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arXiv:2605.03684 · Molecular Physics

Theoretical calculation of electron transfer between calcium ground-state atoms and Rydberg atoms

Alisée Bouillon, Matthieu Génévriez

Published May 11, 2026• 0 citations
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Abstract

We calculated the electronic interaction associated with the exchange of an electron between an atom of calcium excited to a Rydberg state (n∼10−15) and another, neighbouring calcium atom in its ground state. In this range, the Rydberg states have an energy that is comparable to the electron affinity of Ca, enabling resonant or near resonant charge transfer at large internuclear separations (200–700 a0). We calculated the interaction strength while systematically and critically assessing the approximations made, and found it to be large, ranging from 10−5 Eh (70 GHz) to 10−8 Eh. Charge transfer is thus expected to be efficient and to significantly affect the molecular dynamics at a range of internuclear distances where ultra-long-range Rydberg molecules also exist.

DOI
10.1080/00268976.2026.2666935

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We calculated the electronic interaction associated with the exchange of an electron between an atom of calcium excited to a Rydberg state (n∼10−15) and another, neighbouring calcium atom in its ground state. In this range, the Rydberg states have an energy that is comparable to the electron affinity of Ca, enabling resonant or near resonant charge transfer at large internuclear separations (200–700 a0). We calculated the interaction strength while systematically and critically assessing the approximations made, and found it to be large, ranging from 10−5 Eh (70 GHz) to 10−8 Eh. Charge transfer is thus expected to be efficient and to significantly affect the molecular dynamics at a range of internuclear distances where ultra-long-range Rydberg molecules also exist.
Relative yields of Ca+{\mathrm{Ca}}^{+}Ca+ and ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$ ions from thermal-energy collisions between highly excited Ca∗{\mathrm{Ca}}^{\mathrm{*}}Ca∗ 4snd 1^{1}1D Rydberg atoms and Ca ground-state atoms are measured as a function of n. The collisions take place within an effusive Ca atomic beam. The cross section for a collision resulting in a bound ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$ and a ground-state Ca+{\mathrm{Ca}}^{+}Ca+ is expected to be large when the binding energy of the excited Rydberg state nearly matches the electron affinity of Ca. We observe a large increase in positive and negative ions for n=25 only. This result strongly suggests that the binding energy of ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$ is 24\ifmmode\pm\else\textpm\fi{}1.4 meV.
Abstract We present an overview over theoretical models to describe adiabatic potential-energy curves, experimental excitation spectra, and electronic and nuclear dynamics in interacting Rydberg-atom pairs at large internuclear separations. The potential-energy curves and molecular wavefunctions are determined from the multipole expansion of the static Coulomb interaction which is evaluated numerically in a product basis of atomic orbitals. The convergence of this approach both in the truncation of the multipole expansion as well as in the size of the product basis is discussed, and the comparison of simulated excitation spectra is established as a useful criterium to test the convergence of the calculation. We finally discuss the dynamics of electronic and nuclear motions of pairs of Rydberg atoms, focusing on the stability of ultralong range Rydberg molecules with respect to autoionization.
The adiabatic potential energy curves of Rb2{\mathrm{Rb}}_{2}Rb2​ in the long-range Rydberg electronic states are calculated using the two-electron RRR-matrix method [M. Tarana and R. \ifmmode \check{C}\else \v{C}\fi{}ur\'{\i}k, Phys. Rev. A 95, 042515 (2017)] for the intermediate internuclear separations between 37 and 200 a.u. The results are compared with the zero-range models to find a region of the internuclear distances where Fermi's pseudopotential approach provides accurate energies. A finite-range potential model of the atomic perturber is used to calculate the wave functions of the Rydberg electron and their features specific for the studied range of internuclear distances are identified.
Abstract In excited molecules, the interaction between the covalent Rydberg and ion-pair channels forms a unique class of excited states, in which the infinite manifold of vibrational levels are the equivalent of atomic Rydberg states with a heavy electron mass. Production of the ion-pair states usually requires excitation through one or several interacting Rydberg states; these interacting channels lead to loss of flux, diminishing the rate of ion-pair production. Here, we develop an analytical, asymptotic charge-transfer model for the interaction between ultracold Rydberg molecular states, and employ this method to demonstrate the utility of off-resonant field control over the ion-pair formation, with near unity efficiency.
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We introduce a computational method developed for study of long-range molecular Rydberg states of such systems that can be approximated by two electrons in a model potential of the atomic cores. Only diatomic molecules are considered. The method is based on a two-electron RRR-matrix approach inside a sphere centered on one of the atoms. The wave function is then connected to a Coulomb region outside the sphere via a multichannel version of the Coulomb Green's function. This approach is put into a test by its application to a study of Rydberg states of the hydrogen molecule for internuclear distances RRR from 20 to 400 bohrs and energies corresponding to nnn from 3 to 22. The results are compared with previous quantum chemical calculations (lower quantum numbers nnn) and computations based on contact-potential models (higher quantum numbers nnn).