Two-electron Targets Research Articles

Effective one-electron approach to proton collisions with molecular hydrogen

The two-centre wave-packet convergent close-coupling approach to ion–atom collisions is extended to study proton collisions with molecular hydrogen including electron-capture channels. We use a model potential to represent the molecular target as an effective one-electron spherically symmetric system. This greatly simplifies the target structure, allowing us to use already existing code developed for ion collisions with single-electron targets. Calculated total cross sections for electron capture, single ionisation, and excitation processes generally agree well with experimental data and other theoretical calculations where available. However, the total electron capture cross section is found to overestimate the experimental data at low energies, while the total ionisation cross section is slightly underestimated. Additionally, we present state-resolved cross sections for capture into the 1s, 2ell , and 3ell states of the projectile where deviation between various previous calculations is substantial. Our results lead to overall improvement over previous theoretical studies although discrepancies with experiment are observed for 3p and 3d capture. We conclude that treating molecular hydrogen as an effective one-electron system within the two-centre coupled-channel approach to one-electron targets can give reasonably accurate total cross sections at intermediate and high energies, without the need for a complex and computationally demanding two-electron target representation.

A combined experimental and theoretical study of photodouble ionization of water at 32 eV excess energy and unequal energy sharing

The photodouble ionization of water at about 32 eV excess energy has been investigated both experimentally and theoretically. In an energy and angular resolved photoelectron–photoelectron coincidence experiment, the two photoelectrons in unequal energy sharing (25 and 7 eV) condition, have been detected in a plane perpendicular to the propagation direction of the linearly polarized radiation. The measured angular distributions have been compared with, molecular orientation averaged, triple differential cross sections calculated with a recently developed theoretical model (Randazzo et al 2020 Phys. Rev. A 101 033407). The model uses separable products of orbitals as initial electronic state of the water molecule taken as a two-electron target and describes accurately the correlated two electron continuum. The combination of calculated cross sections corresponding to different dication states capture most of the measured features in terms of the evolution of both the shape and the intensity as a function of the faster electron direction which is set at 0°, 30° and 60° with respect to the polarization vector of the incident radiation. A detailed analysis in terms of the different dication states as well as of the partial wave contributions to the electron pair wave function sheds light on the origin of such features.

Revealing the two-electron cusp in the ground states of He and H2 via quasifree double photoionization

We report on kinematically complete measurements and ab initio non-perturbative calculations of double ionization of He and H2 by a single 800 eV circularly polarized photon. We confirm the quasifree mechanism of photoionization for H2 and show how it originates from the two-electron cusp in the ground state of a two-electron target. Our approach establishes a new method for mapping electrons relative to each other and provides valuable insight into photoionization beyond the electric-dipole approximation.

Wave-packet continuum-discretization approach to single ionization of helium by antiprotons and energetic protons

The recently developed wave-packet continuum-discretization approach [I. B. Abdurakhmanov, A. S. Kadyrov, and I. Bray, Phys. Rev. A 94, 022703 (2016)2469-992610.1103/PhysRevA.94.022703] is extended to antiproton-helium collisions. The helium target is treated as a three-body Coulomb system using a frozen-core approximation, in which the electron-electron correlation within the target is accounted for through the static interaction. The Schrodinger equation for the helium target is solved numerically to yield bound and continuum states of the active electron. The resulting continuum state is used to construct wave-packet pseudostates with arbitrary energies. The energies of the pseudostates are chosen in a way that is ideal for detailed differential ionization studies. Two-electron target wave functions, formed from the bound and continuum wave-packet states of the active electron and the 1s orbital of He+, are then utilized in the single-center semiclassical impact-parameter close-coupling scheme. A comprehensive set of benchmark results, from angle-integrated to fully differential cross sections for antiproton impact single ionization of helium in the energy range from 1 keV to 1 MeV, is provided. Furthermore, we use our single-center convergent close-coupling approach to study fully differential single ionization of helium by 1-MeV proton impact. The calculated results are in good agreement with recent experimental measurements [H. Gassert, O. Chuluunbaatar, M. Waitz, F. Trinter, H.-K. Kim, T. Bauer, A. Laucke, C. Muller, J. Voigtsberger, M. Weller, Phys. Rev. Lett. 116, 073201 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.073201] for all considered geometries.

DoubleK-shell photoionization of atomic beryllium

Double photoionization of the core $1s$ electrons in atomic beryllium is theoretically studied using a hybrid approach that combines orbital and grid-based representations of the Hamiltonian. The ${}^{1}\phantom{\rule{-0.16em}{0ex}}S$ ground state and ${}^{1}\phantom{\rule{-0.16em}{0ex}}P$ final state contain a double occupancy of the $2s$ valence shell in all configurations used to represent the correlated wave function. Triply differential cross sections are evaluated, with particular attention focused on a comparison of the effects of scattering the ejected electrons through the spherically symmetric valence shell with similar cross sections for helium, representing a purely two-electron target with an analogous initial-state configuration.

New (e,2e) studies of atomic and molecular targets

We report new coplanar (e,2e) measurements characterised by large energy transfer and close to minimum momentum transfer from the projectile to the target. Ionisation of the two-electron targets He and H2 is investigated under these particular kinematics. The experimental data are compared with the predictions of the most elaborate theoretical models. The obtained good agreement motivated us to extend our research to the case of more complex targets such as Ar. Comparison with the most elaborate models in the case of multi-electron targets is excellent. Destructive and constructive interference effects in the case of H2 are observed and discussed.

Differential investigations of charge transfer processes in low energy ion-atom/molecule collisions

The progress of differential studies of ion-atom/molecule collisions using the reaction microscope was reported. The state-selective and angular differential cross sections were measured for slow ion-atom collisions. In this paper we focus on the two-electron processes, namely double electron capture and transfer ionization, occurring in the collisions of ion impact on two-electron target system of helium and molecular hydrogen, respectively. The molecule Coulomb explosions were investigated by employing the negative ion characteristic. The transfer momentum dependence of two-electron processes for He2+ and H+ impact on He and H2 were compared, and the kinetic energy release in Coulomb explosions induced by He2+ and H+ was measured.

Eikonal model for projectile-electron excitation and loss in relativistic collisions

We present an eikonal model for electron excitation and loss from highly charged ionic projectiles colliding with atomic targets at relativistic collision energies. In this model the distortion of the target transition four-current by the strong field of the projectile nucleus is taken into account using the symmetric eikonal approximation. General expressions are derived for the eikonal transition amplitude in the case of collisions with one- and two-electron targets. The correspondence between the eikonal and first-order transition amplitudes is discussed. Relativistic features and the nonrelativistic limit of the eikonal transition amplitude are considered. It is shown that the higher-order terms in the projectile-target interaction, which are not accounted for by the first-order amplitude, may be of importance even for quite small values of {nu}=Z{sub p}/v, where Z{sub p} is the charge of the projectile nucleus and v the collision velocity.

Electron transfer to individual magnetic substates of 3p 2P in collisions of helium-like ions with two-electron targets

We measured the degree of polarization of the 3s 2S1/2–3p 2P3/2 transition of C3+ ions produced by one-electron transfer in the collisions of C4+ ions with H2 at energies of 30–80 keV by visible spectroscopy. The results in this work were compared with the previous works for the alignment of 3p states of lithium-like carbon ions by means of VUV spectroscopy. We also compared these with the degree of polarization of the isoelectronic transitions of other lithium-like ions, N4+ and O5+, and found the correlation between the polarization degree and the potential crossing distance in which the one-electron transfer reaction takes place. This collision system dependence in the polarization of the 3s 2S1/2–3p 2P3/2 transition was discussed with respect of the linear Stark effect by the residual target ion.

Preferential population of n=2 states in low-energy Li 3+–He collision: a molecular-state close-coupled treatment

The semi-classical, impact parameter, close-coupling method, in its molecular orbital form is employed to investigate the process of state selective charge transfer from a two-electron target (He) to the incident bare nucleus of Li (i.e. Li 3+) in the low-energy region. The effective binding of the active electron in the quasi-diatomic molecule formed during the course of collision is obtained for the first time in an ab initio way. The electron translation factor (ETF) modified Born–Oppenheimer wave function is generated to obtain the adiabatic molecular states of the quasi-molecule (LiHe) 3+. A set of eight close-coupled equations is solved numerically to obtain both the partial and total capture cross-sections at 0.5≤E≤5 keV amu −1. The cross-sections are compared with both the low-energy measurements and other available theoretical results. The explicit n- and l-distributions of the capture cross-sections are also presented for the first time. Comparison is made with a recent calculation carried out in a similar manner for Li 3+–H 2, another two-electron colliding system. The structureless ion of Li, as expected, favors highly state selective population of the Li 2+(2p) state in this collision.

Collision spectroscopy ofAr8++H2at low velocities(v<1a.u.)

Single and double electron transfer have been studied for the collision system ${\mathrm{Ar}}^{8+}{+\mathrm{H}}_{2}$ at low velocities $(v<1\mathrm{a}.\mathrm{u}.).$ X-ray ultraviolet and Auger spectroscopies complemented by translational energy gain and time-of-flight spectroscopies reveal details on the transfer mechanisms: in contrast to the other two-electron target system (He target), a channel is opened where electron capture takes place with further dissociation of ${\mathrm{H}}_{2}^{+}.$ We consider the target fragment dynamics and discuss possible molecule dissociation mechanisms.

Photoionization with excitation and double photoionization of two-electron atomic targets

We review recent theoretical results on the double photoionization and ionization with excitation of two-electron atomic targets obtained with the convergent close coupling (CCC) method. The method proved to be capable of producing accurate total ionization cross-sections for H-, He, and Li + in a wide photon energy range from the double ionization threshold to 10 keV where the results go over continuously to the non-relativistic limit of infinite photon energy. By applying scaling laws these results can be extrapolated to all two-electron systems with an arbitrary nucleus charge Z. Present theory can also describe accurately the angular correlation in the two-electron continuum in the form of the fully-resolved triple-differential cross-section (TDCS). The latest results for the TDCS on He agree very well with recent absolute measurements with linearly polarized light.

Highly charged ion-molecule collisions

Experimental studies of collisions between highly charged ions and molecules have been carried out using the coincidence time of flight technique at high and low collision velocities. We have studied ionization of the target molecule and electron capture caused by ion impact. In general the trends are similar for molecular and atomic targets, and thus one can use the knowledge about one kind of target to help understand the other. Twoelectron processes, like ionization-excitation and double-ionization, become almost as important as single-electron processes in collisions between highly charged ions and two-electron targets. It is shown that in collisions between highly charged ions and molecules the high energy tail of the distribution of kinetic energy released in the dissociation into ion-pairs is associated with one or two electrons in highly excited states.

Quasiclassical-trajectory Monte Carlo methods for collisions with two-electron atoms.

A quasiclassical-trajectory Monte Carlo (QTMC-EB) model is proposed to extend the classical-trajectory Monte Carlo (CTMC) method to targets having more than one electron. Quasiclassical stability is achieved via constraining potentials that enforce lower energy bounds on the one-electron dynamics. Cross sections for all possible electronic rearrangements (single and double electron transfer, single and double ionization, and transfer ionization) in ${\mathrm{H}}^{+}$+H, ${\mathrm{H}}^{+}$+He, ${\mathrm{He}}^{2+}$+He, and ${\mathrm{Li}}^{3+}$+He collisions are calculated with this model and with the previously proposed model (QTMC-KW) of Kirschbaum and Wilets [Phys. Rev. A 21, 834 (1980)]. The results are compared with accurate experimental data. The regime of validity for the two-electron targets is found to be similar to that of the usual CTMC model for one-electron targets. \textcopyright{} 1996 The American Physical Society.

Scaling laws in double photoionization.

Double-photoionization cross sections are calculated for two-electron targets ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}$, He, ${\mathrm{Li}}^{+}$, and ${\mathrm{O}}^{6+}$ using a correlated and an uncorrelated two-electron continuum wave function (C3 and C2 models, respectively). As the target nuclear charge ${\mathit{Z}}_{\mathit{T}}$ is increased, the double-photoionization cross section is found to scale as ${\mathit{Z}}_{\mathit{T}}^{\mathrm{\ensuremath{-}}4}$ and the electron energy distribution as ${\mathit{Z}}_{\mathit{T}}^{\mathrm{\ensuremath{-}}6}$. Conclusions are extracted about the behavior of the cross sections in the high-energy and threshold regions. The ratio of double to single photoionization scales as ${\mathit{Z}}_{\mathit{T}}^{\mathrm{\ensuremath{-}}2}$, as in the case of proton impact.

Electron capture by protons and alpha particles from two-electron targets

The modified two-orthogonal state expansion method published previously is applied to calculate electron capture cross sections for two-electron systems: H+, He2++Be2+, B3+, C4+, N5+ and O6+, H++He and He2++Li(1s2). The active electron is described by the independent-electron model. The calculated results agree well with the existing experimental data for H++He and He2++Li collisions in the ranges 5-130 keV and below 500 keV amu-1 respectively. The author's results for H+, He2++C4+ systems are in good agreement with the experimental values for H+, He2++CH4 collisions in the intermediate energy range. A comparison with other theoretical results is presented. Scaling laws for these cross sections are examined.

Wavefunction effects in theoretical (e,2e) cross sections for ionization of helium with excitation of the residual ion

Calculations of triple differential cross sections for the process where impact of a moderately energetic electron on a two-electron target simultaneously ejects one of the electrons and excites the other are made in the framework of a first Born approximation without exchange. Results obtained using ejected electron wavefunctions calculated with Coulomb potentials of different effective charge, with the static potential due to the unperturbed residual ion, or with Klapisch-type parametric potentials, are compared with experimental data. Strong dependence on the final state wavefunction is found, notably for the ratio between contributions from excitation of the 2s0, 2p0 and 2p+or-1 residual ion states. The cross sections, both globally and for the individual contributions, are however insensitive to the amount of correlation in the initial state wavefunctions.

Transfer excitation in slow collisions between ions of very high charge and two-electron targets.

We argue that a three-step transfer-excitation (capture and target excitation) mechanism enhances (depletes) the cross section for one- (two-) electron removal from a two-electron target. This mechanism, which becomes very important at high projectile charge (q), is mediated through quasimolecular couplings between diabatic double-capture and transfer-excitation channels, in which the inner of two active electrons is transferred to an excited target state. The inclusion of this process in the extended classical over-barrier model gives excellent agreement with unexplained experimental cross sections for one- and two-electron removal from He in slow collisions with Xe ions of high charge (q\ensuremath{\le}31).

Dynamics of neutral vacuum decay.

A time-independent Hamiltonian formulation of relativistic atomic structure and scattering problems is developed in which virtual-pair creation and annihilation effects are explicitly included. The method is discussed in the context of a specific problem---the scattering of a positron by a system consisting of two electrons bound to a nucleus of charge {ital Z}. This provides the basis for a consistent treatment of spontaneous positron production that can occur when {ital Z} exceeds a critical value {ital Z}{sub cr}{approx}173. For {ital Z} not too much greater than {ital Z}{sub cr} the two-electron atom is stable and represents the (doubly charged) vacuum state. In the approach adopted here the one-electron state, which is unstable against spontaneous pair creation, is viewed as a resonance in the scattering of the positron by the two-electron target atom. The lifetime of the unstable state is determined, in the usual way, from a knowledge of the width of the resonance. The formal resonance theory required to carry out this analysis is developed here with the aid of an effective-potential description of the scattering problem of the type familiar from standard treatments of resonant processes in nonrelativistic atomic and nuclear reaction theories.

Double ionization of helium by antiprotons

We have developed a calculational scheme, the forced impulse method, for going beyond the independent particle model in ion-atom collisions. Our first application has been to the double ionization of helium; this requires construction of double ionization pseudostates. Initial calculations yielded good agreement with experimental results on the double ionization by protons, antiprotons, and alpha particles in the MeV/amu collision energy regime, and in particular reproduced the observed difference in double ionization by protons and antiprotons. We report here the results of expanding the angular momenta included in our single-particle basis, double ionization cross sections for other two-electron targets, and impact parameter dependences. Emphasis is on what we learn from our calculations about the mechanism for double ionization, and the physical reason for the observed difference in double ionization by protons and antiprotons.