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Physical Review A

Close-coupling calculations of Ca− formation by charge transfer from Rydberg atoms

I. I. Fabrikant, M. I. Chibisov

Published Jan 14, 2000• 18 citations
Publisher

Abstract

We formulate the semiclassical close-coupling method for a theoretical description of ion-pair formation in Rydberg-atom--ground-state-atom collisions at thermal energies and apply it to the process $\mathrm{Ca}{(4s}^{2})+{\mathrm{Ne}}^{*}(n)\ensuremath{\rightarrow}{\mathrm{Ca}}^{\ensuremath{-}}{(4s}^{2}4p)+{\mathrm{Ne}}^{+}.$ Our results for the formation of an isolated negative-ion state are very close to those obtained previously using the decay model, although the results for S states are somewhat higher, since the decay model underestimates the survival probability for the ion pair. After the inclusion in our close-coupling calculations of the two fine-structure components of ${\mathrm{Ca}}^{\ensuremath{-}},$ we find that the cross section increases substantially (by about a factor of 2) because of correlation between probabilities for population of two fine-structure sublevels.

DOI
10.1103/physreva.61.022718

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Journal of Experimental and Theoretical Physics•Oct 1, 2013•6 citations
We formulate the semiclassical close-coupling method for a theoretical description of ion-pair formation in Rydberg-atom--ground-state-atom collisions at thermal energies and apply it to the process Ca(4s2)+Ne∗(n)\ensuremath→Ca\ensuremath−(4s24p)+Ne+.\mathrm{Ca}{(4s}^{2})+{\mathrm{Ne}}^{*}(n)\ensuremath{\rightarrow}{\mathrm{Ca}}^{\ensuremath{-}}{(4s}^{2}4p)+{\mathrm{Ne}}^{+}.Ca(4s2)+Ne∗(n)\ensuremath→Ca\ensuremath−(4s24p)+Ne+. Our results for the formation of an isolated negative-ion state are very close to those obtained previously using the decay model, although the results for S states are somewhat higher, since the decay model underestimates the survival probability for the ion pair. After the inclusion in our close-coupling calculations of the two fine-structure components of Ca\ensuremath−,{\mathrm{Ca}}^{\ensuremath{-}},Ca\ensuremath−, we find that the cross section increases substantially (by about a factor of 2) because of correlation between probabilities for population of two fine-structure sublevels.
A simple model potential for the electron-Ca-atom interaction is used to describe the process of charge transfer in Rydberg-atom-calcium-atom collisions. The interaction of the final ionic state with degenerate manifolds of Rydberg covalent states is treated by inclusion of the negative ion decay due to the Coulomb field of the positive ion. This effect leads to a strong reduction of the charge transfer cross section and shifting of the value of the principal quantum number n corresponding to the cross section maximum towards higher n . The rates averaged over the experimental velocity distribution agree quite well with the experimental data and with independent calculations using the Landau-Zener model, although the results of the latter are higher than the present for the charge transfer from s states. The distortion of the classical ion trajectories due to the Coulomb interaction plays a minor role in the calculation of the negative-ion decay probability.
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.
We develop the distorted-wave and adiabatic theories of the ion-pair formation in collisions of a Rydberg atom A∗∗{\mathit{A}}^{\mathrm{*}\mathrm{*}}A∗∗ with a ground-state atom B at thermal collision velocities. The e-B interaction is modeled by a zero-range potential. Both theories give results that are in qualitative agreement with the standard Landau-Zener model, although their prediction for m-changing transitions is different, where m is the projection of the angular momentum. To incorporate these transitions into the adiabatic theory, we take into account the rotation of the internuclear axis before and after a nonadiabatic transition. The m-averaged cross sections are substantially higher than those following from the standard Landau-Zener model, and the distorted-wave results are slightly higher than the adiabatic results with the internuclear-axis rotation taken into account. We apply our results to a description of the McLaughlin and Duquette experiment on Ca+{\mathrm{Ca}}^{+}Ca+-${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$ pair formation. The calculated n dependence of the rate for the ion-pair formation is too flat as compared to the experimental observations and does not agree with known values of the electron affinity of Ca. We discuss other possible mechanisms responsible for the ion-pair formation in this process. \textcopyright{} 1996 The American Physical Society.
Electron-transfer processes are studied in thermal collisions of Rydberg atoms with alkaline-earth Ca(4s 2), Sr(5s 2), and Ba(6s 2) atoms capable of forming negative ions with a weakly bound outermost p-electron. We consider the ion-pair formation and resonant quenching of highly excited atomic states caused by transitions between Rydberg covalent and ionic terms of a quasi-molecule produced in collisions of particles. The contributions of these reaction channels to the total depopulation cross section of Rydberg states of Rb(nl) and Ne(nl) atoms as functions of the principal quantum number n are compared for selectively excited nl-levels with l ≪ n and for states with large orbital quantum numbers l = n − 1, n − 2. It is shown that the contribution from resonant quenching dominates at small values of n, and the ion-pair formation process begins to dominate with increasing n. The values and positions of the maxima of cross sections for both processes strongly depend on the electron affinity of an alkaline-earth atom and on the orbital angular momentum l of a highly excited atom. It is shown that in the case of Rydberg atoms in states with large l ∼ n − 1, the rate constants of ion-pair formation and collisional quenching are considerably lower than those for nl-levels with l ≪ n.
Using crossed atomic beams and mass spectrometric ion detection we have studied the formation of negative Ca ions in slow collisions between laser-excited state-selected Ne** ( ns , J = 2) and Ne** ( nd , J = 4) Rydberg atoms and ground state Ca atoms. The rate coefficients exhibit resonant behaviour with maxima at an effective principal quantum number n * of about 11.5 and an estimated peak value of about 10 −8 cm 3 s −1 . Two different theoretical calculations, based on a curve-crossing model and on a modified adiabatic theory, respectively, yield n *-dependences of the rate coefficients in good agreement with the experimental results.
Ion-pair formation processes are studied in collisions of Rydberg atoms with neutral particles possessing small electron affinities. Nonadiabatic transitions from a Rydberg covalent term to an ionic term of a quasi-molecule are considered using the modified Landau-Zener theory supplemented with calculation of survival factors of an anion decaying in the Coulomb field of a positive ion core. Using the technique of irreducible tensor operators and the momentum representation of the wavefunction of a highly excited atom, exact expressions are obtained for transition matrix elements and the ionic-covalent coupling parameter. The approach developed in the paper provides the description beyond the scope of a conventional assumption about a small variation of the wavefunction of the Rydberg atom on the range of electron coordinates determined by the characteristic radius of the wavefunction of the anion. This allows one to correctly consider long-range effects of the interaction between a weakly bound electron and the neutral core of a negative ion in processes under study. It is shown by the example of thermal collisions of Xe( nf ) atoms with CH 3 CN molecules that this is very important for a reliable quantitative description of anion formation with a low binding energy. The results are compared with experiments and calculations performed within the framework of a number of approximate methods.