Theoretical study of differential cross sections for the ionization of helium by fast proton impact

We present the angular distribution of the ejected electron for single ionization of He by fast proton impact.A fourbody formalism of the three-Coulomb wave is applied to calculate the triple differential cross sections at several impact energies in the scattering,perpendicular and azimuthal planes.Moreover,the three-body formalism of three-Coulomb,two-Coulomb and first Born approximation models has also been used to study the many-body effect on electron emission and the validity of the models.In the three-Coulomb wave model,the final state wave function incorporates distortion due to the three-body mutual Coulombic interaction.In this formalism,we use an uncorrelated and correlated Born initial state,which consists of a plane wave for the incoming projectile times a two-electron bound state wavefunction of the helium atom representing the 1s^(2)(1S)state.But,in the case of the three-body formalism,the initial state wavefunction consists of a long-range Coulomb distortion for the incoming projectile and one active electron of the He atom described by the Roothaan–Hartree–Fock wavefunction.The structure with a single or two peaks with unequal intensity is observed in the angular distributions of the triple differential cross sections for the different kinematic conditions.In addition,the influence of static electron correlations is investigated using different bound state wavefunctions for the ground state of the He target.In the four-body formalism,the present computations are very fast by reducing a nine-dimensional integral to a two-dimensional real integral.Despite the simplicity and speed of the proposed quadrature,the comparison shows that the obtained results are in reasonable agreement with the experiment and are compatible with those of other theories.

Experimental study of cross-section ratios in the collisions of C^(q+) and O^(q+) (q=1-4) on atomic helium in strong-interaction region

We have measured the cross-section ratios of helium induced by Cq＋ and Oq＋ （q = 1-4） in an energy range from 20 keV/amu to 500 keV/amu, and obtained the two-dimensional spectra by employing the coincidence method combined with the MPA-3 data acquisition system. Hence, we obtain the ratios of total single-ionization cross-sections （SI, SC, SLSI, and DLSI）, total double-ionization cross-sections （DI, DC, TI, SLDI, and DLDI） and cross-sections of every process （SI, SC, SLSI, DLSI, DI, DC, TI, SLDI, and DLDI）, which induce the single-ionization and double-ionization, to the total cross sections respectively. The competitive relations between the reaction-channels and the experimental data law of each reaction-channel are revealed explicitly, and the qualitative explanations involved in those results are also presented accordingly.

Cross sections of O^(q+)(q=1-4) electron loss in collisions with He,Ne and Ar

Electron-loss cross sections of 0q＋ （q = 1 -4） colliding with He, Ne and Ar atoms are measured in the intermediate velocity regime. The ratios of the cross sections of two-electron loss to that of one-electron loss R21 are presented. It is shown that single-channel analysis is not sufficient to explain the results, but that projectile electron loss, electron capture by the projectile and target ionization must be considered together to interpret the experimental data. The screening and antiscreening effects can account for the threshold velocity results, but cannot explain the dependence of the ratio R21 on velocity quantitatively. In general, the effective charge of the target atom increases with velocity increasing because the high-speed projectile ion can penetrate into the inner electronic shell of target atom. Ne and Ar atoms have similar effective charges in this velocity regime, but He atoms have smaller ones at the same velocities due to its smaller nuclear charge.

Close coupling calculations for excitation partial cross sections in Ne-HF collisions

This paper reports that an exact quantum close coupling calculation is carried out for rotational excitation in Ne HF collisions on the available anisotropic potential. Partial cross sections are obtained separately at the incident energies of 48.35, 75, 120 and 150meV. The reliability of the results is demonstrated by comparison with previously published theoretical findings. Based on the calculations, the effect of the potential energy surface on the excitation partial cross sections is discussed in detail.

Ar^+/Ar, O_2^+/O_2 and N_2^+/N_2 Elastic Momentum Collision Cross Sections: Calculation and Validation Using the Semi-Classical Model

The aim of this paper is to obtain relevant sets of collision cross sections of the parent ions in low pressure discharges in argon, oxygen, and nitrogen, i.e., Ar＋ in Ar, O2＋ in O2 and N2＋ in N2. These ion data are first discussed and then validated from comparisons between the calculated transport coefficients and those measured in the literature. The elastic momentum transfer collision cross sections are determined from a semi-classical approximation for the phase shift calculation based on a 12-6-4 inter-particle potential while ion transport coefficients are determined versus the reduced electric field from Monte Carlo simulations.

Influence of Isotope Substitution Helium Atom on Partial Cross Sections in He-HF Collisions

Close-coupling equation and anisotropic potential developed in our previous research are applied to HE-SHe （4He, 6He, 8He,10He） collision system, and partial cross sections （PCSs） at the incident energy of 40 me V are calculated. By analyzing the differences of these PCSs, change rules of PCSs with the increase of partial wave number, and with the change of the mass of isotope substitution helium atom are obtained. The results show that excitation PCSs converge faster than elastic PCSs for collision energy and each of systems considered here. Also excitation PCSs converge more rapidly for high-excited states. Tail effect is present only in elastic scattering and low-excited states but not in high- excited states. With the increase of the mass of isotope substitution helium atom, converging speed of elastic, total inelastic, and state-to-state excitation PCS slows down, and the maxima of these PCSs undergoes a regular change.

Nucleus-Nucleus Effects in Fully Differential Cross Sections for Energetic C6++He Collisions with Small Momentum Transfer

The modified Coulomb-Born approximation with and without the internuclear interaction （MCB-NN and MCB） is used to calculate the fully differential cross sections （FDCS） for the single ionization of helium by lOO MeV/amu C6＋ impact. The effects of the internuclear interaction on the FDCS are examined in geometries. The results are compared with experimental data and theoretical predictions from a three-body distorted-wave （3DW） model and a time-dependent close-coupling model. It is shown that the present MCB-NN results are in good agreement with the experiments in the scattering plane and the MCB results qualitatively reproduce the experimental structure outside the scattering plane. In particular, the MCB theory predicts the ＇double-peak＇ structure in the perpendicular plane.

Determination of Absorption Cross Section of J/ψ in Relativistic Heavy Ion Collisions

The absorption cross section σabs of J/ψ produced in relativistic heavy ioncollisions is deduced based on the analysis of the absorption length through which theproduced J/ψ passes in the colliding nuclei.The obtained σabs in A-A collisions is con-siderably higher than that in h-A processes.The reason for this different result is dis-cussed in terms of an analysis of the pT-dependence of the produced J/ψ.

Dissociative ionization cross sections of CO_2 at electron impact energy of 5 keV

The dissociative ionization of CO2 induced by 5 keV electrons in two-body and three-body dissociative channels of CO2＋2 and CO3＋2 is identified by the ion-ion coincidence- method using a momentum imaging spectrometer. The partial ionization cross sections （PICSs） of different ionic fragments are measured and the results generally agree with the calculations made by a semi-empirical approach. Furthermore, the PICSs of the dissociative channels are also obtained by carefully considering the detection efficiency of the micro-channel plates and the total transmission efficiency of the time of flight system.

The (e,2e) triple differential cross sections of Cu^+ (3p) in coplanar asymmetric geometry

The three-body distorted=wave Born approximation has been used to calculate the （e, 2e） triple differential cross sections （TDCSs） of Cu＋ （3p） in different kinematical variables in coplanar asymmetric geometry. The angles 4°, 10° and 20° were selected as the scattering electron angles. Under high incident energy （≥500 eV） and high asymmetric detection energy, the binary peaks showed abnormal splits. Such abnormal splits have not been observed in atomic target and outer valence orbitals of ionic target, which indicates that an （e, 2e） process for inner valence orbitals of ionic target would be more complicated than outer valence orbitals. Furthermore, some pronounced peaks appeared at certain ejected angles. We considered that these pronounced peaks are probably related to one kind of double-binary collision.

A modification potential method of calculating total cross sections of electrons scattering from complex molecules C2H6, C2F6, C6H6 and C6F6 at 100 eV-5000 eV

A complex optical model potential modified by incorporating the concept of bonded atom, which takes into consideration the overlapping effect of electron clouds between two atoms in a molecule, is first employed to calculate the total cross sections for electrons scattering from such complex molecules as C2H6, C2F6, C6H6 and C6F6 using the aclditivity rule model at Hartree-Fock level over the energy range from 100 eV to 5000 eV. The total cross sections are quantitatively compared with those obtained by experiments wherever available, and they are in good agreement with each other over a wide energy range. It is shown that the modified potential together with the additivity rule model is completely suitable for the calculation of total cross sections of electrons scattering from such complex molecules as C2H6, C2F6, C6H6 and C6F6 above 200 eV-300 eV.

Total cross sections for electrons scattering from simple molecules containing the larger atom sulfur at 30-5000eV

A complex optical model potential modified by the concept of bonded atom, which takes into consideration the overlapping effect of electron clouds, is employed to calculate the total cross sections for electrons scattering from simple molecules （SO2, H2S, OCS, CS2 and SO3） containing the larger atom, sulfur, at 30-5000eV by using the additivity rule model at Hartree-Fock level. The quantitative molecular total cross section results are compared with those obtained in experiments and other calculations wherever available, and good agreement is obtained. It is shown that the additivity rule model together with the complex optical model potential modified by the concept of bonded atom can give the results closer to the experiments than the one unmodified by it. So, the introduction of bonded-atom concept in complex optical model potential betters the accuracy of the total cross section calculations of electrons from the molecules containing the larger atom, sulfur.

Triple-differential cross section for single ionization of H_2 by electron impact

The triple-differential cross section （TDCS） for the （e,2e） ionization of a hydrogen molecule is calculated using the molecule distorted-wave Born approximation （MDWBA）. Distorted waves are obtained by solving momentum-space coupled-channel Lippmann-Schwinger equations, including the ground state and the lowest-lying electronic state of b3Σu . TDCSs at the incident energy 100 eV in coplanar asymmetric geometry are reported. The present calculations are compared with the available experimental measurements and the theoretical results.

A Modified Potential Method for Electrons Scattering Total Cross Section Calculations on Several Molecules at 30 ～ 5000 eV： CF4, CCl4, CFCl3, CF2Cl2, and CF3Cl

A complex optical model potential modified by the concept of bonded atom, which takes into consideration the overlapping effect of electron clouds between two atoms in a molecule, is employed to calculate the total cross sections （TCS5） for electrons scattering from several molecules （CF4, CCl4, CFCl3, CF2 Cl2, and CF3 Cl） over an incident energy range 30 - 5000 eV using the additivity rule model at Hartre-Fock level. The quantitative TCS5 are compared with those obtained by experiments and other theories wherever available, and good agreement is obtained above 100 eV. It is shown that the modified potential can successfully calculate the TCS5 of electron-molecule scattering over a wide energy range, especially at lower energies.

A Correlation Potential Method for Electron Scattering Total Cross Section Calculations on Several Diatomic and Polyatomic Molecules over Energy Range 10～5000eV

A complex optical model potential correlated by the concept of bonded atom, which considers the overlapping effect of electron clouds between two atoms in a molecule, is firstly employed to calculate the total cross sections for electron scattering on several molecules (NH3, H2O, CH4, CO, N2, O2, and C2H4) over the energy range 10 ～ 5000 eV using the additivity rule model at Hartree-Fock level. The difference between the bonded atom and the free one in states is that the overlapping effect of electron clouds of bonded atoms in a molecule is considered. The quantitative total cross sections are compared with the experimental data and with the other calculations wherever available and good agreement is obtained over the energy range 10 ～ 5000 eV. It is shown that the correlated calculations are much closer to the available experimental data than the uncorrelated ones at lower energies, especially below 500 eV. Therefore,considering the overlapping effect of electron clouds in the complex optical model potential could be helpful for the better accuracy of the total cross section calculations of electron scattering from molecules.

Unimolecular Dissociation of H⁺<sub style="margin-left:-6px;">2n+1</sub>Hydrogen Clusters: Measured Cross Sections and Theoretically Calculated Rate Constants

In this paper, we studied the process of dissociation unimolecular of the evaporation of H+2n+1 hydrogen clusters according to size, using the Rice-Ramsperger-Kassel-Marcus (RRKM) theory. The rate constants k(E) were determined with the use of statistical theory of unimolecular reactions using various approximations. In our work, we used the products frequencies instead of transitions frequencies in the calculation of unimolecular dissociation rates obtained by three models RRKM. The agreement between the experimental cross section ratio and calculated rate ratio with direct count approximation seems to be reasonable.

Investigations on molecular constants of the CD(X^2Π) radical and elastic collisions between ground-state C and D atoms at low temperatures

The potential energy curve of the CD（X2∏） radical is obtained using the coupled-cluster singles-doublesapproximate-triples [CCSD（T）] theory in combination with the correlation-consistent quintuple basis set augmented with diffuse functions, aug-cc-pV5Z. The potential energy curve is fitted to the Murrell-Sorbie function, which is used to determine the spectroscopic parameters. The obtained Do, De, Re, ωe, ωeXe, αe and Be values are 3.4971 eV, 3.6261 eV, 0.11197 nm, 2097.661 cm^-1, 34.6963 cm^-1, 0.2083 cm^-1 and 7.7962 cm^-1, respectively, which conform almost perfectly to the available measurements. With the potential obtained at the UCCSD（T）/aug-cc-pV5Z level of theory, a total of 24 vibrational states have been predicted for the first time when J = 0 by solving the radial Schrodinger equation of nuclear motion. The complete vibrational levels, the classical turning points, the inertial rotation constants and centrifugal distortion constants are reproduced from the CD（X2∏） potential when J = 0, and are in excellent agreement with the available measurements. The total and the various partial-wave cross sections are calculated for the elastic collisions between the ground-state C and D atoms at energies from 1.0×10^-11 to 1.0 × 10^-4 a.u. when the two atoms approach each other along the CD（X2∏） potential energy curve. Only one shape resonance is found in the total elastic cross sections, and the resonant energy is 8.36×10^-6 a.u. The results show that the shape of the total elastic cross section is mainly dominated by the s partial wave at very low temperatures. Because of the weak shape resonances coming from higher partial waves, most of them are passed into oblivion by the strong total elastic cross sections.

Product polarization and mechanism of Li + HF(v=0, j=0) → LiF(v', j') + H collision reaction

A state-to-state dynamics analysis for the Li＋HF （v = 0, j = 0）→LiF （v’, j’）＋H collision reaction has been performed through quasiclassical trajectory （QCT） calculations. It is found that the differential cross section （DCS） of the LiF products from the title reaction is preferentially backward scattering for v’=0, yet forward scattering for v’=1 and 2. For v’=3, the DCS exhibits forward, backward, and sideways scatterings. The variation of the internuclear distances and angles along the propagation time reveals that more than 99.08% of reaction trajectories undergo the direct reaction mechanism. The values of the polarization parameters a1-{1} and a0{2} demonstrate that the product rotational angular moment j’ is not only aligned perpendicular to the reagent relative velocity vector k, but also oriented along the negative y axis. These product polarization results agree well with the recent quantum mechanical studies. The mechanism of these results was proposed and discussed in detail.

Elastic collisions of sulfur and hydrogen in their ground states at low temperatures and spectroscopic parameters of SH(X^2Π ) radical

This paper constructs the interaction potential of the SH（X^2∏） radical by using the coupled-cluster singlesdoubles-approximate-triples theory combining the correlation-consistent quintuple basis set augmented with the diffuse functions, aug-cc-pV5Z, in the valence range. Employing the potential, it accurately determines the spectroscopic parameters. The present De, Re, ωe, ωeχe, ae and Be values are of 3.7767eV, 0.13424nm, 2699.846 cm^-1, 47.7055 cm^-1, 0.2639cm^-1 and 9.4414 cm^-1, respectively, which are in excellent agreement with those obtained from the measure- ments. A total of 19 vibrational states has been found when J = 0 by solving the radial SchrSdinger equation of nuclear motion. The complete vibrational levels, classical turning points, initial rotation and centrifugal distortion constants when J = 0 are reported for the first time, which are in good accord with the experimental results. The total and various partial-wave cross sections are computed for the elastic collisions of sulfur and hydrogen in their ground states at low temperatures when two atoms approach each other along the SH（X^2∏） potential energy curve. Over the impact energy range from 1.0×10^-11 to 1.0×10^-4 a.u., eight shape resonances have been found in the total elastic cross sections. For each shape resonance, the resonant energy is accurately calculated. Careful investigations have pointed out that these resonances result from the 1 = 0, 1, 2, 3, 4, 6, 7, 8 partial-wave contributions.

Nonradiative charge transfer in collisions of protons with rubidium atoms

The nonradiative charge-transfer cross sections for protons colliding with Rb（5s） atoms are calculated by using the quantum-mechanical molecularorbital close-coupling method in an energy range of 10-a keV-10 keV. The total and state-selective charge-transfer cross sections are in good agreement with the experimental data in the relatively low energy region. The importance of rotational coupling for chargetransfer process is stressed. Compared with the radiative charge-transfer process, nonradiative charge transfer is a dominant mechanism at energies above 15 eV. The resonance structures of state-selective charge-transfer cross sections arising from the competition among channels are analysed in detail. The radiative and nonradiative1 charge-transfer rate coefficients from low to high temperature are presented.