A comparative analysis of binding in ultralong-range Rydberg molecules

TL;DR

This paper compares various computational methods for analyzing the electronic structure of ultralong-range Rydberg molecules, highlighting their differences, convergence issues, and the effectiveness of the regularized delta potential.

Contribution

It identifies the regularized delta function potential as the approach that reproduces quantum defect theory results beyond first order perturbation.

Findings

First order perturbation matches Green's function approach

Fermi pseudopotential with bare delta function is non-convergent

Regularized delta potential yields exact results

Abstract

We perform a comparative analysis of different computational approaches employed to explore the electronic structure of ultralong-range Rydberg molecules. Employing the Fermi pseudopotential approach, where the interaction is approximated by an $s$-wave bare delta function potential, one encounters a non-convergent behavior in basis set diagonalization. Nevertheless, the energy shifts within the first order perturbation theory coincide with those obtained by an alternative approach relying on Green's function calculation with the quantum defect theory. A pseudopotential that yields exactly the results obtained with the quantum defect theory, i.e. beyond first order perturbation theory, is the regularized delta function potential. The origin of the discrepancies between the different approaches is analytically motivated.