Ab initio potential energy curves, scattering lengths, and rovibrational levels of the He$_2^+$ molecular ion in excited electronic states

TL;DR

This paper provides highly accurate potential energy curves, rovibrational levels, and scattering lengths for the He$_2^+$ molecular ion in excited states, aiding spectroscopy and ultracold collision studies.

Contribution

It introduces a comprehensive ab initio calculation of excited-state potential energy curves and scattering properties for He$_2^+$, including relativistic and adiabatic corrections.

Findings

Calculated potential energy curves with extrapolated basis sets.

Predicted scattering lengths for ultracold collisions.

Provided rovibrational levels and spectroscopic constants.

Abstract

We calculate accurate potential energy curves for a ground-state He$^+$ ion interacting with a He atom in the lowest-energy metastable $^3\!S$ electronic state. We employ the full configuration interaction method, equivalent to exact diagonalization, with results extrapolated to the complete basis set limit. The leading relativistic and adiabatic corrections are included using perturbation theory. We calculate rovibrational levels and spectroscopic constants of the He$_2^+$ molecular ion in excited electronic states for three stable isotopologues. We predict the scattering lengths for ultracold ion-atom collisions. The theoretical data are presented with their uncertainties and agree well with previous results for the ground state. The reported results may be useful for the spectroscopy of the He$_2^+$ molecular ion in the excited electronic state and collisional studies of He$^+$ ions immersed in ultracold gases of metastable He atoms.