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Quantum-mechanical and semiclassical study of the collinear three-body Coulomb problem: Inelastic collisions below the three-body disintegration threshold

机译：共线三体库仑问题的量子力学和半经典研究：三体崩解阈值以下的非弹性碰撞

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A quantum-mechanical (QM) and semiclassical (SC) study of inelastic collisions in collinear three-body Coulomb systems below the three-body disintegration threshold is presented. The QM results are obtained by solving the stationary Schr?dinger equation in hyperspherical coordinates using the slow/smooth variable discretization method. After appropriate rescaling of the hyperspherical coordinates, an asymptotic parameter 0?h?1 that depends only on the masses of particles and has the meaning of an effective Planck’s constant for the motion in hyperradius emerges. The SC results are obtained in the leading order approximation of the asymptotic expansion in h . The main attention is paid to investigating how the SC and QM results converge as h→0 . It is shown that the overall agreement for a wide spectrum of systems and processes is surprisingly good even for h?1 . However, because of interference effects the convergence is not monotonic, and the SC results may be grossly in error in the situations where a destructive interference occurs. The analysis of hidden crossings clarifies mechanisms of the nonadiabatic transitions. It is shown that if the oppositely charged particle is located between the two others, the nonadiabatic transitions occur near the top of the potential barrier via the well-known T series of hidden crossings. If it is located on one end of the system, then there is no potential barrier for real values of the angular variable, but there still exists an extremum in the complex plane; the mechanism of nonadiabatic transitions in this case is called the complex T series of hidden crossings.
机译：提出了在三体崩解阈值以下的共线三体库仑系统中非弹性碰撞的量子力学（QM）和半经典（SC）研究。通过使用慢/平滑变量离散化方法在超球坐标中求解平稳的薛定？方程来获得QM结果。在对超球面坐标进行了适当的重新缩放后，会出现一个渐近参数0？h？1，该参数仅取决于粒子的质量，并具有超半径运动的有效普朗克常数的含义。 SC结果以h的渐近展开的前导逼近获得。主要注意研究SC和QM结果如何收敛为h→0。结果表明，即使对于h？1，广泛的系统和过程的总体协议也令人惊讶。但是，由于干扰效应，收敛不是单调的，并且在发生相消干扰的情况下，SC结果可能会严重错误。对隐藏交叉的分析明确了非绝热转变的机制。结果表明，如果带相反电荷的粒子位于两个粒子之间，则非绝热跃迁会通过众所周知的T系列隐藏交叉点在势垒顶部附近发生。如果它位于系统的一端，则对于角度变量的实际值没有潜在的障碍，但是在复平面中仍然存在极值；在这种情况下，非绝热过渡的机制称为复杂的T系列隐藏交叉。

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