Quantum reactive scattering in the long-range ion-dipole potential

TL;DR

This paper develops a theoretical framework for ion-dipole reactive scattering considering long-range anisotropic potentials, introducing modified spherical harmonics and analyzing collision rates in different regimes.

Contribution

It introduces a new approach using modified spherical harmonics for ion-dipole scattering and derives formulas for scattering amplitudes and collision rates in the large polarizability limit.

Findings

Derived formulas for elastic and reactive collision rates.

Analyzed behavior of radial solutions in attractive and repulsive regimes.

Studied reactive collisions in the universal loss regime.

Abstract

An ion and a polar molecule interact by an anisotropic ion-dipole potential scaling as $- \alpha \cos (\theta)/r^2$ 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 Schr\"odinger 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 analyse their behaviour 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.