论文标题
固定目标和质量框架中排斥的卢瑟福散射的阴影
A shadow of the repulsive Rutherford scattering in the fixed-target and the center-of-mass frame
论文作者
论文摘要
本文探讨了排斥卢瑟福散射的阴影 - 空间的一部分完全避免接受任何粒子轨迹。弹丸阴影的几何特性在固定目标框架以及质量中心框架中进行了详细分析，在那里，带电的弹丸和带电的目标都施放了自己的各自的阴影。在这两个框架中，都发现阴影具有非常简单的抛物面形状。在固定目标框架中，目标正好是该抛物面形状的重点，而弹丸中心框架中弹丸的焦点和目标阴影一致。在固定目标框架中，当以正确缩放的坐标表达时，阴影采用通用形式，独立于基础物理参数，从而揭示了卢瑟福散射的自然长度尺度。
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.
