Angular-Momentum Couplings in Ultra-Long-Range Giant Dipole Molecules

TL;DR

This paper extends the theoretical understanding of ultra-long-range giant dipole molecules by incorporating angular-momentum couplings, p-wave scattering, and spin interactions, leading to new potential energy surfaces and bound states.

Contribution

It introduces a comprehensive theoretical framework including angular-momentum couplings and p-wave scattering for giant dipole molecules, revealing new mixed-spin states and detailed potential energy surfaces.

Findings

Identification of mixed-spin molecular states

Calculation of exact binding energies and wave functions

Discovery of new potential energy landscapes

Abstract

In this article we extend the theory of ultra-long-range giant dipole molecules, formed by an atom in a giant dipole state and a ground-state alkali atom, by angular-momentum couplings known from recent works on Rydberg molecules. In addition to $s$-wave scattering, the next higher order of $p$-wave scattering in the Fermi-pseudopotential describing the binding mechanism is considered. Furthermore, the singlet and triplet channels of the scattering interaction as well as angular-momentum couplings such as hyperfine interaction and Zeeman interactions are included. Within the framework of Born--Oppenheimer theory, potential energy surfaces are calculated in both first-order perturbation theory and exact diagonalization. Besides the known pure triplet states, mixed-spin character states are obtained, opening up a whole new landscape of molecular potentials. We determine exact binding energies and wave functions of the nuclear rotational and vibrational motion numerically from the various potential energy surfaces.