Charge Transfer Cross Sections Research Articles

Elastic and inelastic processes inH++C2H6collisions below the10−keVregime

Charge-transfer processes in collisions of ${\mathrm{H}}^{+}$ ions with ${\mathrm{C}}_{2}{\mathrm{H}}_{6}$ molecules are investigated theoretically below $10\text{\ensuremath{-}}\mathrm{keV}$ collision energies within a molecular representation. Converged total as well as differential cross sections are obtained in this energy range within a discrete basis of electronic states computed by ab inito methods. The present collision system suggests that the combination of the Demkov-type and Landau-Zener--type mechanisms primarily governs the scattering dynamics for the flux exit from the initial channel. The present charge-transfer cross sections determined are found to agree very well with all available experimental data below a few keV, but begin to deviate above $3\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$, in which the present results slowly decrease, while measurements stay nearly constant. From the study of the electronic state calculation, we provide some information on fragmented species, which should help shed some light on the fragmentation mechanism and process of ${\mathrm{C}}_{2}{\mathrm{H}}_{6}^{+}$ ions produced after charge transfer. In addition, the vibrational effect of the initial target to charge transfer is examined.

Alignment effects in charge transfer and excitation forH+andHe2+collisions withH2+

The study of ion-atom collisions has a long history for both experimental and theoretical techniques. There has been much less effort for ion-molecule collisions. Computationally, the ion-molecule collisions are much more difficult than ion-atom collisions. This is partly due to the multicenter nature of the problem instead of the two centers for ion-atom collisions. Perhaps more importantly, the cross sections may depend on several other coordinates. Thus, there is a dramatic increase in the number of calculations needed to explore the physically relevant parameters. There is also the possibility that interference due to the extended size of the electron orbitals will cause the results to depend sensitively on the accuracy of the calculation. Finally, molecules have a larger number of low-lying excited states compared to similar atoms which may sensitively affect the outcome of collisions. To see where some of the difficulties lie, we examine what is needed for ions scattering from a diatomic molecule that has no initial angular momentum about the internuclear axis. We simplify the picture further by assuming the ion may be treated as a classical particle traveling in a straight line and the nuclei in the molecule may be treated as fixed in space during the collision. In the comparable case for ionatom collisions, one only needs to calculate the probability for a process as a function of the impact parameter. For the ion-molecule collision, the probability for a process needs to be calculated as a function of the impact parameter in a plane i.e., two dimensions, as a function of the separation of the nuclei, and as a function of the angle between the ion’s velocity and the internuclear axis. Thus, we have gone from one parameter to four; assuming we need 5–10 examples of each parameter for an adequate exploration of ion-molecule collision we find there are approximately 100–1000 times more trajectories that are needed for ion-molecule calculations than for a comparable ion-atom calculation. The simplest ion-molecule system is when there is only one electron present. References 1,2 studied the collision of He 2+ with the D 2 + molecular ion. Reference 1 measured the total charge transfer cross section and compared the results to calculations using a model for the electronic orbital for the molecule. The model used a linear combination of atomic orbitals and the transition amplitudes are approximated as a linear superposition of the amplitudes for each atomic orbital 3. The calculated and measured total charge transfer cross sections were in good agreement. Reference 2 measured the dependence of the total charge transfer cross section on the angle between the velocity of the atomic ion and the internuclear axis and compared the measurement to the results of a model calculation again based on Ref. 3. Although the agreement was not as good, the general trends were the same: the cross section is much larger for perpendicular geometry than when the velocity is parallel to the internuclear axis. At velocity 0.4 a.u., the measurement gives a cross section 3–4 times larger at 90° than at 0° while the calculation gives a factor of 7–8. At velocity 0.5 a.u., the measurement gives a cross section 3–6 times larger at 90° compared to 1.5–2 for the calculation. Reference 4 presents calculations for total charge transfer for this system using both classical methods and a 2+1 -center close-coupling approximation. The total charge transfer cross section was 20–30 % lower than the previous measurement and calculation. In this paper, we present the results of calculations for charge transfer from the H 2 + molecular ion to He 2+ ions and to H + ions. Because the protons of the molecular ion are fixed during the collision, our results apply equally well to D2 + . The focus of this paper is the dependence of the cross section on the angle between the ion’s velocity vector and the internuclear axis and the dependence on the internuclear separation. Our method of calculation consists of direct numerical solution of Schrodinger’s equation on a grid of points; grid methods can be thought of as a basis set method with the number of basis functions equal to the number of grid points 10 7 in our case but with a momentum cutoff roughly equal to the inverse of the separation of grid points.

Relative charge transfer cross section fromRb(4d)

Relative charge transfer cross section measurements for the excited state Rb(4d) with 7 keV Na{sup +} is reported. The specific channels reported are Na{sup +}+Rb(4d{sub 5/2}){yields}Na(nl)+Rb{sup +}, where the dominant transfer cross sections channels were nl=3d and 4s. Using a combination of a magneto-optical trap and recoil ion momentum spectroscopy (MOTRIMS methodology), the cross sections were measured relative to the previously studied Na{sup +}+Rb(5s,5p) systems at the same collision energy.

Electron transfer collisions between isolated fullerene dianions and SF6

Electron transfer collisions of trapped doubly charged fullerene anions C76(2-), C(78)2-, and C84(2-) with SF6 are studied in a Fourier transform ion cyclotron resonance mass spectrometer at center-of-mass collisional energies ranging from thermal energy to 77 eV. Collision energy dependencies manifest threshold energies for (nominally exoergic) single electron transfer onto SF6 of 1.46+/-0.3 eV, 1.56+/-0.3 eV, and 1.63+/-0.3 eV for C(76)2-, C78(2-), and C(84)2-, respectively. Kinetics studies reveal charge-transfer cross sections of up to 430+/-200 A2 for C84(2-) at a collision energy of 77 eV. The mechanism and the energetics are discussed in terms of classical electrostatic model calculations. Additionally, we rationalize the collision energy dependencies of the charge-transfer cross sections using the two-state Landau-Zener formalism to describe the associated resonant electron tunneling probability.

Charge transfer in slow collisions ofC6+with H below1keV∕amu

We reexamine the charge transfer cross sections for ${\mathrm{C}}^{6+}+\mathrm{H}$ collisions for energies below $1\phantom{\rule{0.3em}{0ex}}\mathrm{keV}∕\mathrm{amu}$ using a fully quantum mechanical approach, based on the hyperspherical close-coupling method. Whereas most previous theoretical and experimental data agree well for the dominant charge transfer to the ${\mathrm{C}}^{5+}(n=4)$ states, there is significant disagreement among the theories for the transition to the weaker $n=5$ states. Using the present quantum mechanical calculations we analyze the origin of the discrepancy among these previous calculations. We further extend the calculations to collision energies down to about 1 eV and show that electron capture to the $n=5$ states begins to dominate over the $n=4$ states.

Entropy lowering in ion-atom collisions

In ion-atom collisions, the charge transfer cross section is typically a strong function of the energy defect or $Q$ value, typically with smaller energy defects giving rise to higher capture probabilities. In some theoretical treatments, for example those based on the Demkov model, the cross section is a strong function of the magnitude of the $Q$ value, but is independent of its sign. In order to test this predicted sign independence, one must compare capture cross sections from energetically symmetric collision channels. In this work, relative capture cross sections, differential in scattering angle, are measured and compared for the energetically symmetric channels: ${\mathrm{Rb}}^{+}+\mathrm{Rb}(5s)\ensuremath{\rightarrow}\mathrm{Rb}(5p)+{\mathrm{Rb}}^{+}$ and ${\mathrm{Rb}}^{+}+\mathrm{Rb}(5p)\ensuremath{\rightarrow}\mathrm{Rb}(5s)+{\mathrm{Rb}}^{+}$. It is found that not only are the two cross sections not equal, but that in this case the endoergic channel was 3 times more likely. That is, the entropy reducing channel was preferred. An intuitive model, based on molecular potential curves, is suggested. The endoergic propensity is found to be consistent with this model.

Charge transfer in Li2+ + He2+ and Li2+ + Li3+ collisions

True one-electron collision systems provide an ideal testing ground for theory. Absolute cross sections for charge transfer in the collision systems Li2+ + He2+ and Li2+ + Li3+ have been measured for centre-of-mass energies between 52 and 148 keV and 6 and 63 keV, respectively. The data are compared with calculations using the two-centre basis generator method. A fair agreement between the experimental data and the calculations is found.

Semi-classical approaches to the ion–atom scattering

Three semi-classical approaches to the simulation of ion–atom scattering: the Kirschbaum–Wilets, the Cohen energy-bounded, and the wave-packet – are used to calculate the ionization and charge-transfer cross sections for the scattering of fully stripped sulfur ions on atomic hydrogen. Their comparison in the high-energy regime is provided. Elements of microscopic analysis of Kirschbaum–Wilets trajectories are given.

Charge transfer in low-energy collisions ofHe2+with atomic hydrogen

Using the Oak Ridge National Laboratory ion-atom merged-beams apparatus, absolute total charge-transfer cross sections have been measured for collisions of He{sup 2+}+H over a range of energies from 380 to 2620 eV/u. The experimental results are compared to previous measurements using different experimental techniques. A hidden-crossing coupled-channel (HCCC) calculation is performed in the collision energy range of 10 to 3000 eV/u and is compared with the measured data as well as with other theories. The HCCC calculation, which is deemed accurate below 1000 eV/u, is also used to determine differential cross sections. The resultant angular scattering information is used to correct the merged-beams data, which is characterized by a large but limited angular acceptance at these collision energies. Our combined experimental and theoretical study provides an improved benchmark for this fundamental system.

Charge transfer in the collision system He2+ + C 60 + : Theory and experiment

Fullerenes are a direct link between atoms with discrete electronic energy levels and solids with a band structure and a well-defined surface. In this paper, we report on a quantum mechanical treatment of charge transfer and ionization in the ion-ion collision system 3He2+ + C60+. This approach considers under- and over-barrier transitions through the one-dimensional barrier between the collision partners. The calculated cross sections for charge transfer compare favorably with experimental data measured in the center-of-mass energy range from 27 to 196 keV employing the crossed beams technique.

Resonant charge transfer between H+ and H from 1 to 5000 eV

We employ the electron–nuclear dynamics (END) formalism to investigate the resonant charge transfer and scattering processes in the collision of protons on atomic hydrogen as an introduction to investigations of resonant charge transfer in larger atomic and molecular systems. The END method consists of an ab initio, non-adiabatic treatment of the electronic and nuclear degrees of freedom. The results span an energy range from 1 eV to 5 keV. We present electron transfer probabilities, absolute charge transfer differential and integral cross sections, and state-to-state differential cross sections for principal energy levels n = 1 and 2. The present results compare favourably with experimental data and other theoretical results. For the total resonant charge transfer cross section, we confirm the relation σ1/2trans ∼ ln E. The role of non-adiabatic couplings in transfer into the n = 2 level is confirmed, and the effect of basis set size on the dynamics of the transfer is probed.

Theoretical study of charge-exchange and excitation processes in collisions of He+ ions with C5+, N6+, and O7+ hydrogen-like ions

Data on the cross sections for single-electron charge exchange and excitation in collisions of He+ ions with C5+, N6+, and O7+ ions in the He+ ion energy range of 0.2–3.0 MeV are obtained for the first time. The cross sections for the single-electron charge transfer into the singlet and triplet 1snl states of C4+, N5+, and O6+ (2≤n≤5) ions and for the 1s → 2p 0, ±1 electronic excitation of He+(1s) ions are calculated. The calculations were performed by solving close-coupling equations on the basis of ten two-electron quasi-molecular states.

Classical and semiclassical calculations of electron transfer cross sections inkeV-energy ion-molecule collisions

We apply a many-body classical model and a semiclassical coupled-channel approach to study the electronic processes occurring in the course of fast collisions between atomic and molecular species. The methods are applied in a comparative study of electron transfer in ${\mathrm{He}}^{2+}∕{\mathrm{Ar}}^{2+}\ensuremath{-}\mathrm{H}_{2}{}^{+}$ collisions at $\mathrm{keV}\phantom{\rule{0.3em}{0ex}}{\mathrm{u}}^{\ensuremath{-}1}$ impact energies. The classical calculations are in agreement with recent experimental data [H. Br\auning et al., J. Phys. B 34, L321 (2001)] for projectile velocities larger than the initial electron velocity. The semiclassical model is based on the sudden approximation where the electronic wave function is expressed by linear combinations of traveling atomic capture states and target molecular states obtained at fixed nuclei. The related charge transfer cross sections are slightly underestimated (overestimated) for ${\mathrm{He}}^{2+}$ $({\mathrm{Ar}}^{2+})$ when considering $\mathrm{H}_{2}{}^{+}$ in its initial vibrational ground state. These cross sections do, however, depend strongly on the internuclear distance of the hydrogen molecular ion: when involving an initial vibrational excitation of the target, the averaged cross sections obtained from the semiclassical approach become in fair agreement with experiments.

Differential charge-transfer cross sections for systems with energetically degenerate or near-degenerate channels

Resolution plays a vital role in spectroscopic studies. In the usual recoil-ion momentum spectroscopy (RIMS), Q-value resolution is relied upon to distinguish between different collision channels: The better the Q-value resolution, the better one is able to resolve energetically similar channels. Although traditional COLTRIMS greatly improves Q-value resolution by cooling the target and thus greatly reducing the initial target momentum spread, the resolution of the technique is still limited by target temperature. However, with the recent development in RIMS, namely, magneto-optical trap recoil ion momentum spectroscopy (MOTRIMS) superior recoil ion momentum resolution as well as charge transfer measurements with laser excited targets have become possible. Through MOTRIMS, methods for the measurements of target excited state fraction and kinematically complete relative charge transfer cross sections have been developed, even for some systems having energetically degenerate or nearly degenerate channels. In the present work, the systems of interest having energy degeneracies or near degeneracies are ${\mathrm{Rb}}^{+}$, ${\mathrm{K}}^{+}$, and ${\mathrm{Li}}^{+}$ colliding with trapped $\mathrm{Rb}(5l)$, where $l=s$ and $p$.

Experimental and theoretical studies of charge transfer and deuterium ion transfer between D2O+ and C2H4.

The charge transfer and deuterium ion transfer reactions between D(2)O(+) and C(2)H(4) have been studied using the crossed beam technique at relative collision energies below one electron volt and by density functional theory (DFT) calculations. Both direct and rearrangement charge transfer processes are observed, forming C(2)H(4) (+) and C(2)H(3)D(+), respectively. Independent of collision energy, deuterium ion transfer accounts for approximately 20% of the reactive collisions. Between 22 and 36 % of charge transfer collisions occur with rearrangement. In both charge transfer processes, comparison of the internal energy distributions of products with the photoelectron spectrum of C(2)H(4) shows that Franck-Condon factors determine energy disposal in these channels. DFT calculations provide evidence for transient intermediates that undergo H/D migration with rearrangement, but with minimal modification of the product energy distributions determined by long range electron transfer. The cross section for charge transfer with rearrangement is approximately 10(3) larger than predicted from the Rice-Ramsperger-Kassel-Marcus isomerization rate in transient complexes, suggesting a nonstatistical mechanism for H/D exchange. DFT calculations suggest that reactive trajectories for deuterium ion transfer follow a pathway in which a deuterium atom from D(2)O(+) approaches the pi-cloud of ethylene along the perpendicular bisector of the C-C bond. The product kinetic energy distributions exhibit structure consistent with vibrational motion of the D-atom in the bridged C(2)H(4)D(+) product perpendicular to the C-C bond. The reaction quantitatively transforms the reaction exothermicity into internal excitation of the products, consistent with mixed energy release in which the deuterium ion is transferred in a configuration in which both the breaking and the forming bonds are extended.

Charge transfer in slow collisions ofO8+andAr8+ions withH(1s)below2keV∕amu

We calculated the charge-transfer cross sections for ${\mathrm{O}}^{8+}+\mathrm{H}$ collisions for energies from $1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{amu}$ to $2\phantom{\rule{0.3em}{0ex}}\mathrm{keV}∕\mathrm{amu}$, using the recently developed hyperspherical close-coupling method. In particular, the discrepancy for electron capture to the $n=6$ states of ${\mathrm{O}}^{7+}$ from the previous theoretical calculations is further analyzed. Our results indicate that at low energies (below $100\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{amu}$) electron capture to the $n=6$ manifold of ${\mathrm{O}}^{7+}$ becomes dominant. The present results are used to resolve the long-standing discrepancies from the different elaborate semiclassical calculations near $100\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{amu}$. We have also performed the semiclassical atomic orbital close-coupling calculations with straight-line trajectories. We found the semiclassical calculations agree with the quantal approach at energy above $100\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{amu}$, where the collision occurs at large impact parameters. Calculations for ${\mathrm{Ar}}^{8+}+\mathrm{H}$ collisions in the same energy range have also been carried out to analyze the effect of the ionic core on the subshell cross sections. By using diabatic molecular basis functions, we show that converged results can be obtained with small numbers of channels.

Double electron capture cross-sections of the ground state in the collisions of He$^\mathsf{2 + }$ and Li$^\mathsf{3 + }$ with He

We investigate the problem of the double charge transfer cross-section of a helium atom by bare ions of helium and lithium at energies ranging from 60 to 200 keV/amu. The boundary corrected continuum intermediate state approximation (BCCIS) is used to calculate the capture cross-section in the ground state. The continuum state of each electron has been accounted for in the formalism. The present results are compared with existing theoretical and experimental results.

Comparison of hyperspherical versus common-reaction-coordinate close-coupling methods for ion-atom collisions at low energies

We present detailed comparisons between the two quantal approaches---hyperspherical close-coupling and common-reaction-coordinate close-coupling methods---on an exemplary case of ${\text{He}}^{2+}+\mathrm{H}(1s)$ collisions at center-of-mass energy from $20\phantom{\rule{0.3em}{0ex}}\text{eV}$ up to $1.6\phantom{\rule{0.3em}{0ex}}\text{keV}$. It is shown that the partial-wave charge-transfer cross sections from the two approaches agree very well at low energy below $200\phantom{\rule{0.3em}{0ex}}\text{eV}$ down to $30\phantom{\rule{0.3em}{0ex}}\text{eV}$. This good agreement is a strong indication of the validity of both methods. The small difference at very low energies and the convergence with respect to the number of channels in both approaches at higher energies are also discussed.

Charge transfer in slow collisions ofC4+with H below 1 keV/amu

We reexamined charge-transfer cross sections for ${\mathrm{C}}^{4+}+\mathrm{H}$ collisions for energies from 1 meV/amu to 1 keV/amu using the recently developed hyperspherical close-coupling method. Our results agree with several previous theoretical calculations using molecular-orbital expansion. However, these converged theoretical predictions do not agree with total cross sections from the merged-beam experiments.

Modeling of low-altitude quasi-trapped proton fluxes at the equatorial inner magnetosphere

A secondary proton radiation belt can be observed in the equatorial region between the upper atmosphere and the interior edge of the main radiation belt. It is thought that the protons appear there in a result of ionization of energetic neutral hydrogen atoms coming from the internal area of the traditional radiation belt where they were born in charge exchange collisions of the trapped protons with the cold hydrogen of the gecorona. The process of formation of this secondary belt is numerically simulated in this paper assuming this charge exchangeireionization mechanism. Standard models of the trapped radiation, of the atmosphere and geocorona were used to simulate the source and the exospheric media. Experimental data were used for charge transfer cross sections. Result of simulation agrees very good with the experimental observation.