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.

• Received 20 July 2020
• Revised 5 January 2021
• Accepted 25 January 2021

DOI:https://doi.org/10.1103/PhysRevA.103.023324

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society