On the electrostatic interactions involving long-range Rydberg molecules

TL;DR

This paper develops a multipole expansion approach in prolate spheroidal coordinates to analyze electrostatic interactions in long-range Rydberg molecules, providing simplified expressions and insights into their potential behavior.

Contribution

It introduces a spheroidal multipole expansion method that offers more accurate and convergent descriptions of LRRM electrostatic potentials compared to traditional spherical approaches.

Findings

Spheroidal monopole term captures key features of LRRM potential.

Multipole spheroidal expansion converges faster than spherical expansion.

Approximate expressions effectively describe LRRM interactions at various distances.

Abstract

A ground state atom immersed in the wave function of the valence electron of a Rydberg atom can generate a long-range Rydberg molecule (LRRM). In this work, using the multipole expansion of the electrostatic interaction in prolate spheroidal coordinates, approximate and compact expressions of the electrostatic potential that determine the chemistry of trilobite and butterfly LRRM are explored. It is shown that even the spheroidal monopole term can be used to describe general features of the potential generated by a LRRM at short distances. It is also shown that even at long separations that allow a perturbative description of the intermolecular interaction between two LRRM, the convergence of the multipole spheroidal expansion is faster than that of its spherical analogue.