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.

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.