Classical Coulomb Three‐Body Problem
Classical Coulomb Three‐Body Problem
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经典库仑三体问题
DOI：
10.1002/0471712531.ch6
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
M. Sano
中科院分区：
文献类型：
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作者：
M. Sano
两电子原子(He)或离子(H−，Li+，Be2+，…)的经典库仑三体问题使用最初用于天体力学的McGehee爆炸技术进行了研究。首先，我们考虑了总角动量为零的二维情况，特别是原子核具有无限大质量的情况。推导了适用于该设置的三碰撞流形(Tcm)。从中医的角度考察了引力情形与库仑情形的根本区别。接下来，我们利用相关的符号动力学和Tcm(所有粒子都具有有限质量)详细地研究了这些原子离子在共线Eze组态下的经典动力学。结果表明，由于原子核和电子的质量比较大，原子和离子在共线Eze组态中的动力学行为是双曲线的。提出了这一发现的实验表现。最后，为了求出总角动量为零的二维情形的环面，我们研究了自由落体问题。发现原子核的电荷Z对环面的存在起着重要的作用。
Classical Coulomb three‐body problem like two‐electron atom(He) or ions (H−,Li+,Be2+,…) is investigated using the McGehee's blow‐up technique which was originally used in celestial mechanics. First we consider the two‐dimensional case with zero total angular momentum especially the case that the nucleus has infinite mass. A triple collision manifold(TCM) for this setting is derived. A fundamental difference between gravitational case and Coulomb case is examined via the TCM. Next we investigate classical dynamics in the collinear eZe configuration for these atom ions in detail using the associated symbolic dynamics and the TCM(All particles have finite masses). It is numerically revealed and conjectured that thanks to large mass ratio between nucleus and electron, the dynamics of these atom and ions in the collinear eZe configuration is hyperbolic. Experimental manifestations of this finding are proposed. Finally, in order to find tori for the 2D case with zero total angular momentum, we investigate free fall problem. It is found that the chargeZof the nucleus plays an important role for the existence of tori.