Cross Sections For Electron Capture In Collisions Research Articles

Electron-capture cross sections in collisions of $${\mathrm{He}}^{+}$$ with several molecules

Electron-capture cross sections in collisions of $${\mathrm{He}}^{+}$$ with several molecules

Ab initiocalculation of electron-capture cross sections inH++BeHcollisions

We present calculations of electron-capture cross sections in collisions of ${\mathrm{H}}^{+}$ with BeH molecules in the energy range $25\phantom{\rule{0.28em}{0ex}}\mathrm{eV}lEl10\phantom{\rule{0.28em}{0ex}}\mathrm{keV}$. We discuss the validity of the models employed to describe nonadiabatic ion-molecule collisions, specifically the eikonal approximation, the Franck-Condon approximation, and the isotropic approximation to obtain orientation-averaged cross sections, which is based on the infinite-order sudden approximation. The calculation using the Franck-Condon approximation leads to a total electron-capture cross section that is practically independent of the collision energy with a value of around ${25\phantom{\rule{0.28em}{0ex}}\AA{}}^{2}$. The calculations using the more accurate sudden vibrational approximation indicate that the Franck-Condon approximation overestimates the electron-capture cross section by at most 20%. At $El1$ keV, the main product of the electron-capture process is the formation of ${\mathrm{BeH}}^{+}(2{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+})+\mathrm{H}(1s)$. At higher energies, the cross sections for formation of ${\mathrm{BeH}}^{+}(2{\phantom{\rule{0.16em}{0ex}}}^{1}{\mathrm{\ensuremath{\Sigma}}}^{+})+\mathrm{H}(1s)$ and ${\mathrm{BeH}}^{+}(1{\phantom{\rule{0.16em}{0ex}}}^{3}{\mathrm{\ensuremath{\Sigma}}}^{+})+\mathrm{H}(1s)$ are practically identical. The Coriolis couplings are particularly relevant to the mechanism of this reaction, which precludes the merging of semiclassical (including Coriolis couplings) and quantal results (neglecting Coriolis couplings) in the energy range of the present calculation.

Single Electron-Capture Cross Sections in C5+,6++C3+, N6+,7++N4+, and O7+,8++O5+ Collisions

Single electron-capture cross sections in collisions of bare and hydrogen-like ions with lithium-like ions of C, N, and O are calculated in the collision energy range between 0.05 and 16 keV/amu using a molecular-state close-coupling method. For the lithium-like ions, both the ground and first excited states are considered. The cross sections are calculated for capture into n =2 and 3 states of the bare and hydrogen-like ions and for excitation and de-excitation of the lithium-like ions. None of the electron-capture cross sections are larger than 10 -15 cm 2 in the collision energy range considered in the present study. At lower collision energies, the cross sections decrease due to Coulomb repulsion between the ions. Partial cross sections for capture into 1s3s, 1s3p, and 1s3d levels for the hydrogen-like ion collisions are on the same order of magnitude because the final states are mixed with each other by the electric field induced by the helium-like ions.

State-selective electron-capture cross sectionmeasurements forlow-energycollisions of He-like ions on H2

We measured state-selective absolute electron capture cross sections forcollisions of He-like C4+, N5+ and O6+ ions with molecularhydrogen by means of photon emission spectroscopy at impact energiesranging from 4 keV amu-1 down to energies as low as5 eV amu-1. In this low-energy region the total cross sections arefound to be weakly dependent on the projectile energy, whereas thestate-selective ones change drastically with varying impact energy. Up tonow no experiments were available to benchmark theoretical predictions.In our method we combine for the first time decelerated projectile beamswith the possibility of measuring state-selective electron capture.Compared with existing measurements for state-selective cross sectionsour deduced cross sections are in perfect agreement in the overlappingenergy region (E>>100 eV amu-1). Good agreement is also foundon comparing our results with existing total cross sections. In comparisonwith theoretical calculations some remarkable and unexpectedly largediscrepancies of orders of magnitude are found towards lower impactenergies.

Electron captureprocesses in collisions between Beq + ions and He atoms

Theoretical calculations of the electron capture cross sections incollisions of beryllium ions with helium atoms are performed in aclose-coupling methodbased on molecular-state expansion for the Beq + (q = 2,4) ionimpactsbelow 35 keV amu-1, and in the continuum distorted-wavemethod forthe Beq + (q = 1-4) ion impacts above100 keV amu-1.The present results are discussed in comparison with other availabletheoreticalcalculations.

Total and state-selective electron capture cross sections forN4+-H collisions

Electron-capture cross sections in collisions of ${\mathrm{N}}^{4+}$ ions with atomic hydrogen is studied using the close-coupling two-center atomic orbital expansion method by treating the collision system in a quasi-two-electron model. Total electron-capture cross sections to the dominant individual singlet and triplet excited states are evaluated over the energy range of 50--20 000 eV/amu. The results are compared to existing experimental data and to theoretical calculations based on the molecular orbital expansion method. It is found that while the general overall agreement is satisfactory, the large experimental uncertainty cannot be used to discriminate the different theories. For the present energy range our results are closer to the semiclassical close coupling calculations based on the molecular orbital expansion method of Shimakura et al. [Phys. Rev. A 45, 267 (1993)] than the quantum calculations of Zygelman et al. [Phys. Rev. A 56, 457 (1997)].

Ab initiostudy of electron capture in low-energy collisions of N4+with hydrogen

We present cross sections for the direct charge-transfer process ${\mathrm{N}}^{4+}(2s)+\mathrm{H}\ensuremath{\rightarrow}{\mathrm{N}}^{3+}{(nl;n}^{\ensuremath{'}}{l}^{\ensuremath{'}})+{\mathrm{H}}^{+}$ for center-of-mass collision energies between 0.1 eV/amu and 8 keV/amu. The results are in good agreement, at low energies, with merged-beams measurements for the total electron-capture cross sections in collisions of ${\mathrm{N}}^{4+}$ with hydrogen and deuterium targets. We also compare the calculated final-state cross sections with the results of recent translational energy spectroscopy measurements. The calculated final-state cross sections show good agreement with the experiment for ion projectile energies up to 8 keV. Our calculations suggest that the total electron-capture cross sections display Langevin behavior for collision energies below 0.4 eV/amu.

Low-energy electron capture by N4+ ions from H atoms: Experimental study using merged beams and theoretical analysis by molecular representation.

Measurements and theoretical analyses of total electron-capture cross sections for collisions of ${\mathrm{N}}^{4+}$ with ground-state hydrogen (deuterium) are reported in the energy range 1\char21{}300 eV/u. The present measurements have reduced relative uncertainty compared to previous absolute measurements at Oak Ridge National Laboratory [Huq et al., Phys. Rev. A 40, 1811 (1989)] and are used for detailed comparison with more recent coupled-channel molecular-orbital calculations [Shimakura et al., Phys. Rev. A 45, 267 (1992); Zygelman et al., ibid. 46, 3846 (1992)]. The most striking difference between the calculations was the increasing trend in the cross section for collision energies below 4 eV/u, as estimated by Zygelman et al. using only singlet states of the quasimolecule and the decreasing trend predicted by Shimakura et al. using both singlet and triplet states. The latter decreasing trend is consistent with the previous measurement. At 0.5 eV/u, the predicted singlet cross sections differ nearly by a factor of 2. Possible origins for this difference are explored. Strong structure is predicted in the cross section of Zygelman et al. and, to a lesser extent, in that of Shimakura et al. ; however, the phase of the structure is different in the two theories. Structures observed in the measurement at the higher collision energies are not in complete harmony with either prediction.

Charge transfer in collisions of atomic hydrogen with N7+ ions in the high-energy region.

A method to calculate electron-capture cross sections for collisions between an arbitrary ${n}_{i}$${l}_{i}$${m}_{i}$ shell of a hydrogenic target and an arbitrary ${n}_{f}$${l}_{f}$${m}_{f}$ shell of a fast bare projectile has been developed in the framework of the continuum distorted-wave approximation. Analytical expressions are derived for the Coulomb integrals in closed form in terms of Gauss hypergeometric functions in a terminating series. As an application, the cross sections in ${\mathrm{N}}^{7+}$+H(1s) collisions are calculated in the energy range between 10 and 40 MeV and compared with existing theoretical calculations. The total charge-transfer cross sections have been evaluated by applying an ${n}^{\mathrm{\ensuremath{-}}3}$ law for n\ensuremath{\ge}7 levels.

Eikonal calculation of electron-capture cross sections in collisions of H-atoms with fast projectiles

We have employed the eikonal method to calculate the cross section for the capture of an electron into an arbitrary $\mathrm{nl}$ subshell in collisions between hydrogen atoms and fast projectiles. The projectiles were protons, ${\mathrm{C}}^{6+}$, ${\mathrm{O}}^{8+}$, and ${\mathrm{Fe}}^{24+}$. The energy ranges considered were 20-100 keV in the proton case and 40-200 keV per nucleon in the other cases. These projectiles were selected because of their importance in fusion plasmas. For the highly charged case of ${\mathrm{Fe}}^{24+}$ we found that our formulas, while exact, involved a high degree of cancellation and produced unreliable numerical results, so that a numerical integration of the penultimate formula was substituted. In the proton case, agreement with recent experimental data is excellent.

An impact-parameter method for heavy-particle collisions involving one electron. I. Theory and sample results on H+-H and He2+-H collisions

A new impact-parameter method for calculating excitation and electron-capture cross sections in collisions between a one-electron atom or ion and a bare nucleus is described. The wavefunction is expanded in a large number (of the order of 30) of basis functions specially defined for this problem, and the time-dependent Schrodinger equation is solved subject only to the error arising from the truncation of the expansion. The method is applied to proton-hydrogen collisions at incident energies of 25, 49 and 60 keV and to the charge-transfer processes in He2+-H collisions at incident energies of 3He2+ of 30 and 49 keV. Results are compared with those of other investigations, both theoretical and experimental.