# Rotational structure of weakly bound molecular ions

## TL;DR

This paper derives simple formulas to predict the number of rotational states and rotational constants for weakly bound diatomic molecular ions, based solely on their long-range potential, aiding understanding of their rotational structure.

## Contribution

It introduces new analytical formulas and criteria for analyzing the rotational states of weakly bound molecular ions, based on the quantization rule of Raab and Friedrich.

## Key findings

- Derived accurate formulas for rotational states of weakly bound ions
- Provided estimates for rotational constants up to dissociation threshold
- Established a criterion for rotationless vibrational levels

## Abstract

Relying on the quantization rule of Raab and Friedrich [Phys. Rev. A (2009) in press], we derive simple and accurate formulae for the number of rotational states supported by a weakly bound vibrational level of a diatomic molecular ion. We also provide analytic estimates of the rotational constants of any such levels up to threshold for dissociation and obtain a criterion for determining whether a given weakly bound vibrational level is rotationless. The results depend solely on the long-range part of the molecular potential.