Green's function treatment of Rydberg molecules with spins

TL;DR

This paper introduces a Green's function approach to calculate potential curves and wavefunctions of Rydberg molecules, offering an analytical alternative to traditional diagonalization methods that improves convergence and relates spectroscopy to scattering phaseshifts.

Contribution

The authors develop a Green's function method for Rydberg molecules that simplifies calculations and enhances the connection between molecular spectra and scattering data.

Findings

Provides analytical potential energy curves and wavefunctions.

Offers improved convergence over standard diagonalization.

Establishes a quantitative link between spectroscopy and scattering phaseshifts.

Abstract

The determination of ultra-long-range molecular potential curves has been reformulated using the Coulomb Greens function to give a solution in terms of the roots of an analytical determinantal equation. For a system consisting of one Rydberg atom with fine structure and a neutral perturbing ground state atom with hyperfine structure, the solution yields potential energy curves and wavefunctions in terms of the quantum defects of the Rydberg atom and the electron-perturber scattering phaseshifts and hyperfine splittings. This method provides a promising alternative to the standard currently utilized method of diagonalization, which suffers from problematic convergence issues and nonuniqueness, and can potentially yield a more quantitative relationship between Rydberg molecule spectroscopy and electron-atom scattering phaseshifts.