双中心库仑场中电子周期轨道的分岔

Bifurcation of Periodic Orbits of Electronin Two-center Coulomb Field

双中心库仑场中的电子周期轨道可分为Ｐ１，Ｐ２和Ｐ３三类；还可根据轨道在可分离变量的椭圆坐标下的分支比进一步标记．所有的Ｐ１轨道均由绕两中心的一个椭圆轨道分岔；而Ｐ２和Ｐ３轨道则产生或消失于一线状轨道：连接两中心或Ｘ轴上的轨道．在作了Ｔｈｉｅｌｅ－Ｂｕｒｒａｕ变换后，轨道的会聚及分岔特征变得十分清楚．

The periodic orbits of an electron in a two-center Coulomb field can be classified into three types P1,P2 and P3,and then are labeled by using their winding numbers in the separable ellipsoidal coordinates. All the P1 orbits are bifurcated from an ellipse orbit rotating around the two centers; the P2 and P3 orbits are born or annihilated from an orbit in which the electron moves on the line connecting the two centers or the X-axis. The properties of convergence and bifurcation of the periodic orbits are discussed by introducing the Thiele-Burrau's transformation.