Charge Transfer Probability Research Articles

Crossed beam study of He+-O2 charge transfer reactions in the collision energy range 0.5?200 eV

Energy spectra and angular distributions of the O+ and O 2 + product ions resulting from the He+-O2 charge transfer reaction have been measured in the collision energy range 0.5–200 eV using the crossed-beam method. The O 2 + ions represent only a minor fraction of the reaction products (0.2–0.6% over the energy range measured). In the dissociative charge transfer reaction, four main processes are identified leading to O+O+ reaction products in different electronic states. Two different mechanisms can be distinguished, each being responsible for two of the observed processes:(i) a long-distance energy-resonant charge transfer process involving thec4∑ u − (v′=0) state of O 2 + and(ii) a slightly exothermic charge transfer process via the (III)2∏ u state of O 2 + (with the exothermicity depending on the collision energy). Angle-integrated branching ratios and partial cross sections (in absolute units) have been determined. The branching ratios of the individual processes show a pronounced dependence on the collision energy. At low energies, the O+ product ions are preferentially formed in the2P0 and2D0 excited states. The angular distributions of the O+ product ions show an anisotropic behaviour indicating an orientation-dependent charge transfer probability in the He+ −O2 reaction.

Polarization dependence of laser-assisted charge transfer.

The method of expansion of the total state in terms of the products of the atomic eigenstates and photon states is used to study the dependence of laser-assisted charge-transfer probabilities and cross sections upon the polarization of radiation. Calculations are made for electron capture into the ground state of hydrogen in ${\mathrm{H}}^{+}$-He collisions in the presence of radiation polarized perpendicular to the nuclear relative velocity. The results are discussed in the light of earlier work for radiation polarized parallel to the relative velocity.

Charge transfer and excitation processes in p-He collisions studied using a unified atomic-orbital-molecular-orbital matching method.

A comprehensive theoretical study of the charge transfer to hydrogen 1s-italic, 2s-italic, and 2p-italic states and excitation to helium 2 /sup 1/S and 2 /sup 1/P states in p-italic-He collisions in the 1--100 keV energy region is presented. This study is the first demonstration of the application of the recently developed atomic-orbital--molecular-orbital matching procedure to two-electron collision systems. In this method the time-dependent electronic wave function is expanded in terms of traveling atomic orbitals of the two collision centers at large internuclear separation which is matched to the solution in the inner region where it is expanded in terms of molecular orbitals without translation factors. It is shown that the results from the present theoretical method are in good agreement with experimental measurements of (1) total charge-transfer cross sections to 1s-italic, 2s-italic, and 2p-italic states, (2)= charge-transfer probabilities at small impact parameters or large scattering angles, and (3) excitation cross sections to 2 /sup 1/S and 2 /sup 1/P states above 20 keV.

Trajectory investigations of charge transfer reactions of rare gas ions with geometric isomers of dichloroethylene and difluorobenzene

A trajectory calculation is used in conjunction with experimental results to estimate the charge transfer probability functions for the reactions of rare gas ions with dichloroethylene and difluorobenzene isomers. The probability functions are assumed to be exponential functions. It is shown that charge transfer in these systems occurs to a significant extent outside the capture limit.

Correlation effects in ion neutralization scattering with the use of a time-dependent coupled-cluster approach.

We consider the problem of ion neutralization scattering from surfaces. For large kinetic energies, the motion of the ion can be treated classically. The electronic part is assumed to be described by a time-dependent Newns-Anderson Hamiltonian. The ion is supposed to have a closed-shell structure with one empty orbital outside the shell, which can take up, at the most, two electrons from the metal. One can obtain a time-dependent Hartree-Fock (TDHF) solution for this using a procedure suggested earlier. [T. B. Grimley, V. C. Jyothi Bhasu, and K. L. Sebastian, Surf. Sci. 124, 305 (1983)]. We show that this solution is defective in that it predicts that the probability that the ion comes back as a neutral species is always less than 0.5, thus illustrating that one has to include electron correlation in order to describe the process correctly.For this we make use of the time-dependent version of the coupled-cluster approach. In this, one assumes the wave function to have the form exp[${T}_{0}$(t)+${T}_{1}$(t)+${T}_{2}$(t)+. . .]\ensuremath{\Vert}${\ensuremath{\Phi}}_{0}$〉 where \ensuremath{\Vert}${\ensuremath{\Phi}}_{0}$〉 is a Slater determinant and ${T}_{n}$(t) can create n-particle hole excitations in it. We take ${T}_{1}$(t) as a linear combination of all possible single-particle hole-excitation operators while ${T}_{2}$(t) is taken as a linear combination of just those two-particle hole-excitation operators which transfer two electrons to the orbital of the ion from the solid, neglect ${T}_{n}$(t) for n>2, and derive differential equations for the matrix elements of the operators ${T}_{1}$(t) and ${T}_{2}$(t). These differential equations are solved numerically to obtain the wave function at any time t.New theorems which enable us to calculate all the expectation values that arise in our treatment of the problem are presented. Also, we have derived expressions for the excitation spectrum, produced as a result of the collision, by particles which come back as ions and also by those which have taken up one or two electrons from the solid. The method is applied to the scattering of lithium ions from the Ni(100) surface and also from a Ni surface contaminated with alkali atoms. The calculations show that TDHF theory is not a bad approximation if one is concerned just with the approach of the ion to the surface. But, in treating an ion which leaves the surface, TDHF fails. The predicted values of charge-transfer probabilities are considerably different in the two theories. Also, calculation of the excitation spectrum produced as a result of the collision show that the spectra are much broader for a contaminated surface having a lower work function than for the clean surface.

Charge transfer at large scattering angles in the strong-potential Born approximation

The authors have calculated the 1s-1s charge transfer probability for large projectile scattering angles in asymmetric ion-atom collisions, using the strong-potential Born approximation and including the effect of recoil on the projectile states non-perturbatively. A significant angular dependence is found. Numerical results for 1s-1s capture in 0.3-20 MeV proton impact on C and Ne are presented, showing good agreement with recent experimental results.

An exactly solvable Schrodinger equation modelling quasi-resonant ion-atom collisions

Exact solutions to a one-dimensional, time-dependent Schrodinger equation with two colliding delta-function potentials of different strengths are presented. The equation can serve as a model for resonant and quasi-resonant ion-atom collisions. Electrons initially bound to one of the potentials may be transferred to the other potential or to a continuum state and probabilities for these processes are calculated. The model reproduces the damped oscillatory behaviour of the charge-transfer probability seen in quasi-resonant collisions when the collision energy is varied.

Two-state charge-transfer calculation inH+-H2collisions

A molecular two-state model, including translation factors, is used within the "quasidiatomic" approximation to calculate the differential charge-transfer probabilities in ${\mathrm{H}}^{+}$ -${\mathrm{H}}_{2}$ collisions at 3\ifmmode^\circ\else\textdegree\fi{} laboratory scattering angle. The essential features of experiment are reproduced.

Adsorption of ions on semiconductor surfaces. I. Silver and halide ions on silver halides

Interaction potentials of silver and halide ions adsorbed on the surfaces of silver halides crystals are calculated. The adsorption of such ions leads to a redistribution of charges at the interface between the semiconductor and an electrolyte (emulsion) containing such ions. This has important implications for such processes as photography and liquid-junction solar cells. We find that the adsorption of silver and halide ions occurs all over the crystal surface [(100) plane], with a pronounced tendency of Ag+ to be adsorbed onto X− sites, the X− onto Ag+ sites, and both to be adsorbed onto the midpoint site. The adsorption of Ag+ ions is found to be weaker than that of the X− ions, in accordance with experiments. The adsorption of ions when interstitial Ag+ ion and Ag+ vacancy (Frenkel defect) are present close to the surface is also considered. We find that adsorbed X− ions enrich the space-charge layer of the AgX crystal with extra positive charge, shifting the band edges towards a more cathodic potential. The reverse trend is found when Ag+ ions are adsorbed. In a forthcoming publication, we extend the present model to include model of charge transfer processes at these interfaces. From these calculations we obtain some guidelines for the construction of systems with high charge transfer probability. Surprisingly, these guidelines are satisfied by most photoelectrochemical cells as well as by other systems.

Simple heuristic derivation of some charge-transfer probabilities at asymptotically high incident velocities

For asymptotically high incident velocities we provide simple, heuristic, almost classical, derivations of the cross section for forward charge transfer, and of the ratio of the cross section for capture to the elastic-scattering cross section for the projectile scattered through an angle close to $\frac{\ensuremath{\pi}}{3}$.

Semiclassical investigation of vibrational state and molecular orientation effects in electron transfer reactions for the H+2/H2 collision

An accurate interaction potential is used in the semiclassical energy conserving trajectory formulation to investigate electron transfer reactions in the H+2/H2 collision for initial ion vibrational states 0≤ν′0 ≤5. The state-to-state cross sections are calculated at several initial molecular orientations and ion kinetic energies. The relative total charge transfer cross sections as a function of ν0 are in good agreement with experimental data. At the state-to-state level, the cross section for the resonant channel at low energies (16 and 32 eV) contributes more than 75% of the total charge transfer cross section at ν′0 =0, but decreases with ν0 to less than 50% at ν′0 =5. At high energies (400 and 800 eV) the cross section of many off-resonant channels are as large as that of the resonant channel. These detailed state-to-state results depend on the initial molecular orientations. We also show the charge transfer probabilities as a function of impact parameter. The oscillatory variation suggests the number of electron jumps between two colliding ion cores.

Computation of charge transfer probability between protons and excited hydrogen atoms

Computation of charge transfer probability between protons and excited hydrogen atoms

Orbiting charge-transfer cross sections betweenHe+ions and cesium atoms at near-thermal ion-atom energies

The energy dependence of the total charge-transfer cross section for the collision of helium ions with cesium atoms at epithermal energies (0.1 to 1 eV) has been measured. It was observed that the cross section increases with E/sup -1/2/. This can be attributed to orbiting collisions. The charge-transfer cross section is expressed as the product of the classical orbiting cross section and a quantum-mechanical charge-transfer probability which is shown to be energy independent.

Charge transfer at surfaces: A model for ionization in SIMS

A microscopic model is presented to describe the probability of charge transfer for the desorption of ions from surfaces. Results from this model study provide a theoretical basis for understanding the ionization process in SIMS and ESD experiments. Predictions of the model that have a direct bearing on the interpretation of experimental data are emphasized in this study. We examine the effect of angle of ejection, both polar and azimuthal, and the nonconstant velocity during desorption due to a surface binding energy on the ionization probability.

Theory of charge transfer for desorption of ions from surfaces

A microscopic model is presented to describe the probability of charge transfer for the desorption of ions from surfaces. The model explicitly incorporates the electronic structure of the system by including orbitals for each atom that interact via a time dependent hopping integral. This prescription also takes into account the motion of the nuclei which may occur in conjunction with energetic ion bombardment. As a consequence, the model is three-dimensional in nature and incorporates the electronic structure of the system at the time of desorption of the atom. The initial motions studied are ones where the adsorbate atom desorbs perpendicularly to the surface with a given velocity, v. For this motion and velocities less than ∼ 10 6cm/s we find that the ionization probability R + is proportional to v n with n between 2 and 4. For higher velocities R + can depend more exponentially on (-const./ v). The effect of the various parameters in the model including the atomic orbital energies, the coupling strength and effective range, and the assumed motion of the desorbing atom are examined in detail. The relevance of this model to a fundamental understanding of SIMS experiments is also stressed.

Drift Tube Study of Symmetric Resonance Single- and Double-Charge Transfer in Kr++Kr, Xe++Xe, Kr+++Kr, and Xe+++Xe Systems

An injected-ion drift tube mass spectrometer is used to determine the cross sections of processes Kr + +Kr→Kr+Kr + , Xe + +Xe→Xe+Xe + , Kr ++ +Kr→Kr+Kr ++ , and Xe ++ +Xe→Xe+Xe ++ . The drift tube was operated with He buffer gas and cooled with liquid nitrogen so that the energy range studied was widened as from 10 meV to 10 eV. It was found that, at the lowest energy end, the energy dependence of cross section for single charge transfer deviates from that expected by linear trajectory model. For double charge transfer, the cross section below 1 eV almost coincide with the orbiting cross section with a charge transfer probability 1/2. Above 1 eV, the energy dependence of the cross section is like that for single charge transfer. Mobilities of Kr + , Xe + , Kr ++ , and Xe ++ in He at 296 K and 82 K are presented also.

Path-integral method in the theory of the elementary act of the charge transfer in polar media

A new approach using the functional integral method and the Feynman path-integral method is suggested to calculate the transition probability of non-adiabatic charge transfer in a polar medium. It enables us to take into account the dependence of the electronic wavefunctions on the coordinates of slow subsystem and to go beyond the Condon approximation.

Cross sections for symmetric charge transfer and proton transfer reactions of internal energy selected NH3+ (v)

Absolute total cross sections for electron and proton transfer reactions of NH3 selected in vibrational levels from v = 0 to 10 have been measured by photoion–photoelectron coincidence. The proton transfer reactions were determined at relative translational energies between 0.1 and 1 eV, while the electron transfer reactions were measured between 1 and 100 eV and at 3000 eV. Although the Franck–Condon factors between v = 0 and v = 5 of the NH3 (v = 0)→NH3+ (v) transition change by a factor of 35, the cross sections for charge transfer vary only by a factor of two. By comparing the measured cross sections with the Langevin collision cross sections, we show that the internal energy plays a role only for impact parameters larger than the Langevin orbiting impact parameter. A model which divides the charge transfer reaction into two types, one involving intimate collisions, the other large impact parameter collisions, is introduced. The model is used to derive the charge transfer probability as a function of impact parameter for various combinations of NH3+ vibrational and relative kinetic energies.

Charge transfer and rapidity gap analysis inp(?+)n interactions at 195GeV/c

We present charge transfer probabilities between CM hemispheres inpn and π+n interactions at 195 GeV/c. The relative probabilities for charge exchanges |ΔQ|>1 as a function of rapidity gap length,r, are given. Both results are compared with those of π−p interactions at 200GeV/c. The average ofr, viz. , is given as a function of the gap number and of ΔQ for various multiplicities, and the reduced average gap lengths /ymax forpn interactions are compared with data at a lower energy.

Numerical Solution of the Time-Dependent Schrödinger Equation and Application toH+-H

The time-dependent Schr\"odinger equation for the motion of the electron in a ${\mathrm{H}}^{+}$-H collision is solved numerically with a finite-difference method on an axially symmetric spatial mesh. Sample density distributions for ${E}_{\mathrm{lab}}=20$ keV are shown. The calculated charge-transfer probabilities at ${E}_{\mathrm{lab}}=3.92, 7.69, \mathrm{and} 20.1$ keV are in good agreement with experiment.