State-selective Cross Sections Research Articles

State selective classical electron capture cross sections in Be4+ \u2009+\u2009H(1s) collisions with mimicking quantum effect

We present state-selective electron capture cross sections in collision between Be4+ and ground state hydrogen atom. The n- and nl-selective electron capture cross sections are calculated by a three-body classical trajectory Monte Carlo method (CTMC) and by a classical simulation schema mimicking quantum features of the collision system. The quantum behavior is taken into account with the correction term in the Hamiltonian as was proposed by Kirschbaum and Wilets (Phys Rev A 21:834, 1980). Calculations are carried out in the projectile energy range of 1–1000 keV/amu. We found that our model for Be4+ + H(1s) system remarkably improves the obtained state-selective electron capture cross sections, especially at lower projectile energies. Our results are very close and are in good agreement with the previously obtained quantum–mechanical results. Moreover, our model with simplicity can time efficiently carry out simulations where maybe the quantum mechanical ones become complicated, therefore, our model should be an alternative way to calculate accurate cross sections and maybe can replace the quantum–mechanical methods.

Charge transfer and excitation processes in low energy collisions of He+ ions with Li atoms

Electron capture between solar wind ions and neutral species has contributed to the understanding of X-ray production from solar system bodies. The charge transfer and excitation processes in solar wind ions of He+(1s) colliding with Li(1s 22s) atoms are studied by utilizing the full quantum-mechanical molecular-orbital close-coupling (QMOCC) method with impact energies of 0.003–2 keV amu−1. Comparisons of cross sections from single- and multi-configurational calculations for a self-consistent field (SCF and MCSCF) process are carried out. Results show that the dominant reaction channels are He(1s2l 1,3L) + Li+(1s 2 1S). Good consistency is found among present total and state-selective charge transfer and excitation cross sections with other theoretical and experimental data in the same energy region. Due to the differences between coupling matrix elements in high-energy states, the charge transfer cross sections calculated from SCF and MCSCF split slightly as E > 0.4 keV amu−1. Weak Stueckelberg oscillations for charge transfer appear in the present work. In addition, the differences of cross sections for electron excitation to Li(1s 22p) in the singlet/triplet molecular states with He+(1s) are much smaller than those of charge transfer processes because of the similar energy gaps from Li(1s 22p) to the ground state in singlet/triplet states in the large R region.

Single- and double-electron capture in intermediate-energy H++Mg collisions

Single- and double-electron-capture processes occurring in the system of hydrogen ions colliding with alkaline-earth atoms, ${\mathrm{H}}^{+}+\mathrm{Mg}$, are investigated in a broad energy domain ranging from 0.25 to 180 keV. Total and state-selective cross sections are calculated using a two-active-electron semiclassical asymptotic-state close-coupling approach. Our results show the best overall agreement with experimental data, and possible reasons for observed discrepancies are discussed. Comparison of our cross sections with previous theoretical results further demonstrates the importance of electronic correlations between the magnesium valence electrons and the strong couplings between various important channels. Furthermore, our investigations suggest that the oscillatory structures observed in the double-electron-capture cross sections stem from complex coherence effects between double-electron capture, electron transfer to excited states, and transfer-excitation processes.

Integrated total and state-selective cross sections for bare beryllium ion collisions with atomic hydrogen

We apply the two-centre wave-packet convergent close-coupling approach to calculate integrated total and state-selective cross sections for electron capture and ionisation in bare beryllium ion collisions with atomic hydrogen. This is done in the energy region between 1 keV/u to 1 MeV/u. Good agreement was achieved in comparison to previous theoretical works for the total electron capture cross section across all energies, however the total ionisation cross section shows disagreement with preceding calculations. We present accurate n and ℓ-resolved (n and ℓ are the principal and the angular momentum quantum numbers of the final state in electron capture processes, respectively) cross sections required for plasma impurity diagnostics where there have been discrepancies between different approaches for n > 5. Otherwise, excellent agreement between our results and previous calculations of state-selective cross sections for electron-capture is observed for a wide number of different n. The calculations have been performed on a fine energy mesh to identify oscillatory structures in the n- and nl-resolved capture cross sections in the low-energy region. Our results show pronounced oscillations in the cross sections for n ⩾ 5 below 20 keV/u.

Quantum and Classical Dynamics of the N(2D) + N2 Reaction on Its Ground Doublet State N3(12A″) Potential Energy Surface.

The initial state-selected dynamics of the N(2D) + N2(X1∑) → N2(X1∑) + N(2D) exchange reaction on its electronic ground doublet state N3(12A″) potential energy surface (PES) has been studied here by time-dependent quantum mechanics (TDQM) and quasi-classical trajectory (QCT) methods. Dynamical attributes such as total reaction probabilities, state-selected integral cross sections, and initial state-selected rate constants have been calculated. The presence of metastable quasi-bound complexes in the collision process is confirmed by substantial oscillatory structures in the reaction probability curves. Also, rotational excitations of reagent N2 on the reactivity have been examined by calculating the probabilities for the two-body rotational angular momentum up to j = 10. We conclude that the reagent rotational excitation increases the reactivity. The TDQM results are compared with QCT results.

State-selective charge exchange cross sections in Be^{4+} -hbox {H}(2textit{lm}) collision based on the classical trajectory Monte Carlo method

A three-body classical trajectory Monte Carlo method is used to calculate the nl state-selective charge exchange cross sections in hbox {Be}^{mathrm {4+}}+ H(2lm) collisions in the energy range between 10 and 200 keV/amu. We present partial cross sections for charge exchange into hbox {Be}^{mathrm {3+}}(nl) (textit{nl} = 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f) states as a function of impact energy. Our results are compared with the previous classical and quantum-mechanical results. We show that the classical treatment can able to describe reasonably well the charge exchange cross sections.Graphic abstract

Electron removal from hydrogen atoms by impact of multiply charged nuclei

The boundary-corrected continuum intermediate state (BCIS) method is used to compute total cross sections for electron capture by seven heavy nuclei ( $${\mathrm{Li}}^{3+}$$ , $${{\mathrm{Be}}}^{4+}$$ , $$\mathrm{B}^{5+}$$ , $$\mathrm{C}^{6+}$$ , $$\mathrm{N}^{7+}$$ , $$\mathrm{O}^{8+}$$ and $$\mathrm{F}^{9+}$$ ) from atomic hydrogen $${{\mathrm{H}}}(1s)$$ at impact energies 20–3000 keV/amu. In all the cases, regarding the exit channel, we compute the cross sections $$Q_{if}$$ for the specific individual final bound states $$f=(n,l,m)$$ of hydrogen-like ions, where throughout $$i=(1,0,0)=1s$$ (the ground state of the target, H). The maximal value of the principal quantum number n has been taken to be $$n _\mathrm{max}= 4,\,5$$ and 6 for $${\mathrm{Li}}^{3+},$$ $${\mathrm{Be}}^{4+}$$ and $$\mathrm B^{5+},$$ respectively, as well as $$n_\mathrm{max} = 7$$ for $$\mathrm{C}^{6+},$$ $$\mathrm{N}^{7+},$$ $$\mathrm{O}^{8+}$$ and $$\mathrm{F}^{9+}.$$ All the sub-levels (l, m) for every n are included in the computations. Further, the summed cross sections $$Q_{i,{{\Sigma }}}={\sum }_fQ_{if}$$ for all the final (f) states are reported. In $$Q_{i,{{\Sigma }}},$$ the state-selective cross sections $$Q_{if}$$ contain the exact contributions from the final levels with $$n\le n_\mathrm{max}.$$ The collective yield from the final states with $$n>n _\mathrm{max}$$ is approximated by the Oppenheimer $$n^{-3}$$ scaling. To put the present results into perspective, comparisons are made with the boundary-corrected first Born (CB1) and the continuum distorted wave-eikonal final state (CDW-EFS) methods. Both the BCIS and CDW-EFS methods belong to the group of the second-order asymmetric methods for charge-exchange. Most importantly, the available experimental data are used to assess the relative performance of the BCIS method for total cross sections summed over all final states. This type of total cross section databases from our computations can find useful applications in several neighboring disciplines (plasma physics, astrophysics, new energy sources in fusion research) as well as in ion transport physics of relevance to, e.g., radiotherapy in medicine.

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.

Temperature dependence of the rate coefficient of formation of CN radical from C + NH

Rate coefficients of the complex-forming C + NH→H + CN reaction have been calculated at temperatures ranging from 5 K to 800 K using quasi-classical trajectories on a potential energy surface which accurately describes the attractive long-range interaction, along with results using two capture models. In contrast with the constant value recommended in astrochemical databases, a steep decrease of the rates has been found up to 150 K, and then they tends to be nearly constant. Such behavior is analyzed in terms of the rovibrational state-selected rate coefficients and cross sections singling out the role played by the rotational excitation of the initial diatom. The effect of the electronic degeneracy is also discussed.

Measurement of n-resolved State-selective Charge Exchange in Ne(8,9)+ Collision with He and H2

Abstract Charge exchange between highly charged ions and neutral atoms and molecules has been considered as one of the important mechanisms controlling soft X-ray emissions in many astrophysical objects and environments. However, for modeling charge exchange soft X-ray emission, the data of n- and l-resolved state-selective capture cross sections are often obtained by empirical and semiclassical theory calculations. With a newly built cold target recoil-ion momentum spectroscopy (COLTRIMS) apparatus, we perform a series of measurements of the charge exchange of Ne(8,9)+ ions with He and H2 for collision energy ranging from 1 to 24.75 keV/u. n-resolved state-selective capture cross sections are reported. By comparing the measured state-selective capture cross sections to those calculated by the multichannel Landau–Zener method (MCLZ), it is found that MCLZ calculations are in good agreement with the measurement for the dominant n capture for He target. Furthermore, by using nl-resolved cross sections calculated by MCLZ and applying l distributions commonly used in the astrophysical literature to experimentally derived n-resolved cross sections, we calculate the soft X-ray emissions in the charge exchange between 4 keV/u Ne8+ and He by considering the radiative cascade from the excited Ne7+ ions. Reasonable agreement is found in comparison to the measurement for even and separable models, and MCLZ calculations give results in a better agreement.

Electron transfer from atomic hydrogen to multiply-charged nuclei at intermediate and high energies

We report on theoretical total cross sections for electron capture from the ground state of atomic hydrogen H(1s) by fast multiply-charged nuclei H+,He2+,Li3+,Be4+,B5+,C6+,N7+,O8+ and F9+. The prior form of the boundary-corrected continuum intermediate states (BCIS) method is used. For a single fixed initial ground-state (i=1s), comprehensive computations are carried out for a sequence of the transitions to the final state (n,l,m) with 1≤n≤nmax, including all the energy degenerate sub-levels (−l≤m≤l,0≤l≤n−1). The maximal quantum number nmax is respectively set to 4 for H+,He2+ and Li3+, to 5 for Be4+, to 6 for B5+, as well as to 7 for C6+,N7+,O8+ and F9+. The reported nine tables provide these state-selective cross sections (Qif) and their state-summed counterparts (QΣ). The cross sections QΣ for the sum over all the final states are evaluated using the exact results of Qif for n≤nmax and the scaled cross sections for n>nmax. The scaling is based on the Oppenheimer n−3 rule. In addition to these tables, at the same impact energies 20–3000 keV/amu, the cross sections from the BCIS method are presented graphically in eight figures for the nuclei Li3+,Be4+,B5+,C6+,N7+,O8+ and F9+. This complements our recently published cross sections for electron capture by protons (H+) and alpha particles (He2+) from H(1s). In the present figures, whenever available, the corresponding experimental data are compared with our results for QΣ. Also included in these comparisons are the corresponding results for QΣ from the continuum distorted wave (CDW) method. The cross sections tabulated here can be used in versatile applications ranging from plasma physics and astrophysics through fusion research to ion therapy.

Experimental measurement of state-selective charge exchange and test of astrophysics soft X-ray emission model

Charge exchange, or electron capture, between highly charged ions and atoms and molecules has been considered as one of important mechanisms controlling soft X-ray emissions in many astrophysical objects and environments. However, to model charge exchange soft X-ray emission, astrophysicists commonly use principal quantum number <i>n</i> and angular momentum quantum number<i>l</i> resolved state-selective capture cross section data, which are usually obtained by empirical and semi-classical theory calculations. The accuracy of the theoretical model is the key to constructing an accurate X-ray spectrum. With a newly-built cold target recoil ion momentum spectroscopy apparatus, we perform a series of precise state-selective cross section measurements on Ne<sup>8+</sup> ions’ single electron capture with He targets, with the projectile energy ranging from 1.4 to 20 keV/u. The experimentally measured Q value spectrum shows that the process of electron captured to state of Ne<sup>7+</sup> with <i>n</i> = 4 is the main reaction channel, and that with <i>n</i> = 3 and 5 are the small reaction channels. Using Gaussian curve to fit the area of each channel on the Q value spectrum and normalizing the area of all channels, we obtain the <i>n</i>-resolved relative state-selective cross section. By comparing the measured relative cross sections with the results calculated by the multichannel Landau-Zener method and molecular Coulomb over-barrier model, significant difference among the strengths of small reaction channels is found. Specifically, the multichannel Landau-Zener method overestimates the contribution of <i>n</i> = 2 channel and <i>n</i> = 3 channel, and underestimates the contribution of <i>n</i> = 5 channel. The molecular Coulomb over-barrier model overestimates the contribution of <i>n</i> = 5 channel and underestimates the contribution of <i>n</i> = 3 channel. The significant difference between the theoretical model calculation and experimental measurement is due to the limitations of semiclassical theoretical method and classical theoretical method. Furthermore, with <i>l</i> distribution models commonly used in the astrophysical literature, including the statistical model, separable model, Landau-Zener-I model, Landau-Zener-II model and even model, we calculate the soft X-ray emissions in the charge exchange between 1.6 and 2.4 keV/u Ne<sup>8+</sup> and He. It is found that the calculated intensities of X-ray spectra significantly deviate from the existing measurements, and only the separable model can partly match the laboratory simulated solar wind charge exchange X-ray measurement. Furthermore, we find that the intensity of the charge exchange X-ray emission spectrum measured experimentally is dependent on the collision energy, while the emission spectrum calculated based on the model seems to be unchanged with the increase of the collision energy. These results indicate that if the classical and semi-classical models are applied to the astrophysical plasma for studying diffusive soft X-ray background, the obtained parameters of the astrophysical plasma will be inaccurate.

Single- and double-electron capture in intermediate-energy N5++H2 collisions

Single- and double-electron-capture processes occurring in the system of hydrogen ions colliding with alkaline-earth atoms, ${\mathrm{H}}^{+}+\mathrm{Mg}$, are investigated in a broad energy domain ranging from 0.25 to 180 keV. Total and state-selective cross sections are calculated using a two-active-electron semiclassical asymptotic-state close-coupling approach. Our results show the best overall agreement with experimental data, and possible reasons for observed discrepancies are discussed. Comparison of our cross sections with previous theoretical results further demonstrates the importance of electronic correlations between the magnesium valence electrons and the strong couplings between various important channels. Furthermore, our investigations suggest that the oscillatory structures observed in the double-electron-capture cross sections stem from complex coherence effects between double-electron capture, electron transfer to excited states, and transfer-excitation processes.

Three-body boundary-corrected continuum-intermediate-state method for single charge exchange with the general transition amplitude (1s→nlm) applied to the p–H(1s), α–H(1s), and p–He(1s2) collisions with n≤4

We derive a general quantum-mechanical transition amplitude in the prior version of the three-body boundary-corrected continuum-intermediate-state (BCIS-3B) method for single charge exchange in collisions of heavy nuclei with atomic hydrogenlike targets. The obtained expression is valid for all the transitions from the initial ground to any final hydrogenlike bound states $(1s\ensuremath{\rightarrow}nlm),$ where ${n,l,m}$ is the usual triple of the quantum numbers (principal, angular, magnetic). The outcome is semianalytical: a judicious combination of an analytical calculation (as far as feasible) and the subsequent numerical computations (quadrature for integrals that could not be reduced to closed formulas). The final results for the $T$-matrix elements are a compact double integration computed by numerical quadratures over real variables in finite intervals. The ensuing total cross section is a single numerical quadrature of the squared absolute value of this transition amplitude integrated over the magnitude of the transverse momentum transfer vector. This can provide detailed information on the cross sections for each individual subshell ${n,l,m}$ of the newly formed hydrogenlike atom or ion comprised of a projectile nucleus and the captured electron. Using these general expressions, we computed a large number of state-selective and state-summed cross sections (both differential and total) for electron capture in the $p\text{\ensuremath{-}}\mathrm{H}$, $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{H}$, and $p\text{\ensuremath{-}}\mathrm{He}$ collisions at intermediate and high impact energies. The energy dependence of the cross sections for the individual shells and their subshells with the fixed quantum numbers $n$, ${n,l}$, and ${n,l,m}$ are reported via detailed tables and figures. Also, differential cross sections (state selective and summed) are computed for the $p\text{\ensuremath{-}}\mathrm{H}$ collisions at 60, 125, and 5000 keV. All the present results from the BCIS-3B method are found to be in very good agreement with the existing experimental data on differential and total cross sections, both state selective (whenever available) and state summed. The provided cross-section database can find important applications in several investigative fields ranging from plasma physics, astrophysics, and heavy-ion transport physics through fusion research and technology to hadron therapy.

Collisional O2 + N2 State-Selected Cross Sections for Open Science Cloud Reuse.

In this paper, we report a quasi-classical trajectory study of the internal energy state specificity of dissociative O2 + N2 collision rates computed at high temperatures on an accurate potential energy surface (PES). This paper analyzes the outcomes of the trajectory calculations performed by explicitly considering the rotational state of the reactants and compares them with those of a previous study carried out by assuming a thermal rotational distribution. In particular, in order to quantify the deviation of the rotationally thermalized rates from the rotationally state-selected ones, we discuss here the properties of the corresponding state-specific and state-to-state cross sections with the support of both internuclear distance and bond-order reduced dimensionality representations of the isoenergetic contours of the PES. This allows us to single out a suitable bond-order-like process coordinate useful for modeling detailed dissociation cross sections and rate coefficients and relating them, as well, to some specific features of the PES. Furthermore, this is also shown to be useful for structuring data repositories of the molecular section of the European Open Science Cloud Project so as to obtain collaborative production, validation, reuse, and dissemination of chemical processes' knowledge and efficiency parameters.

Charge transfer in low-energy collisions of Be3+ and B4+ ions with He**Project supported by the National Natural Science Foundation of China (Grant Nos. 11774344, 11474033, and 11574326) and the National Key Research and Development Program of China (Grant No. 2017YFA0402300).

The nonradiative charge-transfer processes of Be3+(1s)/B4+(1s) colliding with He(1s2) are investigated by the quantum-mechanical molecular orbital close-coupling (QMOCC) method from 10 eV/u to 1800 eV/u. Total and state-selective cross sections are obtained and compared with other results available. Although the incident ions have the same number of electrons and collide with the same target, their cross sections are different due to the differences in molecular structure. For Be3+(1s) + He(1s2), only single-electron-capture (SEC) states are important and the total cross sections have a broad maximum around E = 150 eV/u. While for B4+(1s) + He(1s2), both the SEC and double-electron-capture (DEC) processes are important, and the total SEC and DEC cross sections decrease rapidly with the energy decreasing.

Nuclear quantum effects in state-selective scattering from ring polymer molecular dynamics.

We present an efficient method to obtain initial state-selective cross sections for bimolecular reactions that can account for certain nuclear quantum effects by employing the ring polymer molecular dynamics approach. The method combines the well known quasiclassical trajectory (QCT) approach with the description of the system in an extended ring polymer phase space. Employing the prototypical Mu/H/D + H2(v = 0, 1) reactions as a benchmark, we show that the presented approach does not violate zero-point energy constraints and that it can also capture the contributions of tunneling through the v = 1 vibrationally adiabatic barrier present for the Mu + H2(v = 1) reaction. This is a significant improvement over the QCT approach with only a small increase in numerical cost.

Line intensities for x-ray emission in Mg12+ collisions with H and He atoms

State selective charge transfer cross sections are calculated in Mg12+ collisions with H and He atoms at incident energies of 1.0, 3.0, and 5.0 keV amu−1 using a time-dependent lattice method. Total capture cross sections using the time-dependent lattice method are found to be larger than those previously calculated using the Landau–Zener method. Lyman line ratios are calculated using the time-dependent lattice capture cross sections and standard radiative transitions for both the H and He atoms. Lyman line probabilities are presented for both H and He. The strongest probability for both H and He is the Lyman α emission, but relatively strong probabilities for He at an incident energy of 1.0 keV amu−1 are found for Lyman β, γ, δ, and ϵ emission.

Сечения образования ионов He-=SUP=-+-=/SUP=- в различных электронных состояниях при столкновениях ионов He-=SUP=-2+-=/SUP=- с атомами водорода

Using collision spectroscopy based on precision measurements of the kinetic energy of projectile ions that capture an electron, we measured the state selective electron capture cross sections of formation of He^+(n) ions at collision 3^He^{2 +} ions with an energy of E = 1.4-10 keV/a.m.u. with hydrogen atoms. The atomic hydrogen target with a degree of dissociation 78% at a temperature of tungsten dissociation cell 2180K has been made.

Electron capture and 2s→2p excitation in Be3+-Li collisions

The electron capture and 2s→2p excitation processes in Be3+-Li collisions are investigated by the quantum-mechanical molecular orbital close-coupling (QMOCC) method and by the two-center atomic orbital close-coupling (TC-AOCC) method in the energy ranges 10−4–1.2 keV/u and 0.5–100 keV/u, respectively. Spin-resolved total, n-shell and state-selective electron capture cross sections are calculated with large expansion of the MO and AO basis sets. In the overlapping energy range the results of the two sets of calculations for the total and n = 4, 3-shell capture cross sections agree very well for both singlet and triplet channels. Good agreement in this energy range between the two calculations is obtained also for the spin-resolved cross sections except some weak reaction channels. It is found that the total and n = 4 shell singlet and triplet capture cross sections differ significantly from each other in the energy region below 0.1 keV/u, and especially for the 4l cross sections this difference becomes considerable at 1 keV/u. For the weak n = 3 and n = 2 capture channels the difference between singlet and triplet cross sections is much smaller. The excitation 2s-2p cross section for Li in this collision system has also been calculated and no significant difference between the singlet and triplet cross sections was found in the entire energy range considered.