顿向量）来解释和阐明前者（抛物面阴影）。ar X iv :2 10 1. 03 54 3v 1 [物理化学。cl as sph ] 1 0 Jan 20 21