Angular-momentum couplings in long-range Rb$_2$ Rydberg molecules

TL;DR

This paper investigates the effects of angular-momentum couplings on the properties of Rb$_2$ Rydberg molecules, providing detailed calculations of their bound states, lifetimes, and dipole moments considering fine and hyperfine interactions.

Contribution

It introduces a comprehensive Fermi model including S-wave and P-wave scattering, fine, and hyperfine couplings to analyze Rb$_2$ Rydberg molecules with new insights into their molecular potentials and bound states.

Findings

Calculated bound-state energies and lifetimes for vibrational ground states.

Analyzed the influence of hyperfine structure on molecular potentials.

Identified conditions supporting high-$ ext{l}$ Rydberg molecules.

Abstract

We study angular-momentum couplings in $^{87}$Rb$_2$ Rydberg molecules formed between Rydberg and 5S$_{1/2}$ ground-state atoms. We use a Fermi model that includes S-wave and P-wave singlet and triplet scattering of the Rydberg electron with the 5S$_{1/2}$ atom, along with the fine structure coupling of the Rydberg atom and hyperfine structure coupling of the 5S$_{1/2}$ atom. We discuss the effects of these couplings on the adiabatic molecular potentials. We obtain bound-state energies, lifetimes, and electric and magnetic dipole moments for the vibrational ground states of the $^{87}$Rb$(n$D$+5$S$_{1/2})$ molecules in all adiabatic potentials, with fine and hyperfine structure included. We also study the effect of the hyperfine structure on the deep $^3$S-wave- and $^3$P-wave-dominated adiabatic molecular potentials, which support high-$\ell$ $^{87}$Rb$_2$ Rydberg molecules.