Atomic Orbital Close-coupling Research Articles

Cross sections for electron capture in collisions of Beq+ (q = 2, 3) and Bq+ (q = 3, 4) with atomic hydrogen

The two-centre atomic orbital close-coupling method is employed to study charge transfer reactions in collisions of Beq+ (q = 2, 3) and Bq+ (q = 3, 4) with ground state atomic hydrogen in the energy region from 0.1 keV/u to 100 keV/u. The interaction of the active electron with the projectile ion is represented by a model potential. Total and sub-shells' state-selective cross sections are calculated and compared with data from other sources when available.

Polarization Degrees for 3p 2P3/2–3s 2S1/2 Transition of C3+ (1s23p) Produced in Collisions of C4+ with He and H2

Charge transfer processes in collisions of C 4+ with ground-state He and H 2 are investigated using the two-center atomic orbital close-coupling method. Total and state-selective single-electron capture cross sections are obtained for collision energies between 1 and 7 keV/amu, and comparison with available experimental data reveals a good agreement. The polarization degrees for the 3 p 2 P 3/2 –3 s 2 S 1/2 transition of C 3+ (3 p 2 P 3/2 ) are calculated from the magnetic substate-selective cross sections, in which the cascade effects are also included. The polarization degree in the C 4+ +H 2 collisions varies smoothly in the considered energy region and generally agrees with the experimental measurements, while if appears minimum at a collision energy of 2 keV/u for C 4+ +He collisions. By studying the time-evolution of electron capture dynamics in the two systems we have found that the polarization difference between the two systems is caused mainly by interactions at relatively small internuclear dis...

Polarization degree differences for the3p 2P3/2–3s 2S1/2transition ofN4+(3p 2P3/2) produced inN5+-He andN5+-H2collisions

The magnetic substate-selective single-electron-capture cross sections in collisions of ${\mathrm{N}}^{5+}$ with He and ${\mathrm{H}}_{2}$ are calculated using the two-center atomic orbital close-coupling method, and the polarization of emitted radiation from the excited state of ${\mathrm{N}}^{4+}$ is investigated for projectile energies between 1.2 and 7 keV/u. The polarization degrees for the $3p {}^{2}{P}_{3/2}--3s {}^{2}{S}_{1/2}$ transition of ${\mathrm{N}}^{4+}$($3p {}^{2}{P}_{3/2}$) produced in ${\mathrm{N}}^{5+}+\mathrm{He}$ and ${\mathrm{N}}^{5+}+{\mathrm{H}}_{2}$ electron-capture collisions are in general agreement with the experimental measurements. It is found both experimentally and theoretically that there exists a large difference between the polarization degrees of this radiation resulting from the ${\mathrm{N}}^{5+}+\mathrm{He}$ and ${\mathrm{N}}^{5+}+{\mathrm{H}}_{2}$ electron-capture collisions, namely, $~$0.25 and $~$0, respectively. By studying the time evolution of electron-capture dynamics in the two systems we have found that this difference is caused mainly by the difference in the interactions in the two systems at relatively small internuclear distances, consistent with the molecular picture of the collision dynamics.

Atomic-orbital close-coupling calculations of Be4+ + H(ls) → Be3+(nℓ) + H+

The atomic-orbital close-coupling (AOCC) method was used to calculate charge exchange cross sections relevant in nuclear fusion research. Here, we present calculations of fully stripped Be ions colliding with H(1s) in the energy range of 1 – 1000 keV/amu. We sketch how we determined an optimized description of this collisional system, compare with previous data and present derived emission cross sections which are used when evaluating data from charge exchange recombination spectroscopy (CXRS) in fusion experiments.

Dynamics of He2+ + He+(1s) and He2+ + He+(2s) excitation and electron-capture processes with screened Coulomb interaction

Collision dynamics of He2+ + He+(1s) and He2+ + He+(2s) excitation and electron capture in hot, dense plasmas is studied by the two-centre atomic orbital close-coupling method in the energy range 2–100 keV/u. The screening of the Coulomb interaction due to the plasma effects introduces significant changes in electronic bound state wavefunctions and energies (including lifting of Coulomb degeneracy), coupling matrix elements, and the number of open reaction channels, thus affecting the entire collision dynamics of the system. With increasing interaction screening, the total electron-capture cross sections for the considered collision systems increase with respect to those of the unscreened case in the lower part of the considered energy range, whereas in its high-energy part they show the opposite behaviour. The excitation cross sections generally decrease with increasing screening but show an oscillatory behaviour almost in the entire energy range considered. The cross section for the He2+ + He+(2s) → He2+ + He+(2p) excitation is several orders of magnitude larger than the cross sections for all other transitions and is highly sensitive to the strength of the interaction screening. This strongly affects the intensity and other spectral properties of the associated He+ Ly-α radiation.

Dynamics ofO8++Helectron capture in Debye plasmas

The electron capture in ${\text{O}}^{8+}\ensuremath{-}\text{H}$ collisions is studied by the two-center atomic-orbital close-coupling method when the interactions of charged particles are screened and have a Yukawa form. Atomic orbitals and eigenenergies of $n\ensuremath{\le}7$ states on ${\text{O}}^{7+}$ and $n\ensuremath{\le}2$ states on H are calculated as a function of the interaction screening parameter and used in the atomic-orbital close-coupling dynamics scheme to calculate the electron capture cross sections in the energy range of 0.2--50 keV/u. It is shown that the degree of interaction screening determines the reduction in electron binding energies, the number of open electron capture channels, and the strength of the exchange couplings, thus affecting the entire collision dynamics and the magnitude and energy behavior of state-selective cross sections. The changes in electron binding energies and capture cross sections when the interaction screening varies introduce dramatic changes in the radiation spectrum of ${\text{O}}^{7+}(nl)$ capture states with respect to the unscreened interaction case. The state-selective electron capture cross sections in this collision system, as well as the intensities of a number of charge exchange spectral lines, for a number of representative screening parameter values are presented and discussed.

Dynamics of the H+ + H− electron capture process in Debye plasmas

Collision dynamics of the H+ + H− system is studied by using the atomic-orbital close-coupling (AOCC) method when the interactions of charged particles are screened. The atomic orbitals and eigenenergies of n ⩽ 6 states for H and ns (n ⩽ 5) states for H− are calculated as a function of the screening parameter and used in the AOCC dynamic scheme to calculate the electron capture cross sections in the energy range 1–100 keV u−1. The e−–H interaction in H− is described by a model potential. With decreasing the Debye screening length, the bound states centred on H+ and H− successively enter the continuum, reducing the number of reaction channels in the discrete spectrum. Furthermore, the interaction screening also introduces significant changes in the direct and exchange couplings, thereby affecting the magnitude and energy behaviour of state-selective cross sections. These cause the change of charge exchange spectrum, which may be applied to diagnose the temperature and density in laboratory and astrophysical plasmas.

Total and state-selective charge transfer in He2+ + H collisions

Total and state-selective cross sections for charge transfer in ∼1–1000 keV/u He2+ + H collisions have been calculated using a variety of theoretical approaches, namely, the classical trajectory Monte Carlo, atomic-orbital close-coupling and lattice, time-dependent Schrödinger equation methods. Comparison of the results with available experimental measurements and other theoretical cross sections indicates the regimes in which each method is most reliable. The present cross sections, tabulated here, and their evaluation in light of existing data, provide a new benchmark for this inelastic channel in the fundamental collision system He2+ + H over a wide range of collision energies and final quantum levels.

Atomic collisions with screened Coulomb interactions: excitation and electron capture in H+ + H collisions

Dynamics of excitation and electron capture processes in the H+ + H(1s) collision system in a Debye plasma is studied as an example of collision systems with screened Coulomb interactions. The two-centre atomic orbital close-coupling method (TC-AOCC) was used with a basis containing all n ⩽ 6 and 7s discrete and 99 quasi-continuum states centred on the target and all n ⩽ 3 discrete states centred on the projectile when describing the excitation process, and vice versa when describing the electron capture. The atomic orbitals and energies of all one-centre states have been determined variationally as a function of screening parameter and used to calculate the state-selective electron capture and excitation cross sections. With an increase of the screening, the bound states successively enter the continuum, thereby reducing the number of reaction channels in the discrete spectrum. The effect of interaction screening on the direct and exchange electronic couplings is also strong. Both these factors significantly affect the dynamics of electron capture and excitation processes. The interaction screening parameter can, thus, be used as a tool for control of the collision dynamics.

Dynamics ofHe2++H(1s)ionization with screened Coulomb interactions

Collision dynamics of ${\mathrm{He}}^{2+}+\mathrm{H}(1s)$ ionization in a hot, dense (Debye) plasma is studied by the two-center atomic orbital close-coupling (AOCC) method in the energy range $5--300\phantom{\rule{0.3em}{0ex}}\mathrm{keV}∕\mathrm{u}$. The target AO basis contained all $n\ensuremath{\le}6$ bound states and 117 quasicontinuum states, while that on the projectile contained all $n\ensuremath{\le}4$ bound states. The eigenenergies and wave functions of all these states were obtained variationally as a function of the screening parameter in a Debye-H\"uckel potential and used in AOCC dynamics calculations. With increasing the screening, more and more discrete states enter the target and projectile continuum and increase the ionization cross section, particularly at low collision energies. The ionization to target continuum is the main ionization channel, while the ionization to the projectile continuum becomes important only for large screenings and collision energies below $\ensuremath{\sim}50\phantom{\rule{0.3em}{0ex}}\mathrm{keV}∕\mathrm{u}$.

Ionization and single electron capture in collision of highly charged Ar16+ ions with helium

This paper uses the two-centre atomic orbital close-coupling method to study the ionization and the single electron capture in collision of highly charged Ar16+ ions with He atoms in the velocity range of 1.2–1.9 a.u. The relative importance of single ionization (SI) to single capture (SC) is explored. The comparison between the calculation and experimental data shows that the SI/SC cross section ratios from this work are in good agreement with experimental data. The total single electron ionization cross sections and the total single electron capture cross sections are also given for this collision. The investigation of the partial electron capture cross section shows a general tendency of capture to larger n and l with increasing velocity from 1.2 to 1.9 a.u.

Dynamics ofHe2++H(1s)excitation and electron-capture processes in Debye plasmas

Collision dynamics of the ${\mathrm{He}}^{2+}+\mathrm{H}(1s)$ system imbedded in a Debye plasma is studied by the two-center atomic orbital close-coupling (AOCC) method in the energy range $5--300\phantom{\rule{0.3em}{0ex}}\mathrm{keV}∕\mathrm{u}$. The atomic orbitals and electron binding energies of atomic states are calculated within Debye-H\"uckel approximation of the screened Coulomb potential and used in AOCC dynamics formalism to calculate the state-selective electron capture and excitation cross sections. The basis contained 174 orbitals centered on the target (all $n\ensuremath{\le}6$ discrete states and 117 quasicontinuum states) and 20 orbitals centered on the projectile (all $n\ensuremath{\le}4$ discrete states). It is demonstrated that the screening of Coulomb interactions in the system progressively reduces the number of available excitation and electron capture channels when the screening parameter increases. The screening of Coulomb interactions introduces changes also in the values of direct and exchange couplings, thus affecting the magnitude and energy behavior of the cross sections. The control of dynamics of collision processes in a Debye plasma by varying the plasma screening of Coulomb interactions in the collision system is discussed.

Numerical study of charge transfer in H+ + He+ and He2+ + Li2+ collisions

The lattice time-dependent Schrödinger equation (LTDSE) and atomic orbital close coupling (AOCC) methods are applied to calculate the charge transfer cross sections for H+ + He+ and He2+ + Li2+ collisions in the velocity range of 0.5–4.0 atomic units. The comparison of the results is made with those of other theoretical methods and with measurements. This analysis is used to provide a test of the accuracy of LTDSE and AOCC, and to help establish a consensus of theoretical results in comparison with the measurements for these ion–ion collisions.

Lattice, time-dependent Schrödinger equation approach for charge transfer in collisions of Be4+ with atomic hydrogen

A test of the lattice, time-dependent Schrödinger equation (LTDSE) method for treating inelastic ion–atom collisions is performed by treating state-selective charge transfer in 10–1000 keV/u Be4+ + H collisions. This system possesses a greater charge asymmetry of the colliding nuclei than has been treated in previous applications of the method. Consequently, its ability to represent well the dynamical evolution of the electronic wavefunction within the combination of a shallow and a deep potential well with a single coordinate- and momentum-space discretization is tested. New results are also computed using other, standard approaches, the atomic-orbital close-coupling and classical trajectory Monte Carlo methods, to provide comparisons with the LTDSE results owing to their well-established regimes of applicability and behaviours.

Excitation and charge transfer inp+H(2s)collisions

Excitation and charge transfer cross sections for proton collisions with $2s$ excited state hydrogen are calculated using time-dependent lattice, atomic-orbital close-coupling with pseudostates, and classical trajectory Monte Carlo methods. The time-dependent lattice calculation yields $\ensuremath{\Delta}n=1$ excitation and $\ensuremath{\Delta}n=0$ and $\ensuremath{\Delta}n=1$ charge transfer cross sections at 5, 10, and $15\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$ incident energy. The atomic-orbital close-coupling with pseudostates calculation yields excitation cross sections to $n=3--5$ and charge transfer cross sections to $n=1--5$ at a number of incident energies between 1 and $100\phantom{\rule{0.3em}{0ex}}\mathrm{keV}$. The time-dependent lattice and close-coupling pseudostates calculations are found to be in good agreement with previous standard close-coupling results. The close-coupling with pseudostates calculations are used to benchmark the classical trajectory Monte Carlo calculations, which are widely used in astrophysical and laboratory plasma modelling.

Single electron capture process of ion-atom collisions by means of close-coupling method

The basic idea of two-centre atomic orbital close coupling method is introduced in ion-atom collision process. We have found a systematic procedure to obtain th e parameter in close coupling calculation. We calculate the single electron capt ure cross sections for the collision of the multiply charged O6+ ion s with hydrogen atoms. The present calculations are in good agreement with exper imental data.

Charge transfer in slow collisions ofO8+andAr8+ions withH(1s)below2keV∕amu

We calculated the charge-transfer cross sections for ${\mathrm{O}}^{8+}+\mathrm{H}$ collisions for energies from $1\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{amu}$ to $2\phantom{\rule{0.3em}{0ex}}\mathrm{keV}∕\mathrm{amu}$, using the recently developed hyperspherical close-coupling method. In particular, the discrepancy for electron capture to the $n=6$ states of ${\mathrm{O}}^{7+}$ from the previous theoretical calculations is further analyzed. Our results indicate that at low energies (below $100\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{amu}$) electron capture to the $n=6$ manifold of ${\mathrm{O}}^{7+}$ becomes dominant. The present results are used to resolve the long-standing discrepancies from the different elaborate semiclassical calculations near $100\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{amu}$. We have also performed the semiclassical atomic orbital close-coupling calculations with straight-line trajectories. We found the semiclassical calculations agree with the quantal approach at energy above $100\phantom{\rule{0.3em}{0ex}}\mathrm{eV}∕\mathrm{amu}$, where the collision occurs at large impact parameters. Calculations for ${\mathrm{Ar}}^{8+}+\mathrm{H}$ collisions in the same energy range have also been carried out to analyze the effect of the ionic core on the subshell cross sections. By using diabatic molecular basis functions, we show that converged results can be obtained with small numbers of channels.

Scattering angle-integrated (total) and magnetic sublevel cross-sections and degree of linear polarization for electron and proton induced excitation [HeI [formula omitted] ( n=2–5)] of helium

Experimental scattering-angle-integrated (total) cross-sections σ ̄ , (scattering) angle-integrated magnetic sublevel cross-sections σ ̄ M L , and degree of linear polarization data have been measured in the extreme ultraviolet (EUV) wavelength region following decay of HeI (1 snp) 1P 0 ( n=2–5) states induced by electron and proton impact on a neutral helium target. These measurements are compared with a first Born approach as well as more sophisticated theoretical calculations. Specifically, theoretical values for electron impact include convergent close-coupling (CCC) and R-matrix with pseudo states (RMPS) methods in addition to first Born (Born 1) approximation while proton induced excitation cross-sections are compared with atomic-orbital close-coupling (AOCC) and first Born predictions.

Electron capture in collisions of S4+ with helium

Charge transfer due to collisions of ground-stateS4+(3s2 1S) ions with helium is investigated for energiesbetween 0.1 meV u-1 and 10 MeV u-1. Total and state-selective singleelectron capture (SEC) cross sections and rate coefficients areobtained utilizing the quantum mechanical molecular-orbitalclose-coupling (MOCC), atomic-orbital close-coupling (AOCC),classical trajectory Monte Carlo (CTMC) and continuum distorted wavemethods. The MOCC calculations utilize ab initio adiabaticpotentials and nonadiabatic radial coupling matrix elements obtainedwith the spin-coupled valence-bond approach. Previous data arelimited to a calculation of the total SEC rate coefficient using theLandau-Zener model that is, in comparison to the results presentedhere, three orders of magnitude smaller. The MOCC SEC cross sectionsat low energy reveal a multichannel interference effect. True doublecapture is also investigated with the AOCC and CTMC approaches whileautoionizing double capture and transfer ionization (TI) is exploredwith CTMC. SEC is found to be the dominant process except forE>200 keV u-1 when TI becomes the primary capture channel.Astrophysical implications are briefly discussed.

Electroncapture in collisions of S4+ with atomic hydrogen

Charge transfer processes due to collisions of ground stateS4+(3s2 1S) ions with atomic hydrogen areinvestigated for energies between 1 meV u-1 and10 MeV u-1 using thequantum mechanical molecular-orbital close-coupling (MOCC),atomic-orbital close-coupling, classical trajectory Monte Carlo(CTMC) and continuum distorted wave methods. The MOCCcalculations utilize ab initio adiabatic potentials andnonadiabatic radial coupling matrix elements obtained with thespin-coupled valence-bond approach. A number of variants of theCTMC approach were explored, including different momentum andradial distributions for the initial state, as well aseffective charge and quantum-defect models to determine thecorresponding quantum state after capture into finalpartially stripped S3+ excited classical states. Hydrogentarget isotope effects are explored and rate coefficients fortemperatures between 100 and 106 K are also presented.