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Journal of Experimental and Theoretical Physics

Moment coupling in the interaction of atoms and their ions with a 3d-electron shell

A. V. Kosarim, Борис М. Смирнов, M. Capitelli, Annarita Laricchiuta

Published Sep 1, 2011• 0 citations
Publisher

Abstract

The moment coupling of an interacting ion and an atom with a 3 d -electron shell is analyzed for the ground state of identical atoms and ions where resonant charge exchange proceeds with transition of a 4 s -electron. The interaction of the ion charge with the atom quadrupole moment is important for this system along with the exchange interactions and spin-orbit interactions inside an isolated atom and an ion. The quadrupole moment for 3 d -atoms in the ground states is evaluated. The hierarchy of interactions in a molecular ion is analyzed depending on ion-atom distances and is compared with the standard Hund scheme. The resonant charge exchange proceeds effectively at separations corresponding to an intermediate case between cases “a” and “c” of the Hund coupling scheme.

DOI
10.1134/s1063776111070053

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The moment coupling of an interacting ion and an atom with a 3 d -electron shell is analyzed for the ground state of identical atoms and ions where resonant charge exchange proceeds with transition of a 4 s -electron. The interaction of the ion charge with the atom quadrupole moment is important for this system along with the exchange interactions and spin-orbit interactions inside an isolated atom and an ion. The quadrupole moment for 3 d -atoms in the ground states is evaluated. The hierarchy of interactions in a molecular ion is analyzed depending on ion-atom distances and is compared with the standard Hund scheme. The resonant charge exchange proceeds effectively at separations corresponding to an intermediate case between cases “a” and “c” of the Hund coupling scheme.
The quadrupole interaction between the Rydberg electronic states of a Rydberg ion and the radio frequency electric field of the ion trap is analyzed. Such a coupling is negligible for the lowest energy levels of a trapped ion but it is important for a trapped Rydberg ion due to its large electric quadrupole moment. This coupling cannot be neglected by the standard rotating-wave approximation because it is comparable to the frequency of the trapping electric field. We investigate the effect of the quadrupole coupling by performing a suitable effective representation of the Hamiltonian. For a single ion we show that in this effective picture the quadrupole interaction is replaced by rescaled laser intensities and additional Stark shifts of the Rydberg levels. Hence this detrimental quadrupole coupling can be efficiently compensated by an appropriate increase of the Rabi frequencies. Moreover, we consider the strong dipole-dipole interaction between a pair of Rydberg ions in the presence of the quadrupole coupling. In the effective representation we observe reducing of the dipole-dipole coupling as well as additional spin-spin interaction.
The formulation of Bardsley et al (Phys. Rev. A 11 1911) for evaluating the asymptotic electron exchange interaction between an alkali ion and its parent atom is extended by the use of a more accurate representation of the asymptotic wavefunction of the isolated atom and also by the inclusion of a further term in the series that accounts for the presence of the ion. The Bardsley analysis is compared with a purely numerical approach in which the Holstein–Herring integrand is constructed from a polarized wavefunction built from numerical solutions of the differential equations of Rayleigh–Schrodinger perturbation theory and the ¨ required quadrature is performed numerically. Values of the asymptotic exchange interactions are given for the molecular ions Li+ 2 , Na+ 2 , K+ 2 , Rb+ 2 and Cs+ 2 . As an example, exchange interactions for Cs+ 2 evaluated by an ab initio method are compared to those predicted by the Bardsley formula. Potentials for the lowest states of Cs+ 2 are constructed from the ab initio values matched to the asymptotic exchange and long-range polarization interactions, and these potentials are used to predict the 12+ g and 12+ u scattering lengths and low-energy charge transfer cross sections.
We consider a system composed of a trapped atom and a trapped ion. The ion charge induces in the atom an electric dipole moment, which attracts it with an ${r}^{\ensuremath{-}4}$ dependence at large distances. In the regime considered here, the characteristic range of the atom-ion interaction is comparable or larger than the characteristic size of the trapping potential, which excludes the application of the contact pseudopotential. The short-range part of the interaction is described in the framework of quantum-defect theory, by introducing some short-range parameters, which can be related to the sss-wave scattering length. When the separation between traps is changed we observe trap-induced shape resonances between molecular bound states and vibrational states of the external trapping potential. Our analysis is extended to quasi-one-dimensional geometries, when the scattering exhibit confinement-induced resonances, similar to the ones studied before for short-range interactions. For quasi-one-dimensional systems we investigate the effects of coupling between the center of mass and relative motion, which occurs for different trapping frequencies of atom and ion traps. Finally, we show how the two types of resonances can be employed for quantum state control and spectroscopy of atom-ion molecules.
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.
The potential energy curves, permanent and transition dipole moments, and the static dipolar polarizability, of molecular ions composed of one alkali-metal atom and a strontium ion are determined with a quantum chemistry approach. The molecular ions are treated as effective two-electron systems and are treated using effective core potentials including core polarization, large gaussian basis sets, and full configuration interaction. In the perspective of upcoming experiments aiming at merging cold atom and cold ion traps, possible paths for radiative charge exchange, photoassociation of a cold lithium or rubidium atom and a strontium ion are discussed, as well as the formation of stable molecular ions.
Alkaline-earth dimers are now been used, as new grounds for, testing fundamental physics laws, precision measurements and quantum computation. As a starting point for such experiments, one needs a very good knowledge of the electronic structure, energetics and long-range behavior of these molecular ions. We perform accurate ab initio calculations for the ground and low-lying excited states of Be2+, Mg2+, Ca2+ and Sr2+ molecular ions. We have also calculated the spectroscopic constants, electronic transition dipole moments, polarizabilities and long-range dispersion coefficients for the various alkaline-earth ionic dimers. We have extended our calculations to study heteronuclear species of alkaline-earth molecular ions, like BeCa+, and also mixed alkali alkaline-earth species like NaCa+. We calculated photoassociation (PA) pathways for formation of cold molecular ions and also studied corrections to the Born-Oppenheimer Hamiltonian: non-adiabatic couplings and hyperfine structure due to nuclear spins and electric quadrupoles. We believe, this work would lay foundation, not only for new experiments in ultracold physics and chemistry, but would also provide valuable starting point for theoretical calculations involving low temperature scattering and resonant charge transfer.