Calculation of cross sections of simultaneous ionization in ion-atom collisions by the generalized geometrical model

The geometrical model (GM) of ionization in ion—atom collisions [8, 9] was generalized to describe ionization of both colliding particles (simultaneous ionization) due to electron—electron interaction. The generalized GM (GGM) allows calculation of the cross sections for electron loss by an incident particle with simultaneous target ionization at collision velocities higher than characteristic electron velocities, accurate within a factor of two with respect to the Born or impulse approximation. An advantage of the GGM, except for its simplicity, is easy calculation of p(b) (p is the ionization probability and b is the impact parameter), which makes it possible to include the contribution of simultaneous ionization into more general approximate schemes for calculating cross sections of multielectron ionization of atoms or ions.     

Study of cross sections for the loss of outer 1s, 2s, and 2p electrons by fast ions and atoms of light elements

In the case of light-element ions propagating with velocities V = 1.83 and 3.65 au in H₂, He, N₂, Ne, and Ar, the loss cross sections σ_{i, i+m} for m electrons (m = 1, 2, 3) are considered. The partial loss cross sections σ_i(nl) for one of the outer 1s, 2s, or 2p electrons are determined using the obtained data. It is shown that the experimental cross sections for the loss of the 1s and 2s electrons by positive ions qualitatively agree with the theoretical values calculated in the Born approximation. In the case of the ion velocity V = 1.83 au, the cross sections σ_i for 2p electrons are greater than the cross sections σ_i (1s) and σ_i (2s) by a factor of 1.2–3 for the same binding energies of electrons in the ion (I _nl > 20 eV). It is found experimentally that, at V = 1.83 au, the cross sections σ_i (2p) for I _nl ～ 10–20 eV are less than the cross sections σ_i (1s) by a factor of 2–3, which is probably caused by a decrease in the screening parameter (θ_2p < 1) of the outer shell of atoms.     

About the effect of a bound state on ionization cross sections in ion-atom collisions

The cross sections σ_nl for ionization of hydrogen-like ions by heavy particles from the nl = 3s, 3p, 3d, 4s and 4p states have been calculated in the Born approximation. A structure in the energy dependence of the cross sections σ_nl and the ratios of the cross sections σ_nl/σ_1s due to the radial wave function of a bound state is discussed.     

Electron Transitions during the Capture of an Electron by a He<Superscript>2+</Superscript> Ion at the Argon Atom

We have measured the absolute values of the total cross section of the one-electron capture by He²⁺ ions in the kinetic energy range 2–30 keV at the Ar atoms. The absolute values of the differential scattering cross sections of He⁺ ions formed during the one-electron capture and the electron capture with ionization at energies of 2.2, 5.4, and 30 keV have been determined. The electronic states of the formed ions have been determined using collision spectroscopy based on analysis of the change in the kinetic energy of He⁺ after the interaction. We have measured doubly differential (with respect to the kinetic energy and the scattering angle) cross sections of the formation of free electrons. The free electron formation channels (direct ionization and electron capture with ionization) have been analyzed by calculating the electron terms of the (HeAr)²⁺ system. The calculated cross section of capture with ionization is in conformity with the cross section measured using collision spectroscopy.     

Cross sections of electron capture and electron capture ionization versus the impact parameter in collisions of a proton with multielectron atoms

The absolute differential cross sections of scattering of hydrogen atoms resulting from an electron capture and an electron capture ionization are measured for collisions of 4.5- and 11-keV protons with argon and xenon atoms. The range of scattering angles is 0°–2°. From the scattering differential cross section found experimentally, the probabilities of single-electron capture and electron capture ionization as a function of the impact parameter are calculated. The dependences of the incident particle scattering angle on the impact parameter (deviation function) for interactions with Ar and Xe atoms are calculated in terms of classical mechanics using the Moliére—Yukawa potential to describe the interaction of atomic particles. Analysis is given to the probabilities of electron capture and electron capture ionization versus the impact parameter and to the distribution of the electron density on different electron shells in a target atom versus a distance to the core. It is concluded that only electrons from the outer shell of the target atom are involved in the process of electron capture ionization. The cross section of electron capture ionization is calculated in the proton energy range 5–20 keV.     

Effect of the target density on the cross section of charge exchange between fast ions and atoms

When fast X^q+ X^{q^ + } ions collide with atomic or molecular targets, the total charge exchange cross section decreases with increasing target density. This is because the excitation levels of resulting X^{(q - 1)+} X^{(q - 1)^ + } ions are suppressed because of ionization by target atoms. The effect of target density on the total charge exchange cross section may amount to one order of magnitude or more depending on the charge and energy of an incident ion, as well as on the density and inner shell configuration of target atoms. Numerical calculations are performed for partial (in the principal quantum number n) cross sections σ(n) and total cross sections σ_tot=Σ_nσ(n) of charge exchange in the case of collisions of fast multiply charged ions having an energy E in the range 100 keV/u-10 MeV/u with gas or solid targets.     

Scattering of charged particles by atoms

A closed variant of the Born approximation for calculating differential scattering cross sections in ion-atom collisions is developed. An expression in terms of the matrix elements J _ij with respect to the single-electron states of the atom is found for the matrix element describing the target atom in the formula for the differential cross section. The matrix elements J _ij are averaged over the relative orientation of the momentum transferred in the collision and the symmetry axis of the electronic orbitals of the target atom, using the single-electron Rutaan-Hartree-Fock wave functions. The algebraic representation of the matrix elements J _ij makes it possible to perform calculations for atoms with any value of Z. The model developed is used to calculate the cross sections σ_Σ and characteristic scattering angles θ_c for the process of electron loss by H^? ions with energy E = 0.1–100 MeV in targets consisting of atoms with Z = 2–54. It is shown that σ_Σ ∝ E ^?1 and θ_c ∝ E ^?1/2 for all Z, and for fixed E the behavior of σ_Σ(Z) and θ_c(Z) is determined by the order of filling of the electronic shells of the target atoms (the ionization potential). The computational results are analyzed and compared with the experimental data and the results of other calculations.     

Multiple ionization of argon accompanied by electron loss and capture of 0.22-6.35 MeV C^q＋ ions

In this paper a projectile ions recoil ions coincidence technique is employed to investigate the target ionization and projectile charge state changing processes in the collision of 0.22-6.35 MeV Cq^＋ （q = 1 - 4） ions with argon atoms. The partial cross section ratios of the double, triple, quadruplicate ionization to the single ionization （or the single capture） of argon associated with single electron loss （or single electron capture） by the projectile are measured and compared with the previous experimental results. In the present experiment, it is observed that the ratios of ionization cross sections R associated with single loss and single capture depend strongly on the projectile charge state and vary significantly with different reaction channels as impact energy increases. In addition, this paper gets empirical scaling laws for the ionization cross section ratios R corresponding to the projectile single loss and finds that the ratios of the double ionization to the single ionization associated with single electron capture remain constant in the present energy range.     

Resonant charge exchange with the p-electron transition

The asymptotic resonant charge exchange theory is developed for slow collisions of atoms and ions with valent p-electrons. Because of a small rotation angle of the molecular axis in the course of the p-electron transition, the resonant charge exchange cross section is not sensitive to the rotational energy of colliding particles, and the cross sections are nearly equal for cases “a”, “b”, and “d” of the Hund coupling, and also for cases “c” and “e” of the Hund coupling. The cross sections of the resonant charge exchange process are evaluated under various conditions and for various elements of the periodical table with p-electron shells of atoms and ions.     

K-shell ionization cross sections in nearly symmetric collisions by S and Cl impact

K-shell ionization cross sections in collisions of S and Cl ions with target atoms with atomic numberZ ₂=11–22 have been measured in the energy range from 3.9 to 48 MeV. The data are interpreted in terms of the statistical model of electron diffusion to the continuum. The distribution ofK-vacancies between the projectile and the target atoms are discussed in the framework of the vacancy sharing process.     

Ionization cross sections and rate coefficients for the ground state of AsI-like ions

Detailed level-by-level calculations of cross sections and rate coefficients for electron impact direct ionization and excitation-autoionization of AsI-like ions in the 3d ¹⁰4s ²4p ³ (⁴S_3/2) ground state have been performed. The cross sections are presented in the energy range near the threshold for the five ions Mo⁹⁺, Xe²¹⁺, Pr²⁶⁺, Dy³³⁺ and W⁴¹⁺. The rate coefficients are given for all the ions from Sr⁵⁺ to U⁵⁹⁺ in the AsI sequence at the seven electron temperatures (k T _e = 0.1E _I ,0.3E _I ,0.5E _I ,0.7E _I ,E _I ,2E _I and 10E _I , where E _I is the first ionization energy). The calculations include the contribution of direct ionization (DI) calculated using the Lotz formula approximation and the contributions of excitation-autoionization (EA) computed in the framework of the Distorted Wave (DW) approximation for the 4s ? nl, 3d ? nl and 3p ? nl resonant inner-shell excitations. The ionization enhancement due to the EA channels is presented as a function of Z along the AsI isoelectronic sequence. The present results show the great importance of the EA processes; an ionization enhancement factor of up to 6.5 is predicted for instance for Dy³³⁺ (Z = 66) at electron temperature of coronal equilibrium maximum abundance.     

H<Superscript>+</Superscript> and He<Superscript>2+</Superscript> impact charge transfer cross sections of magnesium

H⁺ impact single and He²⁺ impact single and double electron capture cross sections of magnesium atoms have been calculated in the modified binary encounter approximation (BEA). The accurate expressions of ion impact s_DE\sigma _{\Delta {E}} (cross section for energy transfer DE\Delta E) and Hartree-Fock momentum distributions of the target electrons have been used throughout the calculations. On the basis of the present work it is concluded that inner shell captures by H⁺ and He²⁺ ions incident on magnesium atoms contribute partly to single electron capture and partly to transfer ionization cross sections. The calculated He²⁺ impact double electron capture cross sections of magnesium are in reasonably good agreement with the experimental observations. This indicates the success of the present theoretical approach in study of charge transfer cross sections of atoms as indirect mechanisms do not interfere with double electron capture processes in this case.     

Autoionization cross section of potassium atom excited by electron impact

The autoionization cross section of potassium atoms excited by electron impact is measured in the energy range from the first autoionization threshold at 18.72 eV to 202 eV. The data are obtained by deter-mining the total intensity of electron spectra resulting from the decay of the 3p ⁵ n ₁ l ₁ n ₂ l ₂ autoionizing states. The cross section has two maxima, 1.8 × 10^?16 and 2.2 × 10^?16 cm², at 21 and 32 eV, respectively. The excitation dynamics of autoionization states suggests that the first maximum is associated with the resonance character of the near-threshold excitation. The second maximum, as well as the behavior of the cross section at energies above 50 eV, reflects the dynamics of electron excitation of quartet and doublet autoionizing states. The measured autoionization cross section is compared with known data for the total single ionization cross section of potassium atom by electron impact. The relative contribution of the autoionization cross section to the total single ionization cross section is found to reach 30% at 32 eV.     

Electron impact ionization rate coefficients and cross sections for highly ionized iron

Electron impact ionization cross sections for the ions Fe(XVII)-(XXVI) have been computed in a distorted wave exchange approximation. Analytic fits are provided for the cross section data, as well as for the rate coefficients assuming a Maxwellian electron velocity distribution. For ejection of a 2p ground state electron, the scaled ionization rate was found to depend linearly on the number of 2p electrons in the ion.     

Structure and thermal stability of AgCu chiral nanoparticles

Theoretical studies of electron impact double ionization cross sections of Ne⁵⁺ and Ne⁶⁺ ions have been performed in the binary encounter approximation (BEA). Direct double ionization (DDI) has been investigated in the modified double binary encounter model. The K-shell ionization cross sections have been also calculated in the BEA to take into account the contributions to double ionization from the ionization-autoionization (IA) process. The effect of the Coulombic field of the target ion on the incident electron has been considered in the present work. Accurate expression of σ _ΔE (cross section for energy transfer ΔE) and the Hartree-Fock (HF) velocity distributions for the target electrons have been used throughout the calculations. The present results are in overall moderate agreement with the experimental observations. Possible reasons behind the discrepancies between the theory and the experiment have been discussed.     

Scattering of slow neutrons by arsenic and selenium isotopes

Coherent neutron scattering lengths and free cross sections were measured for arsenic, for ordinary selenium and its isolated isotopes. By means of the Cristiansen filter technique the following scattering lengths for the bound atoms were obtained (in fm):b(As) =6.58(1) [b ₊=6.04(5) andb _?=7.47(8)],b(Se)=7.970(9),b(⁷⁶Se)=12.2(1),b(⁷⁷Se) =08.25(8),b(⁷⁸Se)=8.24(9),b(⁸⁰Se)=7.48(3) andb(⁸²Se)=6.34(8). Transmission measurements with neutrons of 1.26 eV and 5.19 eV resulted in an energy independent free scattering cross section for arsenic ofσ _{s, t}=5.40(3)b (in the eV-region). For ordinary selenium energy dependent free cross sections ofσ _{s, t}(1.26 eV)=7.9(1)b andσ _{s, t} (5.19 eV)=7.55(3)b were found. The results were compared with the resonance parameters of the nuclei and with different sets of potential scattering radii. Thus it could be concluded that there is no evidence for a bound state of the neutron-nucleus compound⁷⁵As+n but a clear evidence for strong bound levels of⁷⁶Se+n and⁷⁷Se+n.     

K-shell X-ray production for fluorine ions on target elements Ti to La

The production of target atomK-shell X-rays has been studied for 2 to 28 MeV fluorine ions incident on thin solid targets of 14 elements with atomic numbers Z₂=22 to 57. Total X-ray production cross sections, energy shifts ofK _α andK _β lines andK _α/K _β intensity ratios were measured with a Si(Li) detector. The results of cross section measurements are compared with theoretical predictions of inner shell ionization. In most cases, satisfactory agreement between measured cross sections and theoretical Coulomb ionization cross sections, corrected for the perturbation of the target atom by the projectile charge and for relativistic effects, was obtained.     

Photoionization of helium-like ions with excitation of <Emphasis Type="Italic">nl</Emphasis> states

Photoionization of helium-like ions accompanied by the excitation of the residual ion to the nl-state is considered. Calculations are made in first-order perturbation theory in the electron-electron interaction using Coulomb wavefunctions as the zeroth approximation. Formulas derived for the ionization cross sections exhibit scaling behavior in the target nuclear charge Z and principal quantum number n. Numerical calculations are performed in the entire nonrelativistic energy domain. Simple power expansions of the cross sections in Sommerfeld parameter ξ are obtained in the high- and low-energy limits. The results are compared with experiment.     

Transfer of a weakly bound electron in collisions of Rydberg atoms with neutral particles. II. Ion-pair formation and resonant quenching of the Rb(nl) and Ne(nl) States by Ca, Sr, and Ba atoms

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.     

类钠Ni~(17+)离子双电子复合过程理论研究

使用基于相对论多组态方法的FAC程序,研究了类钠Ni17+(3s)离子通过双激发态Ni16+(3pnl,3dnl)(Δn=0激发)的双电子复合过程,得到了态选择的双电子复合截面和速率系数,并与文献中的实验和理论数据进行了对比.结果发现,计算通过3p3/210l和3p1/211l共振态的双电子复合积分截面在实验误差范围内与实验测量很好地符合,并好于全相对论的多体微扰理论计算结果.结合量子亏损理论,发现包含高里德伯态的共振双激发态的辐射跃迁和自电离速率具有较好的标度关系,利用该关系给出了近激发阈值的所有共振态的双电子复合积分截面和速率系数.比较3pnl和3dnl两个系列,发现在低温(大约小于100eV)等离子体情况下前者速率系数比后者大,更高的温度后者大.