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Full-Text Articles in Physics

Electron Attachment To Molecules In A Cluster Environment, Ilya I. Fabrikant, S. Caprasecca, Gordon A. Gallup, J. D. Gorfinkiel Jan 2012

Electron Attachment To Molecules In A Cluster Environment, Ilya I. Fabrikant, S. Caprasecca, Gordon A. Gallup, J. D. Gorfinkiel

Gordon Gallup Publications

Low-energy dissociative electron attachment (DEA) to the CF2Cl2 and CF3Cl molecules in a water cluster environment is investigated theoretically. Calculations are performed for the water trimer and water hexamer. It is shown that the DEA cross section is strongly enhanced when the attaching molecule is embedded in a water cluster, and that this cross section grows as the number of water molecules in the cluster increases. This growth is explained by a trapping effect that is due to multiple scattering by water molecules while the electron is trapped in the cluster environment. The trapping increases ...


Semiclassical Complex-Time Method For Tunneling Ionization: Molecular Suppression And Orientational Dependence, Gordon A. Gallup, Ilya I. Fabrikant Jan 2010

Semiclassical Complex-Time Method For Tunneling Ionization: Molecular Suppression And Orientational Dependence, Gordon A. Gallup, Ilya I. Fabrikant

Gordon Gallup Publications

We apply a previously developed semiclassical complex time method to the calculation of tunneling ionization of several diatomic molecules and CO2.We investigate the presence or absence of the molecular suppression effect by calculating ionization rates of N2 versus Ar, O2 versus Xe, F2 versus Ar, and CO versus Kr. Comparisons with other theories, including the molecular-orbital-Ammosov-Delone-Krainov (MO-ADK) model and the strong-field approximation, are given. We also analyze the dependence of the ionization rate on the angle θF between the molecular axis and the field direction. The theoretical results agree quite well with experiment for ...


Electron-Induced Bond Breaking At Low Energies In Hcooh And Glycine: The Role Of Very Short-Lived Σ* Anion States, Gordon A. Gallup, Paul Burrow, Ilya I. Fabrikant Jan 2009

Electron-Induced Bond Breaking At Low Energies In Hcooh And Glycine: The Role Of Very Short-Lived Σ* Anion States, Gordon A. Gallup, Paul Burrow, Ilya I. Fabrikant

Gordon Gallup Publications

Cross sections for dissociative electron attachment (DEA) to formic acid and glycine are calculated by the resonant R-matrix theory. A model with one effective reaction coordinate close to the O-H stretch motion is employed. The choice of the anion R-matrix pole and the surface amplitude as functions of the reaction coordinate for formic acid are based on scattering phase-shift calculations using the finite element discrete model. For glycine the input parameters are adjusted to reproduce experimental data. The results show that the mechanism of DEA in these molecules is similar to that for the hydrogen halides and involves electron ...


Scattering And Bound-State Solutions To The Wave Equation For One Electron In The Presence Of A Physical Dipole, Gordon A. Gallup Jan 2009

Scattering And Bound-State Solutions To The Wave Equation For One Electron In The Presence Of A Physical Dipole, Gordon A. Gallup

Gordon Gallup Publications

This paper presents a quantum-mechanical analysis of the interaction of one electron with a physical dipole (two physically separated charges). Aspects of threshold laws in the continuous spectrum are treated. In addition there are determinations of energies of some dipole bound states. The bound-state calculations are used as a model for certain high dipole moment molecules, where, together with empirical data, an equivalent dipole length may be determined. These model calculations predict that the bound dipole orbital in high dipole molecule ions should have a node between its valence part and the more remote part where the majority of the ...


Reply To “Comment On ‘Electron-Induced Bond Breaking At Low Energies In Hcooh And Glycine: The Role Of Very Short-Lived Σ Anion States’ ”, Gordon A. Gallup, Paul Burrow, Ilya I. Fabrikant Jan 2009

Reply To “Comment On ‘Electron-Induced Bond Breaking At Low Energies In Hcooh And Glycine: The Role Of Very Short-Lived Σ Anion States’ ”, Gordon A. Gallup, Paul Burrow, Ilya I. Fabrikant

Gordon Gallup Publications

Rescigno et al. [Phys. Rev. A 80, 046701 (2009)] criticized our theoretical treatment of dissociative electron attachment in formic acid in which we show that this process can be explained by electron attachment into the temporary negative ion state formed by occupation of the σ*(OH) orbital. We argue that their objections do not hold up to scrutiny.


Semiclassical Propagation Method For Tunneling Ionization, Ilya I. Fabrikant, Gordon A. Gallup Jan 2009

Semiclassical Propagation Method For Tunneling Ionization, Ilya I. Fabrikant, Gordon A. Gallup

Gordon Gallup Publications

We apply the semiclassical propagation technique to tunneling ionization in atomic and molecular systems. Semiclassical wave functions and the tunneling flux are calculated from the solution of the classical equations of motion in the complex time plane. We illustrate this method by rederiving the known result for the decay rate of a negative ion in a weak electric field. We then obtain numerical results for atomic hydrogen, H2+, H2, and Ar, and compare them with the results of the asymptotic [Ammosov-Delone-Krainov (ADK)] theory. The asymptotic theory gives surprisingly good results for the atomic and molecular ionization rates. In ...


Total Dissociative Electron Attachment Cross Sections Of Selected Amino Acids, A.M. Scheer, P. Mozejko, Gordon A. Gallup, Paul Burrow Apr 2007

Total Dissociative Electron Attachment Cross Sections Of Selected Amino Acids, A.M. Scheer, P. Mozejko, Gordon A. Gallup, Paul Burrow

Gordon Gallup Publications

Total dissociative electron attachment cross sections are presented for the amino acids, glycine, alanine, proline, phenylalanine, and tryptophan, at energies below the first ionization energy. Cross section magnitudes were determined by observation of positive ion production and normalization to ionization cross sections calculated using the binary-encounter-Bethe method. The prominent 1.2 eV feature in the cross sections of the amino acids and the closely related HCOOH molecule is widely attributed to the attachment into the –COOH π * orbital. The authors discuss evidence that direct attachment to the lowest σ * orbital may instead be responsible. A close correlation between the energies ...


Resonances And Threshold Effects In Low-Energy Electron Collisions With Methyl Halides, Gordon A. Gallup, Ilya I. Fabrikant Mar 2007

Resonances And Threshold Effects In Low-Energy Electron Collisions With Methyl Halides, Gordon A. Gallup, Ilya I. Fabrikant

Gordon Gallup Publications

Cross sections for elastic and inelastic electron collisions with CH3X(X =Cl,Br, I) molecules are calculated. For the lowest partial wave, the resonance R-matrix theory, and for the higher partial waves, the theory of scattering by dipolar plus polarization potential, are used. It is shown that the rotationally elastic scattering amplitude for a polar molecule in the fixed-nuclei approximation is logarithmically divergent for the forward direction, and a closure formula is derived to speed up the convergence at small angles. In treating the nuclear motion, only C-X stretch vibrations are taken into account. The dipole moment ...


Errors In The Application Of The Jwkb Method To Calculating The Survival Factor In Dissociative Electron Attachment Using The Local Complex Potential, Gordon A. Gallup Feb 2007

Errors In The Application Of The Jwkb Method To Calculating The Survival Factor In Dissociative Electron Attachment Using The Local Complex Potential, Gordon A. Gallup

Gordon Gallup Publications

The accuracy of the JWKB method for determining the survival factor defined for dissociative electron attachment (DEA) processes is examined for a range of electronic resonance lifetimes within the local complex potential approximation. The author concludes that the accuracy is inadequate for molecules with properties commonly found for shape resonance induced DEA. More accurate methods using the uniform Airy function approximation give much better results, but the direct numerical integration of Schrödinger’s equation appears simpler still. © 2007 American Institute of Physics.


Remote Bond Breaking By Interacting Temporary Anion States, Paul Burrow, Gordon A. Gallup Oct 2006

Remote Bond Breaking By Interacting Temporary Anion States, Paul Burrow, Gordon A. Gallup

Gordon Gallup Publications

The cross section for bond breaking at the site of a dissociative temporary negative ion state through the dissociative electron attachment process can be considerably enhanced by the presence of a second longer-lived temporary negative ion state elsewhere in the molecule, even one quite remote from the first. In a series of chloroalkenes possessing both C–Cl and C=C bonds separated by various distances, we show that the cross sections are determined by the lifetime of the lower anion state created by the mixing of the anion states of these two moieties, with the wave function’s coefficients giving ...


An Investigation Of Electron Helicity Density In Bromocamphor And Dibromocamphor As A Source Of Electron Circular Dichroism, A.M. Scheer, Gordon A. Gallup, Timothy J. Gay Sep 2006

An Investigation Of Electron Helicity Density In Bromocamphor And Dibromocamphor As A Source Of Electron Circular Dichroism, A.M. Scheer, Gordon A. Gallup, Timothy J. Gay

Gordon Gallup Publications

We investigate the causes of electron-circular dichroism (ECD) in bromocamphor and dibromocamphor, focusing specifically on the electron helicity density of the target. Using electron transmission spectroscopy (ETS) and quantum chemical calculations, we have observed and assigned temporary negative ion states of bromocamphor and dibromocamphor. Further calculations were conducted to determine the helicity densities of these compounds. Large helicity densities are found in the regions of large wave function amplitude of the normally unoccupied molecular orbitals responsible for resonances in the scattering cross sections. We relate our ETS assignments and helicity density results to the chiral asymmetry data observed in electron-circular ...


Complex Energy Shift And Background Phase Shift For Simulated Electron-Molecular Shape Resonances, Gordon A. Gallup Feb 2005

Complex Energy Shift And Background Phase Shift For Simulated Electron-Molecular Shape Resonances, Gordon A. Gallup

Gordon Gallup Publications

Feshbach-Fano resonance theory (FFRT) is used to determine the energy dependence of the complex energy shift function, consisting of the real energy shift and the resonance width, and the background phase shift for several simulated molecular shape resonances. Attention is paid to the way the choice of the quasibound state (QBS) function required in the FFRT affects these energy dependencies. An overlap criterion for choosing an optimal QBS function is proposed. Using our treatment on t-butylchloride, carbon tetrachloride, ethylene, and benzene, we give numerical results for specific cases of l = 1 through 4. We find that the real energy ...


The Structures Of C-C4F8 And C-C4F8¯ And The Adiabatic Electron Affinity Of C-C4F8, Gordon A. Gallup Nov 2004

The Structures Of C-C4F8 And C-C4F8¯ And The Adiabatic Electron Affinity Of C-C4F8, Gordon A. Gallup

Gordon Gallup Publications

Calculations at the 6311G(dps) level have been used to elucidate the structures of octafluorocyclobutane c-C4F8 and its negative ion c-C4F8¯. With no empirical adjustments, we obtain 0.640 eV for the adiabatic electron affi nity of c-C4F8. This may be compared with an experimental value of 0.63 ± 0.05 eV from the FALP method. c-C4F8 has unusual features in that there is an increase in symmetry, D2d to D4h, in going from the neutral molecule to the negative ion, and the ...


Spin-Exchange-Induced Circularly Polarized Molecular Fluorescence, A.S. Green, Gordon A. Gallup, Mark A. Rosenberry, Timothy J. Gay Mar 2004

Spin-Exchange-Induced Circularly Polarized Molecular Fluorescence, A.S. Green, Gordon A. Gallup, Mark A. Rosenberry, Timothy J. Gay

Gordon Gallup Publications

We have measured the circular polarization of light emitted from both atomic H and molecular H2 after bombarding H2 with longitudinally polarized electrons. For both atomic and molecular fluorescence near threshold we observe a circular polarization as great as 10% of the electron polarization. This represents the first direct observation of spin transfer in electron-molecule collisions.


A Short History Of Valence Bond Theory, Gordon A. Gallup Apr 2002

A Short History Of Valence Bond Theory, Gordon A. Gallup

Gordon Gallup Publications

Shortly after quantum mechanics evolved Heitler and London [1] applied the then new ideas to the problem of molecule formation and chemical valence. Their treatment of the H2 molecule was qualitatively very successful, and this led to numerous studies by various workers applying the same ideas to other substances. Many of these involved refinements of the original Heitler-London procedure, and within three or four years, a group of ideas and procedures had become reasonably well codified in what was called the valence bond (VB)* method for molecular structure.

A few calculations were carried out earlier, but by 1929 Dirac ...


Quantum-Mechanical Analysis Of A Longitudinal Stern-Gerlach Effect, Gordon A. Gallup, Herman Batelaan, Timothy J. Gay May 2001

Quantum-Mechanical Analysis Of A Longitudinal Stern-Gerlach Effect, Gordon A. Gallup, Herman Batelaan, Timothy J. Gay

Gordon Gallup Publications

We present the results of a rigorous quantum-mechanical calculation of the propagation of electrons through an inhomogeneous magnetic field with axial symmetry. A complete spin polarization of the beam is demonstrated assuming that a Landau eigenstate can be inserted into the field. This is in contrast with the semiclassical situation, where the spin splitting is blurred.


Comparative Studies Of Dissociative Electron Attachment To Methyl Halides, R. S. Wilde, Gordon A. Gallup, Ilya I. Fabrikant Nov 2000

Comparative Studies Of Dissociative Electron Attachment To Methyl Halides, R. S. Wilde, Gordon A. Gallup, Ilya I. Fabrikant

Gordon Gallup Publications

The dissociative electron attachment cross sections for the methyl halides vary in an enormous range from the virtually unmeasurable 10−23 cm2 for CH3Cl at room temperature to 10−14 cm2 for CH3I. In this paper we supplement our previous studies by calculations of dissociative electron attachment to CH3Br and compare results for all methyl halides studied so far. The rate as a function of temperature for CH3Cl and CH3Br exhibits an exponential dependence on 1/T (Arrhenius law) with the activation energy lower for CH3Br ...


Dissociative Electron Attachment To Vibrationally And Rotationally Excited H2 And Hf Molecules, Yinfan Xu, Gordon A. Gallup, Ilya I. Fabrikant Apr 2000

Dissociative Electron Attachment To Vibrationally And Rotationally Excited H2 And Hf Molecules, Yinfan Xu, Gordon A. Gallup, Ilya I. Fabrikant

Gordon Gallup Publications

The vibrational and rotational state dependence of dissociative attachment (DA) in low-energy e-H2 and e-HF collisions is studied within the framework of nonlocal resonance theory. The dynamics of nuclear motion in the nonlocal complex potential is treated by the quasiclassical approach. The resonance energy, width function, and level-shift function are taken from our previous calculations based on the projection operator formalism. Results for all vibrational states up to the dissociative attachment thresholds and selected rotational states are presented. Our cross sections for H2 exhibit a plateau structure in the energy range above the dissociation threshold, and ...


Semiempirical R-Matrix Theory Of Low Energy Electron–Cf3Cl Inelastic Scattering, R. S. Wilde, Gordon A. Gallup, Ilya I. Fabrikant May 1999

Semiempirical R-Matrix Theory Of Low Energy Electron–Cf3Cl Inelastic Scattering, R. S. Wilde, Gordon A. Gallup, Ilya I. Fabrikant

Gordon Gallup Publications

We apply a semiempirical R-matrix theory to calculations of vibrational excitation and dissociative attachment in the CF3Cl molecule for electron energies below about 3 eV. We employ two sets of model parameters corresponding to two different forms of the CF3Cl potential curve. We find that our present, ab initio calculated anion curve gives vibrational excitation and dissociative attachment cross sections in good agreement with experimental measurements. We also compare the results of our theory with those of a recently published classical theory.


Nonlocal Theory Of Dissociative Electron Attachment To H2 And Hf Molecules, Gordon A. Gallup, Y. [Yuanguang] Xu, Ilya I. Fabrikant Apr 1998

Nonlocal Theory Of Dissociative Electron Attachment To H2 And Hf Molecules, Gordon A. Gallup, Y. [Yuanguang] Xu, Ilya I. Fabrikant

Gordon Gallup Publications

We develop a method for calculation of dissociative electron attachment cross sections based on the Fano- Feshbach projection-operator approach. The coupling between the diabatic state and electron continuum is calculated with the inclusion of orthogonality scattering and long-range electron-molecule interaction. The dynamics of nuclear motion in the non-local complex potential is treated by semiclassical theory. We apply the theory to the calculation of dissociative attachment to the H2 and HF molecules. Our results for attachment to ground-state hydrogen molecules and the near-threshold vibrational enhancement of H2 are essentially the same as previous non-local results. However, the shape of ...


Symmetry Selection Rules For Vibrational Excitation By Resonant Electron Impact And A Unified Treatment Of Vibronic Coupling Between Resonances And To The Continuum: A Complete Symmetry Analysis Of Vibrational Excitation In Benzene, Gordon A. Gallup Jul 1993

Symmetry Selection Rules For Vibrational Excitation By Resonant Electron Impact And A Unified Treatment Of Vibronic Coupling Between Resonances And To The Continuum: A Complete Symmetry Analysis Of Vibrational Excitation In Benzene, Gordon A. Gallup

Gordon Gallup Publications

A symmetry analysis of the contributions to the transition operator from vibronic coupling provides symmetry selection rules for vibrational excitation by resonant electron impact in polyatomic molecules. In the context of electron scattering vibronic coupling operates in two modes. These are named internal and external vibronic coupling. Internal vibronic coupling operates within and among the quasibound states giving rise to the resonances. External vibronic coupling operates between the quasibound states and the continuum. We discuss the differences, particularly with respect to the angular distribution of electron scattering. A complete symmetry analysis of vibrational excitation is given using benzene as an ...


H+-H- Coincidences From The Three-Body Dissociation Of Excited H3+, Orhan Yenen, D. Calabrese, L.M. Wiese, Duane H. Jaecks, Gordon A. Gallup Feb 1993

H+-H- Coincidences From The Three-Body Dissociation Of Excited H3+, Orhan Yenen, D. Calabrese, L.M. Wiese, Duane H. Jaecks, Gordon A. Gallup

Gordon Gallup Publications

The laboratory energy distribution of protons in coincidence with an H- ion, resulting from the dissociation of excited H3+, has been measured for H+-H- pairs emitted along the beam for 4.0-keV H3+-He collisions. An approximate energy distribution of H+-H- pairs for the collinear configuration of the dissociation products is obtained by transforming the measured laboratory spectrum to the H3+ center-of-mass (c.m.) frame. Coincidence data suggest that the reaction producing H+-H- pairs where the H+ ion has near-zero energies (3+ ions using a full configuration-interaction calculation with a basis set of atomic ...


The Relationship Of The Virtual Orbitals Of Self-Consistent-Field Theory To Temporary Negative Ions In Electron Scattering From Molecules, Donghai Chen, Gordon A. Gallup Dec 1990

The Relationship Of The Virtual Orbitals Of Self-Consistent-Field Theory To Temporary Negative Ions In Electron Scattering From Molecules, Donghai Chen, Gordon A. Gallup

Gordon Gallup Publications

The theory given here shows how certain of the virtual orbitals of self-consistent field (SCF) theory provide a natural ingredient for constructing basis functions to study the shape resonances associated with temporary molecular ions. We give specific calculations of resonant behavior in H2, N2, ethylene, cyclopropene, and cyclobutene. In addition, we show how the theory can rationalize the relationship between Koopmans' theorem values of the energy of a resonance and the experimental values. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.


The Breakdown Of Hund's Rule In Systems Of Fourfold Symmetry, Gordon A. Gallup Apr 1987

The Breakdown Of Hund's Rule In Systems Of Fourfold Symmetry, Gordon A. Gallup

Gordon Gallup Publications

The lowest energies of molecular systems with fourfold symmetry can violate Hund's multiplicity rule. We derive relationships between two electron integrals that in favorable cases allow one to predict when this will happen. These relationships result in a fairly simple inequality as a criterion. The systematics of the phenomenon are illustrated with a series of calculations on model systems consisting of hydrogen atoms. These are rings of three, four, five, six, seven, and eight members as well as octahedral and square planar arrangements. These show how the results and simple ideas of molecular orbital theory can be qualitatively modified ...


Nonorthogonal Configuration-Interaction Calculations Of Molecular States: The Low-Lying Molecular States Of Arhsup+ And Two-Electron Charge Exchange In Ar-H+ Collisions, Gordon A. Gallup Jan 1987

Nonorthogonal Configuration-Interaction Calculations Of Molecular States: The Low-Lying Molecular States Of Arhsup+ And Two-Electron Charge Exchange In Ar-H+ Collisions, Gordon A. Gallup

Gordon Gallup Publications

A nonorthogonal configuration-interaction procedure has been used to calculate adiabatic energy curves of ArH+. The basis functions are a mixture of typical molecular-orbital configurations and typical valence-bond (Heitler-London) configurations. This gives an economical description of the wave functions, allowing an easy tracing of various diabatic states through the adiabatic states and a clear identification of the asymptotic states. The results are used to rationalize the unexpectedly large production of Ar2++H- from collisions of H+ with Ar.


Selection Rules For Vibrational Energy Loss By Resonant Electron Impact In Polyatomic Molecules, Gordon A. Gallup Oct 1986

Selection Rules For Vibrational Energy Loss By Resonant Electron Impact In Polyatomic Molecules, Gordon A. Gallup

Gordon Gallup Publications

Approximate expressions for inelastic elements of the S matrix are given in terms of integrals over vibrational functions and R-matrix electron states. The magnitude and symmetry of these integrals determine the vibrations that are excited by various resonances, and the present analysis successfully predicts the spectra measured for benzene, ethylene, and formaldehyde. The recently observed s-wave component in the rotational excitation of N2 is also explained by the treatment. The theory shows how vibrational excitation can give information about the symmetries of resonant electronic states. This can be particularly useful when angular distribution measurements are unavailable.


Comment On ‘‘Valence-Bond Theory And The Evaluation Of Electronic Energy Matrix Elements Between Nonorthogonal Slater Determinants’’, Gordon A. Gallup Jul 1986

Comment On ‘‘Valence-Bond Theory And The Evaluation Of Electronic Energy Matrix Elements Between Nonorthogonal Slater Determinants’’, Gordon A. Gallup

Gordon Gallup Publications

In a recent article [Phys. Rev. A 31, 2107 (1985)] Leasure and Balint-Kurti claim to give a more efficient algorithm than any previously available for determining matrix elements of the Hamiltonian in valence-bond calculations. Actually, an algorithm of no significant difference and the same efficiency has been available since 1972 and has been applied to valence-bond calculations.


A Variation-Perturbation Method For Atomic And Molecular Interactions. Ii. The Interaction Potential And Van Der Waals Molecule For Ne–Hf, Gordon A. Gallup, J. Gerratt Sep 1985

A Variation-Perturbation Method For Atomic And Molecular Interactions. Ii. The Interaction Potential And Van Der Waals Molecule For Ne–Hf, Gordon A. Gallup, J. Gerratt

Gordon Gallup Publications

A recently developed variation-perturbation theory for calculating intermolecular forces has been applied to the Ne–HF system for fixed H–F distances. The maximum well depth is 0.49 kJ/mol (41 cm-1) for a linear configuration with the H between the Ne and F and the Ne–H distance approximately 5.5 bohr. A secondary minimum of depth 0.24 kJ/mol (20 cm-1) was found for the other linear configuration at a Ne–F distance of about 7.0 bohr. A saddle point, about 0.20 kJ/mol (17 cm-1) deep, for the T-shaped configuration ...


A Variation-Perturbation Method For Atomic And Molecular Interactions. I. Theory, Gordon A. Gallup, J. Gerratt Sep 1985

A Variation-Perturbation Method For Atomic And Molecular Interactions. I. Theory, Gordon A. Gallup, J. Gerratt

Gordon Gallup Publications

We have developed a variation-perturbation procedure for calculating intermolecular forces. It is based on the valence bond method of constructing wave functions and involves a number of interlocking techniques and approximations that are justified by the small size of the interaction potential relative to the total energy. In this article we give an outline of the theory of our technique. We have used this procedure to determine the potential between a Ne atom and a rigid HF molecule. The results of this calculation are given in the next article. The Journal of Chemical Physics is copyrighted by The American Institute ...


Computed Cross Sections For Electron Transfer In Ba+ + Ba+ Collisions , Stanley J. Sramek, J.H. Macek, Gordon A. Gallup Oct 1980

Computed Cross Sections For Electron Transfer In Ba+ + Ba+ Collisions , Stanley J. Sramek, J.H. Macek, Gordon A. Gallup

Gordon Gallup Publications

Cross sections have been computed for the electron-transfer process Ba++Ba+→Ba+Ba++, for collision energies ranging from 25 to 500 keV. The straight-line classical-trajectory method has been used, with basis functions obtained by the multiconfiguration valence-bond method. Several numerical procedures applicable to future treatments of similar large systems were developed. The maximum cross-section value is found to be around 27π a02 (2.4 × 10-15 cm2), and occurs near collision energy 500 keV. The system's transient behavior has also been studied in detail during the collision, and it has been found that most electron-transfer events ...