Interaction potentials and ultracold scattering cross sections for the $^7$Li$^+$-$^7$Li ion-atom system

TL;DR

This study computes isotope-independent interaction potentials and ultracold scattering cross sections for the $^7$Li$^+$-$^7$Li system, providing precise low-energy scattering parameters crucial for understanding ultracold ion-atom collisions.

Contribution

It offers new calculations of potential energy curves and scattering lengths for the Li$^+$-Li system, including bounds on the accuracy of these parameters in the ultracold regime.

Findings

The scattering length for the A$^2\Sigma_u^+$ state is positive and well-constrained.

The scattering length for the X$^2\Sigma_g^+$ state is large and sensitive to potential variations.

The study emphasizes the importance of potential accuracy in ultracold scattering predictions.

Abstract

We calculate the isotope independent Li$^+$-Li potential energy curves for the electronic ground and first excited states. Scattering phase shifts and total scattering cross section for the $^7$Li$^+$-$^7$Li collision are calculated with emphasis on the ultra-low energy domain down to the $s$-wave regime. The effect of physically motivated alterations on the calculated potential energy curves is used to determine the bound of accuracy of the low-energy scattering parameters for the ion-atom system. It is found that the scattering length for the A$^2\Sigma_u^+$ state, $a_u$ = 1325 a$_0$, is positive and has well-constrained bounds. For the X$^2\Sigma_g^+$ state, the scattering length, $a_g$ = 20465 a$_0$ has a large magnitude as it is sensitive to the restrained change of the potential, due to the presence of a vibrational state in the vicinity of the dissociation limit.