An ion and a polar molecule interact by an anisotropic ion-dipole potential scaling as $-\alpha cos\left(\theta \right)/r^2$ at large distances. Due to its long-range character, it modifies the properties of angular wave functions, which are no longer given by spherical harmonics. In addition, an effective centrifugal potential in the radial equation can become attractive for low angular momenta. In this paper, we develop a general framework for an ion-dipole reactive scattering, focusing on the regime of large $\alpha$. We introduce modified spherical harmonics as solutions of the angular part of the Schrödinger equation and derive several useful approximations in the limit of large $\alpha$. We present a formula for the scattering amplitude expressed in terms of the modified spherical harmonics and we derive expressions for the elastic and reactive collision rates. The solutions of the radial equation are given by Bessel functions, and we analyze their behavior in two distinct regimes corresponding, basically, to attractive and repulsive long-range centrifugal potentials. Finally, we study reactive collisions in the universal regime, where the short-range probability of loss or reaction is equal to unity.

中文翻译：

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远距离离子偶极势中的量子反应性散射

离子和极性分子通过各向异性的离子-偶极势标度相互作用 $-\alpha cos（\theta ）/{\mathrm{[R}}^2$在远处。由于其远距离特性，它修改了角波函数的特性，而不再由球谐函数给出。另外，对于低角动量，径向方程中的有效离心势可能变得有吸引力。在本文中，我们针对离子偶极反应性散射建立了一个通用框架，重点关注大范围的态$\alpha$。我们引入修正的球谐函数作为Schrödinger方程角部分的解，并导出了在大极限范围内的一些有用的近似值$\alpha$。我们提出了一个以修正的球谐函数表示的散射幅度的公式，并得出了弹性和反应碰撞率的表达式。径向方程的解由贝塞尔函数给出，我们分析了它们在两种截然不同的状态下的行为，这些状态基本上对应于吸引和排斥的远程离心势。最后，我们研究了在普遍状态下的反应性碰撞，在这种情况下，短距离的损失或反应概率等于1。