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Physical Chemistry Chemical Physics

Computing charge-exchange cross sections for Ca+ collisions with Rb at low and ultralow energies

M. Tacconi, Franco Antonio Gianturco, Andrey K. Belyaev

Published Jan 1, 2011• 35 citations
Publisher

Abstract

Collisions between Ca cations and Rb atoms are computed within a quantum approach that generates the most relevant potential energy curves from accurate ab initio methods and carries out the low-energy scattering calculations by including nonadiabatic and spin-orbit coupling terms. The cross sections are obtained at relative energies typical for the likely arrangements of Rb atoms in a Magneto-Optical Trap overlapped with a Coulomb Crystal of Ca cations. The dominant nonadiabatic process is clearly identified and the efficiency of the nonadiabatic coupling terms which lead to the charge-exchange process is discussed.

DOI
10.1039/c1cp20916g

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Collisions between Ca cations and Rb atoms are computed within a quantum approach that generates the most relevant potential energy curves from accurate ab initio methods and carries out the low-energy scattering calculations by including nonadiabatic and spin-orbit coupling terms. The cross sections are obtained at relative energies typical for the likely arrangements of Rb atoms in a Magneto-Optical Trap overlapped with a Coulomb Crystal of Ca cations. The dominant nonadiabatic process is clearly identified and the efficiency of the nonadiabatic coupling terms which lead to the charge-exchange process is discussed.
Low-energy collisions of the Ca and Yb cations with Rb atoms are investigated theoretically using accurate ab initio potential energy curves and coupling matrix elements to elucidate the dominant charge transfer mechanisms. The cross sections calculated at collision energies above 10 −5 cm −1 exhibit the features typical to Langevin ion-atom collision regime, including a rich structure associated with the centrifugal barrier tunnelling (orbiting) resonances. It is shown that the dominant process in Yb + + Rb collisions is the radiative charge transfer, while in the case of Ca + + Rb collisions nonadiabatic transitions due to spin-orbit coupling dominate. Theoretical results are in a good agreement with available experimental data.
Nonadiabatic inelastic collision cross sections have been computed at low and ultralow energies, focusing in the present work on the Ca+{}^{+}+(4s2S)(4s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}S)(4s2S) + Rb(5s2S)(5s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}S)(5s2S) $\ensuremath{\rightarrow}$ Ca(4s4p3P)(4s4p{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}P)(4s4p3P) + Rb+(1S){}^{+}{(}^{1}\phantom{\rule{-0.16em}{0ex}}S)+(1S) charge-exchange process at ultralow collision energies (EEE $\ensuremath{\leqslant}$ 10${}^{\ensuremath{-}6}$ eV) induced by spin-orbit nonadiabatic coupling terms. The calculations reveal a wealth of sharp resonances which can substantially enhance charge-exchange probabilities over a specific energy window of around 10${}^{\ensuremath{-}6}$ to 10${}^{\ensuremath{-}8}$ eV. Such resonances are analyzed in detail, and the corresponding molecular mechanism is discussed for a specific example, where the nonadiabatic transition probabilities are seen to increase by nearly 2 orders of magnitude.
Charge-transfer cold Yb+{}^{+}++++ Rb collision dynamics is investigated theoretically using high-level ab initio potential energy curves, dipole moment functions, and nonadiabatic coupling matrix elements. Within the scalar-relativistic approximation, the radiative transitions from the entrance $A{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ to the ground $X{\phantom{\rule{0.16em}{0ex}}}^{1}{\ensuremath{\Sigma}}^{+}$ state are found to be the only efficient charge-transfer pathway. The spin-orbit coupling does not open other efficient pathways, but alters the potential energy curves and the transition dipole moment for the $A\ensuremath{-}X$ pair of states. The radiative, as well as the nonradiative, charge-transfer cross sections calculated within the ${10}^{\ensuremath{-}3}--10$ cm${}^{\ensuremath{-}1}$ collision energy range exhibit all features of the Langevin ion-atom collision regime, including a rich structure associated with centrifugal barrier tunneling (orbiting) resonances. Theoretical rate coefficients for two Yb isotopes agree well with those measured by immersing Yb+{}^{+}+ ions in an ultracold Rb ensemble in a hybrid trap. Possible origins of discrepancy in the product distributions and relations to previously studied similar processes are discussed.
The nonradiative charge-transfer processes in Na+{}^{+}++87{}^{87}87Rb(5sss) collisions have been investigated by using the quantum-mechanical molecular-orbital close-coupling method and the two-center atomic-orbital close-coupling method for the energy range of 10${}^{\ensuremath{-}4}$--5 and 0.3--100 keV/u, respectively. The radiative charge-transfer, radiative-decay, and radiative-association processes have been investigated by using the fully quantum, optical-potential, and semiclassical methods for the energy range of 10${}^{\ensuremath{-}18}$--0.2 eV/u. The nonradiative charge-transfer processes dominate the collisions for energies above 0.2 eV/u and radiative-decay processes dominate in the lower-energy region. At the very low collision energies of 10${}^{\ensuremath{-}18}$--10${}^{\ensuremath{-}3}$ eV/u, the radiative-association process is more important than the radiative charge-transfer process. Most importantly, it is found that the radiative cross sections exhibit Langevin behavior as ${E}^{\ensuremath{-}1/2}$ for energies less than 10${}^{\ensuremath{-}2}$ eV/u.
The ratio of the charge exchange cross sections for Ba + (5d) and Ba + (6s) on Na, Rb and Cs, for Sr + (4d) and Sr + (5s) on Na and Rb, and for Ca + (3d) and Ca - (4s) on Na have been measured for ion impact energies between 0.5 keV and 30 keV. For the collisions with Na, absolute charge exchange cross section values are derived using data for the resonant process Na+Na + as a reference. The results are compared to theoretical near-resonance predictions. A method is proposed to study the polarization dependence of the neutralization cross sections for reactions involving ionic D states.