State-selective Cross Sections Research Articles

Rate coefficients for C and O2 reactive collisions relevant to interstellar clouds from QCT and machine learning.

The chemical reactions between certain interstellar molecules are exothermic in nature and barrierless in the entrance channel, allowing these reactions to occur rapidly even at low astronomical temperatures, e.g., C and O2 interaction. Obtaining detailed rovibrational transition parameters for the reaction between C and O2, such as state-selected rate coefficients, is crucial for studying the associated atmospheric and astronomical environments. Hence, this work presents an approach that combines quasi-classical trajectory calculations with machine learning techniques based on Neural Network (NN) and Gaussian Process Regression (GPR) to determine state-selected rate coefficients. Employing this approach, we significantly reduced the computational requirements while simultaneously obtaining the accurate state-selected reaction cross sections and rate coefficients for the collision of C and O2. Both the NN-based and GPR-based models established in this work accurately predict the results calculated from explicit numerical calculations in the explored temperature range of 50-1500K, achieving a coefficient of determination R2 > 0.96. Most importantly, the current work provides the most comprehensive dataset of rovibrational rate coefficients of v = 0-4, j = 0-70 → v' = 0-15 for the astrophysical modeling of the C-O2 collision system.

State selective total and angular differential cross sections for positronium formation in [formula omitted]+[formula omitted] collisions

State-selective total and angular differential cross sections for positronium formation are presented in the collision of positron with helium atoms in their ground state by using the four-body formalism of the boundary-corrected continuum-intermediate-states approximation. The main purpose of the present study is to investigate the relative importance of intermediate ionization continuum states that has been incorporated with a suitable choice of distorting potential. In addition, the nine-dimensional integrals of the transition amplitude are analytically reduced to a one-dimensional real integral, which can be easily calculated numerically. The influence of the target static electron correlations on the capture probability is investigated using the different bound-state wave functions of He. The theoretical model for the calculation is fairly accurate and predicts a number of interesting features of the state-selective total and differential cross sections in the range of positron impact energy varies from 20 to 250eV. The total cross sections are highly peaked at an impact energy of 50 eV. The results are compared with those of other theories and the available experimental data. The present theoretical results and other measurements show satisfactory agreement in the wide energy range. Moreover, surface plots for the state-selective differential cross sections are also presented to illustrate the interesting feature of the positronium formation in this collision process.

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.

Experimental measurement of state selective double electron capture in 1.4-20 keV/u Ar<sup>8+</sup> collision with He

Electron(s) capture in highly charged ions collision with atoms and molecules is a fundamental process related to the electron transition between bound states belongs to two atomic-centers. The X-ray emission following electron capture is important for X-ray astrophysical modeling, fusion plasma diagnosing, and ion irradiated biophysics. Over past decades, momentum-imaging cold-target recoil ion momentum spectroscopy is one of significantly developed techniques and has been widely applied to measure the quantum state-selective population in electron(s) capture processes. Based on the cold target recoil ion momentum spectroscopy mounted at the 150 kV highly charged ion platform in Fudan University, the state-selectivity of double electron capture in 1.4-20 keV/u Ar<sup>8+</sup> on He collision was measured, and the relative cross sections of the 3<i>l</i>3<i>l</i>’to 3<i>l</i>7<i>l</i>’ double excited states were obtained. It is found that with the increase of collision energy, more quantum state-selectivity channels are open in the double electron capture (DEC) of Ar<sup>8+</sup>-He collision. It is also found that the relative cross section of the quantum state population is strongly dependent on the collision energy of the projectile ion. This present measurement not only enriches the state-selective cross-section repository and collision dynamics for highly charged ion charge exchange processes, but also provides experimental benchmarks for the available theoretical calculations.

State-selective charge exchange cross sections in collisions of highly-charged sulfur ions with helium and molecular hydrogen

The state-selective cross section data are useful for understanding and modeling the x-ray emission in celestial observations. In the present work, using the cold target recoil ion momentum spectroscopy, for the first time we investigated the state-selective single electron capture processes for S q+–He and H2 (q = 11–15) collision systems at an impact energy of q × 20 keV and obtained the relative state-selective cross sections. The results indicate that only a few principal quantum states of the projectile energy level are populated in a single electron capture process. In particular, the increase of the projectile charge state leads to the population of the states with higher principal quantum numbers. It is also shown that the experimental averaged n-shell populations are reproduced well by the over-barrier model. The database is openly available in Science Data Bank at 10.57760/sciencedb.j00113.00091.

Theoretical investigation of electron capture processes in slow O7+–H collisions

Aims. The total and n-, l-, and S -resolved single-electron-capture cross sections for the collisions of O7+ with atomic hydrogen are studied in the energy region from 10−3eV u−1−5keV u−1. Methods. These state-selective cross sections were calculated by employing the full quantum-mechanical molecular-orbital close-coupling (QMOCC) method. The ab initio multireference single- and double-excitation configuration interaction approach, with optimized atomic basis sets to accurately describe the highly excited states, was used to obtain the adiabatic potentials and the radial and rotational coupling matrix elements that are required in the QMOCC calculation. Results. Our results are compared with other available theoretical and experimental data. The n = 5 manifold is the dominant reaction channel for the chasrge-transfer process for this collision system over the entire energy range, and our results agree better with the experimental data than the other theoretical results in the energy region in which they overlap because we included the necessary highly excited states in the expansion basis set. These charge-exchange cross-section data are useful for understanding and modeling the X-ray emission in astrophysical environments.

Study of single electron capture in O6+ + He collisions

Research on electron capture (EC) process are undoubtedly helpful for maturing theoretical models on ion-induced collision especially for low-energy region. In this work, a two-active-electron semiclassical asymptotic-state close-coupling method was used to calculate the total and l-solved state-selective single EC cross sections of O6+ + He collisions in the energy range of 0.3–100 keV u−1, accompanied with experimental measurements in the energy range of 2.63–37.5 keV u−1 with an uncertainty of 11% in good agreement. Above 4.5 keV u−1, the state-selective cross section of n = 5 was reported experimentally for the first time. Calculations with multiple theoretical methods were gathered and compared with present calculations. The importance of two-active-electrons correlation and large basis sets in theoretical calculations was found, and discrepancies between previous theoretical and experimental results can be explained by the present results.

Electron capture and ionisation in He^{2+} collisions with H_2

State-selective non-dissociative electron capture and ionisation cross sections are calculated for collisions between bare helium-ions and molecular hydrogen. The two-centre wave-packet convergent close-coupling approach is used and the hydrogen molecule is represented as an effective one-electron target. For the electron-capture cross section, our results are in good agreement with experimental measurements at energies above 100 keV/u. However, near the peak of the cross section, they are larger than the experimental data. The total ionisation cross section is also in good agreement with experiment, particularly at low and high energies. The results for the state-selective electron-capture cross section are generally in good agreement with the limited experimental measurements. However, we find that our results appear to consistently overestimate the experimental data for electron capture into the s states at intermediate energies. The present results are the first calculations capable of producing electron capture and ionisation cross sections over a wide incident energy range within a single unified theoretical framework.Graphical

State-selective Charge Exchange in 19.5–100 keV amu−1 O6+ Collision with He and H2

The cross sections of state-selective charge exchange (CX) between highly charged ions and neutrals are important for modeling extreme ultraviolet and soft X-ray emissions in many astrophysical objects with hot plasma impacting cold media. By using cold-target recoil-ion momentum spectroscopy, we measure O6+ CX collisions with He and H2 in the collision energy range of 19.5 to 100 keV amu−1. The relative cross sections of state-selective single CX are reported for electron capture into O5+(1s 2 nl) n = 2, 3, 4, 5, ≥6 and n = 3, 4, 5, ≥6 for He and H2, respectively. With the collision energy increasing to 100 keV amu−1, the main capture channel shifts to higher n for both target species as compared to available theoretical results. We also report state-selective cross sections for double CX with He, where doubly excited states of with being 2s 2 (1S), 2s2p (1P), 2p 2 (1D), and 2p 2 (1S) [symmetric configurations] and 2s3l, 2p3l−2s4l, and 2s5l−2p5l [asymmetric configurations] are distinguished. It is found that the contributions of doubly excited states with asymmetric configurations are dominant and symmetric configurations increasingly come into play with the increase of collision energy. The present results provide experimental benchmarks available for theoretical calculations.

Mutual neutralization in low-energy collisions of Na+ + H- ions

Abstract The low-energy mutual neutralization (MN) reactions Na+ + H- → Na(nl) + H have been studied by employing the full quantum-mechanical molecular-orbital close-coupling (QMOCC) method over a wide energy range of 10-3 to 103 eV/u. Total and state-selective cross sections have been investigated and compared with the available theoretical and experimental data, and the state-selective rate coefficients for the temperature range of 100-10000 K have been obtained. In the present work, all the necessary highly excited state are included, and the influence of rotational couplings and 10 active electrons are considered. It is found that in the energy below 10 eV/u, the Na(4s) state is the most dominant exit state with a contribution of approximately 78% to the branch fraction, which is in best agreement with the experimental data. For energies above 10 eV/u, the MN total cross section is larger than those obtained in other theoretical calculations and shows a slow decreasing trend because the main exit states change, when the energy is above 100 eV/u, the dominant exit state becomes the Na(3p) state, while the Na(4s) state becomes the third most important exit state.

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.

One-electron transfer from helium targets to protons: the BCIS-4B and CDW-3B methods for state-selective and state-summed total cross sections vs measurements

One-electron transfer from helium targets to protons: the BCIS-4B and CDW-3B methods for state-selective and state-summed total cross sections vs measurements

Dissociation cross sections and rates in O2 + N collisions: molecular dynamics simulations combined with machine learning.

The collision-induced dissociation reaction of O2 (v, j) + N, a fundamental process in nonequilibrium air flows around reentry vehicles, has been studied systematically by applying molecular dynamics simulations on the 2A', 4A' and 6A' potential energy surfaces of NO2 in a wide temperature range. In particular, we have directly investigated the role of the 6A' surface in this process and discussed the applicability of the simplified approximate rate models proposed by Esposito et al. and Andrienko et al. based on the lowest two surfaces. The present work indicates that the state-selected dissociation of O2 + N is dominated by the 6A' surface for all except for the low-lying O2 states. Furthermore, a complete database of rovibrationally detailed cross sections and rate coefficients is a prerequisite for modeling the relevant nonequilibrium air flows in spacecraft reentry. Here, the combination of the quasi-classical trajectory (QCT) and the neural network (NN) has been proposed to predict all state-selected dissociation cross sections and further construct dissociation parameter sets. All NN-based models established in this work accurately reproduce the results calculated from QCT simulations over a wide range of rovibrational quantum numbers with R2 > 0.99. Compared with the explicit QCT simulations, the computational requirement for predicting cross sections and rates based on the NN models significantly reduces. Finally, thermal equilibrium rate coefficients computed from NN models match remarkably well the available theoretical and experimental results in the whole temperature range explored.

The BCIS-4B method for state-selective and state-summed total cross sections: Proton–helium​ charge exchange at 10–4000 keV

This work is on single electron capture by protons from helium targets at intermediate and high impact energies (10–4000 keV). Assessed is the overall performance of the second-order four-body boundary-corrected continuum intermediate state (BCIS-4B) method by detailed comparisons with all the available measurements. The state-selective Qnl,Qn and state-summed QΣ total cross sections are computed for n≤4, including all the sub-levels. Cross sections Qn are the sum of Qnl for 0≤l≤n−1. The state-summed cross sections QΣ are obtained by using Qn exactly for 1≤n≤3 and approximately for n≥4 through the Oppenheimer n−3 scaling rule. Overall, the measured cross sections are extremely favorably represented by the BCIS-4B method for Qnl,Qn and QΣ, even toward the lowest part of the considered intermediate energy region. Most notably, at all the energies above 10 or 20 keV, e.g. cross sections Q2p,Q3p and Q3d from the BCIS-4B method are in excellent agreement with the corresponding experimental data. This is very important since it is precisely for the non-spherically symmetric states (l≠0) of the captured electron that the existing discrepancies between measurements and other theories are the largest or even enormous.

Electron excitation processes in low energy collisions of hydrogen–helium atoms

The electron excitation processes of H(1s) + He(1s2) → H(2s/2p) + He(1s2) are studied in impact energy range of 20--2000 eV/u by using the quantum-mechanical molecular orbital close-coupling (QMOCC) method. Total and state-selective cross sections have been obtained and compared with the available theoretical and experimental results. The results agree well with available measurements in the overlapping energy regions overall. The comparison of our results with other theoretical calculations further demonstrates the importance of considering a sufficient number of channels. The datasets presented in this paper, including the excitation cross sections, are openly available at https://www.doi.org/10.57760/sciencedb.j00113.00083.

Nl-Selective Classical Charge-Exchange Cross Sections in Be4+ and Ground State Hydrogen Atom Collisions

Charge-exchange cross sections in Be4+ + H(1s) collisions are calculated using the three-body classical trajectory Monte Carlo method (CTMC) and the quasi-classical trajectory Monte Carlo method of Kirschbaum and Wilets (QCTMC) for impact energies between 10 keV/amu and 300 keV/amu. We present charge-exchange cross sections in the projectile n = 2 and nl = 2s, 2p states. Our results are compared with the previous quantum-mechanical approaches. We found that the QCTMC model is a powerful classical model to describe the state-selective charge-exchange cross sections at lower impact energies and the QCTMC results are in good agreement with previous observations.

Total, state-selective, and angular-differential cross sections for electron capture in He2++H collisions in warm dense plasmas

The total, state-selective, and angular-differential cross sections for He2++H collision system in warm dense plasmas are studied by using the two-center atomic orbital close-coupling method in the energy range 0.1–300 keV/u. The calculations are performed for plasma density and temperature ranges ne ∼1018 to ∼1021 cm−3, Te = 0.3 eV–1.2 eV, typical for the H- and He-rich white dwarfs. The plasma environments are described by a unified screened potential involving electron degeneracy, finite-temperature gradient, and exchange-correlation effects. The results for H++H cases with the same plasma parameters are also presented for comparison to elucidate the discrepancies of plasma screening effects on the electron capture dynamics for collision systems with different nuclear symmetries. Moreover, classical Debye screening results are also given for comparison to clarify the effects of quantum correlations in warm dense plasmas on the electron capture dynamics. The present work is expected to provide theoretical and data support for the astrophysical plasmas.

State-selective electron capture in collisions of fully stripped neon ions with ground-state hydrogen

Electron capture and ionisation in bare neon ion collisions with ground-state atomic hydrogen are modelled over the energy range from 1 to 2000 keV/u using the two-center semiclassical wave-packet convergent close-coupling method. The calculated total electron-capture cross section agrees very well with the molecular and atomic orbital close-coupling calculations at low and intermediate energies. Our results slightly overestimate the experimental results by Meyer et al [1985 Phys. Rev. A 32 3310], but underestimate the measurements by Panov et al [1983 Phys. Scr. T3 124] available only below 10 keV/u. At higher energies, where there are no measurements, the results also agree very well with the classical trajectory Monte-Carlo results. Partial n and nl-resolved electron-capture cross sections, important for fusion plasma diagnostics, have also been calculated for final states up to n = 10, where n and l are the final state principal and angular momentum quantum numbers, respectively. The results are generally in good agreement with the atomic calculations. However, due to the finer energy grid used, we are able to detect pronounced oscillations in the state-selective cross sections for n ⩾ 8 at energies below 10 keV/u. Our results for the total ionisation cross section are overall in good agreement with the latest classical trajectory Monte-Carlo results.

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 electron capture cross sections in collision between fully striped ions and ground state hydrogen atom—Classical treatment of the collision

We present a state-selective electron capture cross sections database from the ground state hydrogen atom. A standard three-body classical trajectory Monte Carlo (CTMC) and quasi-classical trajectory Monte Carlo (QCTMC) models were employed for impact energies between 10 and 200 keV/amu. The projectile ions are H+, He2+, Li3+, Be4+, B5+, C6+, N7+, and O8+. The cross sections are tabulated for each value of the final quantum numbers n, l, m, summed over m for the given n and l and over l and m for the given n. The maximum quantum number nmax is set to 4 for H+, He2+ and Li3+, as well as to 5 for Be4+, B5+, C6+, N7+ and O8+, respectively.