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Physical Review A

Resonances in Ca ++ Rb nonadiabatic collisions at ultralow energies

Andrey K. Belyaev, Svetlana A. Yakovleva, M. Tacconi, Franco Antonio Gianturco

Published Apr 23, 2012• 18 citations
Publisher

Abstract

Nonadiabatic inelastic collision cross sections have been computed at low and ultralow energies, focusing in the present work on the Ca${}^{+}$$(4s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}S)$ + Rb$(5s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}S)$ $\ensuremath{\rightarrow}$ Ca$(4s4p{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}P)$ + Rb${}^{+}{(}^{1}\phantom{\rule{-0.16em}{0ex}}S)$ charge-exchange process at ultralow collision energies ($E$ $\ensuremath{\leqslant}$ 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.

DOI
10.1103/physreva.85.042716

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Nonadiabatic inelastic collision cross sections have been computed at low and ultralow energies, focusing in the present work on the Ca{}^{+}$$(4s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}S) + Rb(5s2S)(5s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}S)(5s2S) \ensuremath→\ensuremath{\rightarrow}\ensuremath→ 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⩽\ensuremath{\leqslant}\ensuremath⩽ 10\ensuremath−6{}^{\ensuremath{-}6}\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{}^{\ensuremath{-}6}\ensuremath−6 to 10\ensuremath−8{}^{\ensuremath{-}8}\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.
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.
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.
Cold chemical reactions between laser-cooled Ca^+ ions and Rb atoms were studied in an ion-atom hybrid trap. Reaction rate constants were determined in the range of collision energies /k_B = 20 mK-20 K. The lowest energies were achieved in experiments using single localized Ca^+ ions. Product branching ratios were studied using resonant-excitation mass spectrometry. The dynamics of the reactive processes in this system (non-radiative and radiative charge transfer as well as radiative association leading to the formation of CaRb^+ molecular ions) have been analyzed using high-level quantum-chemical calculations of the potential energy curves of CaRb^+ and quantum-scattering calculations for the radiative channels. For the present low-energy scattering experiments, it is shown that the energy dependence of the reaction rate constants is governed by long-range interactions in line with the classical Langevin model, but their magnitude is determined by short-range non-adiabatic and radiative couplings which only weakly depend on the asymptotic energy. The quantum character of the collisions is predicted to manifest itself in the occurrence of narrow shape resonances at well-defined collision energies. The present results highlight both universal and system-specific phenomena in cold ion-neutral reactive collisions.
We show that the cross sections for a broad range of resonant inelastic processes accompanied by excitation exchange (such as spin exchange, F\"orster resonance, or angular momentum exchange) exhibit a near-threshold scaling ${E}^{\mathrm{\ensuremath{\Delta}}{m}_{12}}$, where EEE is the collision energy, $\mathrm{\ensuremath{\Delta}}{m}_{12}={m}_{1}^{\ensuremath{'}}+{m}_{2}^{\ensuremath{'}}\ensuremath{-}{m}_{1}\ensuremath{-}{m}_{2}$, and mi{m}_{i}mi​ and ${m}_{i}^{\ensuremath{'}}$ are the initial and final angular momentum projections of the colliding species (i=1,2i=1,2i=1,2). In particular, the inelastic cross sections for $\mathrm{\ensuremath{\Delta}}{m}_{12}=0$ transitions display an unconventional E0{E}^{0}E0 scaling similar to that of elastic cross sections, and their rates vanish as ${T}^{\mathrm{\ensuremath{\Delta}}{m}_{12}+1/2}$. For collisions dominated by even partial waves (such as those of identical bosons in the same internal state) the scaling is modified to ${\ensuremath{\sigma}}_{\text{inel}}\ensuremath{\propto}{E}^{\mathrm{\ensuremath{\Delta}}{m}_{12}+1}$ if $\mathrm{\ensuremath{\Delta}}{m}_{12}$ is odd. We present accurate quantum scattering calculations that illustrate these modified threshold laws for resonant spin exchange in ultracold Rb+Rb\text{Rb}+\text{Rb}Rb+Rb and O2+O2{\mathrm{O}}_{2}+{\mathrm{O}}_{2}O2​+O2​ collisions. Our results illustrate that the well-known ${k}^{\ensuremath{-}1}$ threshold scaling of inelastic cross sections only applies to exothermic, rather than resonant, inelastic processes.
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.
Symmetric resonant charge transfer (RCT) in H+{\mathrm{H}}^{+}H++H and He2+{\mathrm{He}}^{2+}He2++He collisions has been investigated in the ultralow-collision-energy range ${10}^{\mathrm{\ensuremath{-}}3}$--${10}^{\mathrm{\ensuremath{-}}7}$ eV. The RCT cross section has been computed by partial-wave expansion in the molecular-orbital expansion method within the fully quantum-mechanical formalism. The calculated RCT cross sections become constant below E\ensuremath{\simeq}${10}^{\mathrm{\ensuremath{-}}6}$ eV, corresponding to a scattering length of \ensuremath{\sim}6a0{a}_{0}a0​ and \ensuremath{\sim}2a0{a}_{0}a0​ for H2{\mathrm{H}}_{2}H2​+{\mathrm{}}^{+}+ and He2{\mathrm{He}}_{2}He2​2+{\mathrm{}}^{2+}2+, respectively.