Abstract

A solution of the scattering problem is obtained for the Schrödinger equation with the potential of induced dipole interaction, which decreases as the inverse square of the distance. Such a potential arises in the collision of an incident charged particle with a complex of charged particles (for example, in the collision of electrons with atoms). An integral equation for the wave function is constructed for an arbitrary value of the orbital momentum of relative motion. By solving this equation, an exact integral representation for the \(K\)-matrix of the problem is obtained in terms of the wave function. This representation is used to analyze the behavior of the \(K\)-matrix at low energies and to obtain comprehensive information on its threshold behavior for various values of the dipole momentum. The resulting solution is applied to study the behavior of the scattering cross sections in the electron–positron–antiproton system.

中文翻译：

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关于势能随距离平方反比减小的散射问题

摘要

得到了薛定谔方程的散射问题的解，其具有诱导偶极子相互作用的潜力，其随着距离的平方反比而减小。这种电势在入射带电粒子与带电粒子复合体的碰撞中产生（例如，在电子与原子的碰撞中）。对于相对运动的轨道动量的任意值，构造了波函数的积分方程。通过求解该方程，可以根据波函数获得问题的\(K\)矩阵的精确积分表示。该表示用于分析低能量下K矩阵的行为，并获取有关偶极子动量的各种值的阈值行为的综合信息。所得解决方案用于研究电子-正电子-反质子系统中散射截面的行为。