Energy loss in collisions of charged projectiles with many-electron systems can be dealt with in time-dependent density functional theory by invoking Ehrenfest's theorem for the time evolution of expectation values of observables. We derive an exact expression for the evaluation of energy loss for systems described in a target reference frame, which is a functional of the electron density. Using an approximation scheme, we then apply the expression to antiproton-atom collisions at intermediate and high energies within the framework of the basis generator method. The calculations are performed within the semiclassical approximation for the nuclear motion, and a straight-line trajectory is employed. The energy loss is evaluated from an expectation value of the time derivative of the time-dependent projectile potential, and it avoids the problem of identifying the excited and ionized many-electron contributions in the many-electron wave function. There is also no need to invoke the independent-event model, since the calculations are performed within the framework of the independent-electron mean-field model. Detailed comparisons are provided for net ionization and total energy loss of antiprotons colliding with hydrogen, helium, neon, carbon, nitrogen, and oxygen. Reasonable agreement is found with the results from one-electron and two-electron calculations for atomic hydrogen and helium, and with experiment in the latter case. For the $\overline{p}\text{\ensuremath{-}}\mathrm{Ne}$ system at intermediate collision energies, we find discrepancies with previous work that included only single-electron transitions. The sequence of results for C, N, O, and Ne allows one to paint a consistent picture that awaits experimental verification.

Calculation of energy loss in antiproton collisions with many-electron systems using Ehrenfest's theorem

The research progresses on the investigations of atomic structure and collision dynamics with highly charged ions based on the heavy ion storage rings and electron ion beam traps in recent 20 years are reviewed. The structure part covers test of quantum electrodynamics and electron correlation in strong Coulomb field studied through dielectronic recombination spectroscopy and VUV/x-ray spectroscopy. The collision dynamics part includes charge exchange dynamics in ion–atom collisions mainly in Bohr velocity region, ion-induced fragmentation mechanisms of molecules, hydrogen-bound and van de Waals bound clusters, interference, and phase information observed in ion–atom/molecule collisions. With this achievements, two aspects of theoretical studies related to low energy and relativistic energy collisions are presented. The applications of data relevant to key atomic processes like dielectronic recombination and charge exchanges involving highly charged ions are discussed. At the end of this review, some future prospects of research related to highly charged ions are proposed.

Atomic structure and collision dynamics with highly charged ions

We report on double and single differential cross section measurements of the $1s2{s}^{2}\phantom{\rule{0.16em}{0ex}}^{2}S$, $1s2s2p\phantom{\rule{0.16em}{0ex}}^{2}P_{\ifmmode\pm\else\textpm\fi{}}$, and $1s2s2p\phantom{\rule{0.16em}{0ex}}^{4}P$ doubly excited states produced by single-electron capture in 6--15 MeV collisions of pre-excited ${\mathrm{C}}^{4+}(1s2s\phantom{\rule{0.16em}{0ex}}^{3}S)$ ions with ${\mathrm{H}}_{2}$, He, Ne, and Ar targets. Ab initio cross section calculations based on a three active electrons atomic orbital close-coupling approach are compared to the measurements for collisions with the lighter ${\mathrm{H}}_{2}$ and He targets, showing an overall good agreement. Theoretical details concerning Auger electron angular distributions, partial cross sections, impact parameter dependencies, and radiative cascade feeding effects are discussed. The populations of the $1s2s2p\phantom{\rule{0.16em}{0ex}}^{4}P$, $^{2}P_{\ensuremath{-}}$, $^{2}P_{+}$ multiplets concerning the spin symmetry are finally presented for the four collision systems and discussed following the comparisons between theory and experiment. 

State-resolved differential cross sections of single-electron capture in swift collisions of 
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For more than 40 years since the first ion-atom collision investigations of the two-electron process of electron transfer with excitation and its resonant and nonresonant features, a satisfactory quantum mechanical treatment has been lacking. We present now such a comprehensive transfer excitation treatment using a three-electron atomic orbital close-coupling approach within a full configuration interaction formalism, exemplified by ${\mathrm{C}}^{4+}(1{s}^{2})+\mathrm{He}$ collisions at 0.5--18 MeV impact energies. The calculated cross sections for the production of ${\mathrm{C}}^{3+}(1s2{p}^{2}\phantom{\rule{0.16em}{0ex}}^{2}D)$, which shows the strongest resonance signature among the KLL Auger transitions, are found to be in excellent agreement with zero-degree Auger projectile spectroscopy measurements covering the maximum of the resonance peak and its high energy wing. At the lower energies, the theoretical results show a second maximum which is interpreted through a nonresonant one-step transfer excitation mechanism, never considered to date. The present, fully coherent, many-body treatment provides an important advance in the modeling and understanding of multielectronic processes in quantum systems under strong and ultrafast perturbations. 

Coherent treatment of transfer-excitation processes in swift ion-atom collisions

We report on an ab initio model to describe single- and double-ionization processes in antiproton collisions with atoms and molecules. Our model is based on a fully correlated close-coupling approach and a Dyson orbital analysis. Furthermore, we employ the concept of a correlation integral in order to quantify and gain insights into the effects of electronic correlation on the ionization processes. Our model is applied to the prototype antiproton-helium and antiproton--molecular hydrogen collision systems in the keV energy range. 

Single- and double-ionization processes of antiproton-helium and antiproton–molecular hydrogen collisions in the keV energy range

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.

State-selective single-electron capture in intermediate-energy C 4 + + He collisions

We present a simple and efficient method for computing single and double ionization cross sections in ion-atom and ion-molecule collisions using ${L}^{2}$ Gaussian basis sets. Gaussian functions are widely employed to compute bound states of ions, atoms, and molecules. However, the description of continuum states, and therefore ionization phenomena, remains a theoretical challenge. Our approach is tested on the benchmark system antiproton-helium collisions in the so-called intermediate energy range. A good agreement with numerically exact calculations is observed. The proposed method is general and can thus be employed in any collisional systems in the challenging nonperturbative regime. Our work opens the way to investigate multiple ionization processes by ion impact in multicenter polyelectronic systems.

/pdf/single-and-double-ionization-processes-using-gaussian-type-4m9fpjowu5.pdf

J. W. Gao

Papers

State-selective single-electron capture in intermediate-energy C 4 + + He collisions

Single- and double-ionization processes using Gaussian-type orbitals: Benchmark on antiproton-helium collisions in the keV-energy range