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 explained.
Highlights
Diatomic ultralong-range Rydberg molecules consisting of a Rydberg atom whose electron, upon frequent scattering off a ground state atom, binds the atom, localized at large distances (∼ 103 Bohr radii), to the ion core of the Rydberg atom were predicted theoretically in Ref. [1]
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
We consider a Rydberg atom whose ionic core is located at the origin and a neutral ground state atom located at the position R within the Rydberg electron orbit
Summary
Diatomic ultralong-range Rydberg molecules consisting of a Rydberg atom whose electron, upon frequent scattering off a ground state atom, binds the atom, localized at large distances (∼ 103 Bohr radii), to the ion core of the Rydberg atom were predicted theoretically in Ref. [1]. For electronic s-wave scattering of the Rydberg electron from the ground state atom, two types of ultralong-range molecular states can be distinguished: the non-polar, low angular momentum quantum defect states and the polar, high angular momentum “trilobite” states. Modeling the pseudopotential instead by a regularized delta function reproduces potential energy curves which agree exactly with those obtained by the quantum defect theory approach. Throughout our analysis we give limits of the bare delta function potential and its validity as an approximation in first order perturbation theory.
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