Cross Sections For Single Electron Capture Research Articles

The n-resolved single-electron capture in slow O6+–Ne collisions

Abstract A study of single-electron capture (SEC) in 18–240 keV O6+–Ne collisions has been conducted employing a combination of experimental and theoretical methodologies. Utilizing a reaction microscope, state-selective SEC cross sections and projectile scattering angle distributions were obtained. The translational energy spectra for SEC reveal the prevailing capture into n = 3 states of the projectile ion, with a minor contribution from n = 4 states. Notably, as the projectile’s energy increases, the relative contribution of SEC n = 4 states increases while that of SEC n = 3 states diminishes. Furthermore, we computed state-selective relative cross sections and angular differential cross sections employing the classical molecular Coulomb over-the-barrier model (MCBM) and the multichannel Landau–Zener (MCLZ) model. A discernible discrepancy between the state-selective cross sections from the two theoretical models is apparent for the considered impact energies. However, regarding the angular differential cross sections, an overall agreement was attained between the current experimental results and the theoretical results from the MCLZ model.

Electron Capture from Molecular Hydrogen by Metastable Sn2+* Ions

Over a wide and partly overlapping energy range, the single-electron capture cross-sections for collisions of metastable Sn2+(5s5p Po3) (Sn2+∗) ions with H2 molecules were measured (0.1–10 keV) and calculated (0.3–1000 keV). The semi-classical calculations use a close-coupling method on a basis of electronic wavefunctions of the (SnH2)2+ system. The experimental cross-sections were extracted from double collisions in a crossed-beam experiment of Sn3+ with H2. The measured capture cross-sections for Sn2+∗ show good agreement with the calculations between 2 and 10 keV, but increase toward lower energies, whereas the calculations decrease. Additional Landau–Zener calculations were performed and show that the inclusion of spin-orbit splitting cannot explain the large cross-sections at the lowest energies which we now assume to be likely due to vibrational effects in the molecular hydrogen target.

Single Electron Capture in Collisions of Fast Ions with Molecular Hydrogen in the Impact Parameter Representation

A theoretical method for evaluating the single-electron capture (SEC) cross sections in collisions of fast ions with a ground-state H2molecule is presented. The scattering problem for ion-molecule collisions is formulated in the impact parameter representation using the relation between the quantum-mechanical amplitude and quasi-classical impact parameter one. The capture amplitudes and corresponding probabilities of capture to (nlm) states of an incident ion are derived within the framework of the Brinkman–Kramers approximation. The general expressions for the SEC probability amplitudes ton-states, summed overlandmquantum numbers, are deduced, from which the corresponding SEC probabilities can be then calculated using a procedure of multichannel normalization. The dependence of the differential cross sections, integrated over projectile impact parameters, on the molecular orientation for charge exchange in H++ H2collisions is considered and compared with measurements and other calculations. Total SEC cross sections, integrated over the molecular orientations and summed overn-states for several bare and dressed ions, are calculated and compared with available experimental data and results of calculations by means of other theoretical methods.

Ionization and electron capture in O6+ + He collisions at 0.86, 1.5, 1.94 a.u. velocities

Using the projectile-ion-recoil-ion coincidence method, relative cross sections for single-electron capture, single ionization, double-electron capture, transfer ionization and double ionization in collisions of multiply charged O6+ ions with helium atoms have been measured at 0.86, 1.5, 1.94 a.u. velocities. Calculations based on the semi-classical over-barrier model in the framework of independent electron approximation is employed to discuss various competing reaction mechanisms. These results are also compared with other experimental and theoretical results available in the velocity range considered.

Cross sections for single-electron capture from heliumlike targets by fast heavy nuclei

Single charge-exchange in collisions of heavy bare nuclei with the ground state of two-electron atomic targets is described perturbatively as a four-body problem. The employed four-body boundary-corrected continuum intermediate state (BCIS-4B) method considers the correlated and uncorrelated target wave functions ${\ensuremath{\varphi}}_{i}.$ A thorough examination is performed for the formation of any final hydrogen-like $nlm$ state of the captured electron. For arbitrary projectile and target nuclear charges, the nine-dimensional integral in the transition amplitude is reduced to a two-dimensional numerical quadrature. The general analysis is applied to one-electron capture by protons from helium targets beginning with the lower edge (10 keV) of intermediate energies and extending to the higher (12.5 MeV) domain. These include the main peaks (Massey, Thomas) due to single and double scattering, respectively. The results encompass over 70 state-selective and state-summed cross sections $(n\ensuremath{\le}6,\phantom{\rule{0.16em}{0ex}}0\ensuremath{\le}l\ensuremath{\le}n\ensuremath{-}1,\phantom{\rule{0.16em}{0ex}}\ensuremath{-}l\ensuremath{\le}m\ensuremath{\le}l).$ In comparison to measurements, the electronic correlations in ${\ensuremath{\varphi}}_{i}$ greatly improve the overall performance of the BCIS-4B method around the Massey peak, below about 100 keV. Moreover, while largely outperforming the three-body boundary-corrected continuum intermediate state method, the cross sections in the BCIS-4B with the correlated ${\ensuremath{\varphi}}_{i}$ compare excellently overall with the available experimental data at 10 to 12 500 keV. Hence, the BCIS-4B method, with its built-in two main capture mechanisms (one-step Massey and two-step Thomas) is capable of spanning impact energies covering three or more orders of magnitude at which the state-summed cross sections vary over 11 orders of magnitude.

Single-electron transfer from helium atoms to energetic multiply-charged nuclei

The three-body boundary-corrected continuum intermediate state (BCIS-3B) method is employed to compute single-electron capture cross sections. These data are for collisions in which a target helium atom in its ground state He(1s2) is impacted by multiply charged nuclei (specifically H+,He2+,Li3+,Be4+,B5+,C6+,N7+,O8+,F9+). Intermediate and high projectile energies are considered (20 keV/amu-3 MeV/amu). The obtained results are tabulated for total cross sections (state-selective Qnlm as well as state-summed Qnl,Qn and QΣ). Cross section Qnlm corresponds to a fixed triple of the hydrogenlike quantum numbers {n,l,m}. In Qnl,Qn and QΣ, the sums over m∈[−l,l],l∈[0,n−1] and n∈[1,nmax] are carried out, respectively. For n>nmax in QΣ, the Oppenheimer n−3 scaling rule is adopted. The values of nmax are set to 4 (for H+,He2+,Li3+), 5 (for Be4+), 6 (for B5+) and 7 (for C6+,N7+,O8+,F9+). Exhaustive comparisons of the theoretical findings for QΣ with the corresponding experimental data are performed. It is determined that the BCIS-3B method is in excellent agreement with the available measurements. The present database for the examined capture processes is deemed to be of notable practical usefulness in versatile applications of particular relevance to plasma physics, astrophysics, fusion research and ion therapy in medicine.

State-selective differential and total cross sections for single-electron capture in $$He^{+}$$–He collisions

State-selective differential and total cross sections for single-electron capture in $$He^{+}$$–He collisions

State-selective single-electron capture in intermediate-energy C4+ + He collisions

A combined experimental and theoretical study on single capture in 15--$50\phantom{\rule{0.28em}{0ex}}\mathrm{keV}/\mathrm{u}\phantom{\rule{0.16em}{0ex}}{\mathrm{C}}^{4+} +$ He collisions was performed. State-selective single-electron capture cross sections and projectile scattering angle distributions were obtained by using a reaction microscope. A comparison of the state-selective cross sections with theoretical calculations based on the two-active-electron semiclassical atomic-orbital close-coupling method showed an excellent agreement for the considered impact energies. For the angular differential cross sections, an overall agreement was also obtained between the present experimental and theoretical results. Simulations performed using an extended Fraunhofer-type diffraction model suggest that the undulatory structures observed at small scattering angles for capture to ${\mathrm{C}}^{3+}(1{s}^{2}2s$) and ${\mathrm{C}}^{3+}(1{s}^{2}2{p}_{0}$) can be interpreted as the diffraction pattern of the incident projectile de Broglie wave confined by an aperture defined as the region around the target where the considered capture process is likely. The strong competition between single-electron capture to ${\mathrm{C}}^{3+}(1{s}^{2}2{p}_{0}$) and ${\mathrm{C}}^{3+}(1{s}^{2}2{p}_{1}$) is also discussed to interpret the differences observed between their respective differential cross sections.

Calculation of electron capture probability of energetic protons colliding with rare-gas atoms: A comparison study on four methods

We calculate the probability of electron capture of energetic protons colliding with rare-gas atoms, comparing four methods based on time-dependent density-functional theory (TDDFT). By approximating the pair-correlation function of the system with an explicit dependence on the fractional number of bound electrons, a new effective model of pair-correlation function is built up. Benchmark calculations are given over a wide range of impact energy, demonstrating that the new designed read-out functional reproduces quite accurately the single-electron capture cross sections and the double-electron capture features which were not properly described by previous TDDFT calculations.

Radiative Cascade Repopulation of 1s2s2p 4P States Formed by Single Electron Capture in 2–18 MeV Collisions of C4+ (1s2s 3S) with He

This study focuses on the details of cascade repopulation of doubly excited triply open-shell C3+(1s2s2p)4P and 2P± states produced in 2–18 MeV collisions of C4+(1s2s3S) with He. Such cascade calculations are necessary for the correct determination of the ratio R of their cross sections, used as a measure of spin statistics [Madesis et al. PRL 124 (2020) 113401]. Here, we present the details of our cascade calculations within a new matrix formulation based on the well-known diagrammatic cascade approach [Curtis, Am. J. Phys. 36 (1968) 1123], extended to also include Auger depopulation. The initial populations of the 1s2snℓ4L and 1s2snℓ2L levels included in our analysis are obtained from the direct nℓ single electron capture (SEC) cross sections, calculated using the novel three-electron close-coupling (3eAOCC) approach. All relevant radiative branching ratios (RBR) for n≤4 were computed using the COWAN code. While doublet RBRs are found to be very small, quartet RBRs are found to be large, indicating cascade feeding to be important only for quartets, consistent with previous findings. Calculations including up to third order cascades, extended to n→∞ using an n−3 SEC model, showed a ∼60% increase of the 1s2s2p4P populations due to cascades, resulting, for the first time, in R values in good overall agreement with experiment.

Single- and Double-Electron Capture Processes in Low-Energy Collisions of N4+ Ions with He**Supported by the National Natural Science Foundation of China under Grant Nos. 11774344, 11474033 and 11574326, and the National Key Research and Development Program of China under Grant No. 2017YFA0402300.

We investigate the electron capture processes of N4+(1s22s) colliding with He(1s2) in the energy range of 10–1700 eV/amu using the quantum-mechanical molecular-orbital close-coupling (QMOCC) method. Total and state-selective single-electron capture and double-electron capture (SEC and DEC) cross sections are obtained and compared with other available studies. The results agree better with the experimental data in both trend and magnitude when the electron translation factor (ETF) effects are included. Our results indicate that both the SEC and DEC processes play important roles in the considered energy region. For the SEC processes, the N3+(1s22p2) + He+(1s) states are the dominant capture states, and the N2+(1s22s2p2) + He2+ states are the main DEC states.

Single electron capture cross sections for collisions of multi-charged ions with helium-like atomic system

SynopsisA four-body distorted wave method (DW-4B) is applied to calculate the total cross section for single electron capture in the collisions of multi-charged ions with helium-like atomic system. The proper long range behavior of the Coulomb potential is introduced. The present theoretical method is satisfactory in the intermediate and high-energy regime and is quite reliable compared to other theoretical methods.

Single-electron capture in ion-ion collisions

The prior versions of the three-body boundary-corrected first Born approximation (CB1-3B) and the three-body boundary-corrected continuum intermediate states method (BCIS-3B) are applied to calculate the state-selective and state-summed total cross sections for single-electron capture from hydrogen-like ion targets (He+, Li2+) by fast completely stripped projectiles (H+, He2+, Li3+). All calculations are carried out for single-electron capture into arbitrary n l m final states of the projectiles, up to n = 4. The contributions from higher n shells are included using the Oppenheimer n?3 scaling law. The present results are found to be in satisfactory agreement with the available experimental data.

Collision dynamics of proton to water dimer at 250 eV

Applying a real-space, real-time implementation of time-dependent density functional theory coupled to molecular dynamics (TDDFT-MD) non-adiabatically, we study the ionization and fragmentation of water dimer in collision with a proton at 250 eV. Four different incident orientations with various impact parameters are employed to account for orientation effects. The reaction channels, electronic density evolution, scattering pattern and energy loss of proton are obtained. We find that proton is scattered away for all impact parameters and the head-on collision effects the energy loss of proton dominantly as well as the scattering angle. The locations of peaks of the scattering angles are similar to those corresponding to the energy loss. The single-electron capture, the double-electron capture as well as the total electron capture cross-sections are obtained. We find that the single-electron capture cross-section contributes most to the total electron capture cross-section and the calculated total electron capture cross-section is in reasonable agreement with experimental and other theoretical results with respect to water gas and liquid water.

Capture and Dissociative Capture of a Single Electron in the Process of Interaction of Doubly Charged Ions with CO Molecules

The absolute cross sections of single-electron capture and single-electron capture with dissociation in the interaction between incident He2+, C2+, N2+, and O2+ ions with energies from 6.4 to 36.4 keV and СО molecules were measured. It is demonstrated that the cross section of dissociative capture is much larger than the cross section of single-electron capture for O2+ projectile ions. A qualitative explanation for this effect is provided.

The influence of pseudo states on the single-electron capture processes in low-energy collisions of N5+ with He

The nonradiative single-electron capture (SEC) processes for N5+(1s2) colliding with He atoms are investigated by using the quantum-mechanical molecular-orbital close-coupling method. Total and state-selective SEC cross sections are obtained in the energy range of 3–1700 eV amu−1, for which the ab initio potential curves and nonadiabatic coupling matrix elements (involving physical and pseudo states) are computed by using the multireference single- and double-excitation configuration-interaction method. It is found that the pseudo states are also important to obtain the convergent results, especially in the low-energy region. Moreover, our results indicate that the n = 3 states are the dominant states in the considered energy region, and that the electron translation factor effects become important when the energy is above 1 keV amu−1. In addition, it is observed that the total and state-selective cross sections for SEC are in general agreement with all available experimental data.

Процессы захвата и диссоциативного захвата одного электрона при взаимодействии двухзарядных ионов с молекулами CO

AbstractThe absolute cross sections of single-electron capture and single-electron capture with dissociation in the interaction between incident He^2+, C^2+, N^2+, and O^2+ ions with energies from 6.4 to 36.4 keV and СО molecules were measured. It is demonstrated that the cross section of dissociative capture is much larger than the cross section of single-electron capture for O^2+ projectile ions. A qualitative explanation for this effect is provided.

Charge Exchange of Highly Charged Ne and Mg Ions with H and He

Abstract Cross sections for single electron capture (SEC), or charge exchange (CX), in collisions of Ne(8–10)+ and Mg(8–12)+ with H and He, are computed using an approximate multichannel Landau–Zener (MCLZ) formalism. Final-state-resolved cross sections for the principal (n), orbital angular momentum (ℓ), and where appropriate, total spin angular momentum (S) quantum numbers are explicitly computed, except for the incident bare ions Ne10+ and Mg12+. In the latter two cases, -resolution is obtained from analytical ℓ-distribution functions applied to n-resolved MCLZ cross sections. In all cases, the cross sections are computed over the collision energy range 1 meV/u to 50 keV/u with LZ parameters estimated from atomic energies obtained from experiment, theory, or, in the case of high-lying Rydberg levels, estimated with a quantum defect approach. Errors in the energy differences in the adiabatic potentials at the avoided crossing distances give the largest contribution to the uncertainties in the cross sections, which are expected to increase with decreasing cross section magnitude. The energy differences are deduced here with the Olson–Salop–Tauljberg radial coupling model. Proper selection of an ℓ-distribution function for bare ion collisions introduces another level of uncertainty into the results. Comparison is made to existing experimental or theoretical results when available, but such data are absent for most considered collision systems. The -resolved SEC cross sections are used in an optically thin cascade simulation to predict X-ray spectra and line ratios that will aid in modeling the X-ray emission in environments where CX is an important mechanism. Details on a MCLZ computational package, Stueckelberg, are also provided.

Differential and total cross sections for charge transfer and transfer-excitation in ion-helium collisions

Total cross sections for single charge transfer in collisions of multicharged bare ions with ground-state helium atoms at incident energy ranging from 40 to 5000 keV/amu have been calculated in the framework of a four-body model of final channel distorted-wave (FC-DW-4B) approximation. In this formalism, distortion in the final channel related to the Coulomb continuum of the target and the Coulomb interaction between the passive electron in the target with the projectile are included. In all cases, total single electron-capture cross sections have been calculated by summing over all contributions up to $n=3$ shells and subshells. It has been observed that the contribution of the capture cross sections into excited states have insignificant contributions for symmetric collisions. Comprehensive comparisons are made between the four body model of boundary corrected continuum intermediate-state approximations [Phys. Rev. A 83, 032706 (2011)] and the present FC-DW-4B model. The main purpose of the present study is to investigate the relative importance of dynamic electron correlation and the role of passive electron in the target at intermediate and high impact energies. In addition, projectile angular differential cross sections (DCS) for charge transfer and transfer-excitation in $p\text{-He}$ collisions are calculated at different impact energies. At low projectile energies, the present DCS data exhibits the typical steeply decreasing dependence on the projectile scattering angles, whereas at high impact energies, the double-scattering region centered on the Thomas angle is obtained. Detailed comparisons with the available experimental data and other theories are reported with the purpose of further assessing the relevance of the present model at different impact energies. Overall, the calculated cross sections show good agreement with the available experimental findings.

Total single electron capture cross sections for collisions of multicharged ions with He atoms

The three-body boundary corrected Born distorted wave method is utilized to compute the total cross sections for single electron capture in the collisions of the fast ions (, He, Li, and ) with helium targets in their ground states. Both post and prior forms of the transition amplitude are obtained in terms of two-dimensional integrals and the total cross sections are computed via three-dimensional numerical integrations. The present results show reasonable agreement with the measurements and three- and four-body theoretical computations, especially at higher incident energies.