Continuum Distorted-wave Research Articles

Binary Encounter Electrons in Fast Dressed-Ion–H2 Collisions: Distorted Wave Theories and Experiment

We report measurements of double differential cross section for zero-degree binary encounter electrons emitted in collisions of 4.9 MeV and 13 MeV B(2−5)+ ions with H2 targets. The corresponding calculations based on continuum distorted-wave (CDW) theories are critically compared to the measurements. CDW in its post form exhibits a very good agreement with the measurements in all cases. The CDW theories utilized along with the well-known eikonal-initial-state (CDW-EIS) approximation are also examined and their results are compared to both the measurements and the CDW calculations. In particular, CDW-EIS using a recently proposed dynamic effective charge for the final channel projectile distortion exhibits a substantial improvement in comparison with an effective net-charge approximation.

Subshell contributions to electron capture into the continuum in MeV/u collisions of deuterons with multielectron targets

The process of the capture of a target electron into the projectile continuum (ECC) is investigated both experimentally and theoretically for collisions of 1.25--6.00 MeV deuterons with multielectron gas targets. Double-differential cross sections (DDCS), ${d}^{2}\ensuremath{\sigma}/d\mathrm{\ensuremath{\Omega}}\phantom{\rule{0.16em}{0ex}}dE$, of the ECC cusp-shaped electron peak involving He, Ne, and Ar gas targets were measured at the emission angle of zero degrees with respect to the ion-beam velocity. Corresponding DDCS calculations, obtained using continuum distorted-wave (CDW) and continuum distorted-wave eikonal initial-state (CDW-EIS) theories, were critically compared to the measurements. The role of each atomic subshell of the multielectron Ne and Ar targets is examined employing the CDW-EIS theory with numerical target wave functions, which is found to best agree with the measurements.

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.

A Complete CDW Theory for the Single Ionization of Multielectronic Atoms by Bare Ion Impact

A complete form of the post version of the continuum distorted wave (CDW) theory is used to investigate the single ionization of multielectronic atoms by fast bare heavy ion beams. The influence of the non-ionized electrons on the dynamic evolution is included through a residual target potential considered as a non-Coulomb central potential through a GSZ parametric one. Divergences found in the transition amplitude containing the short-range part of the target potential are avoided by considering, in that term exclusively, an eikonal phase instead of the continuum factor as the initial channel distortion function. In this way, we achieve the inclusion of the interaction between the target active electron and the residual target, giving place to a more complete theory. The present analysis is supported by comparisons with existing experimental electron emission spectra and other distorted wave theories.

Multicenter continuum-distorted-wave eikonal-initial-state description of the electron-impact ionization of aligned H2 molecules

In this work, the multicenter continuum-distorted-wave (CDW) eikonal-initial-state (EIS) model is introduced. In contrast to previously reported CDW EIS analyses for electron-molecule collisions, in which the ionized electron interacted with the molecular ion via a one-center effective potential, the multicenter nature of the molecular ion is explicitly taken into account. Results obtained for electron-impact ionization of oriented ${\mathrm{H}}_{2}$ molecules at the fully differential level are presented and contrasted with recent experimental data and reported theoretical calculations obtained with the time-dependent close-coupling method. The present results suggest that this simple molecule still represents a challenging target from a theoretical point of view and that many aspects of the ionization process at the fully differential level remain to be understood.

Intra- and intercycle interference of angle-resolved electron emission in laser-assisted XUV atomic ionization

A theoretical study of ionization of the hydrogen atom due to an XUV pulse in the presence of an infrared (IR) laser is presented. Well-established theories are usually used to describe the laser-assisted photoelectron effect: the well-known soft-photon approximation firstly posed by Maquet et al (2007 J. Mod. Opt. 54 1847) and Kazansky’s theory in (2010 Phys. Rev. A 82, 033420). However, these theories completely fail to predict the electron emission perpendicularly to the polarization direction. Making use of a semiclassical model (SCM), we study the angle-resolved energy distribution of PEs for the case that both fields are linearly polarized in the same direction. We thoroughly analyze and characterize two different emission regions in the angle-energy domain: (i) the parallel-like region with contribution of two classical trajectories per optical cycle and (ii) the perpendicular-like region with contribution of four classical trajectories per optical cycle. We show that our SCM is able to assess the interference patterns of the angle-resolved PE spectrum in the two different mentioned regions. Electron trajectories stemming from different optical laser cycles give rise to angle-independent intercycle interferences known as sidebands. These sidebands are modulated by an angle-dependent coarse-grained structure coming from the intracycle interference of the electron trajectories born during the same optical cycle. We show the accuracy of our SCM as a function of the time delay between the IR and the XUV pulses and also as a function of the laser intensity by comparing the semiclassical predictions of the angle-resolved PE spectrum with the continuum-distorted wave strong field approximation and the ab initio solution of the time-dependent Schrödinger equation.

Influence of eikonal-initial-state on ionization of atom by proton

Apart from its fundamental importance, ionization phenomenon of atoms by impact of energetic charged particles has practical applications in various kinds of plasmas, in radiation physics and in the study of penetration of charged particles through matter. Compared with other processes, this particular reaction helps to reveal many details about the dynamical process and the level population, and, in fact, can provide a new insight into and a promising route to studying the e-p interactions in the presence of Coulomb field. The development of ion sources producing multiply charged ions and of antiproton beams allow us to change the potentials and hence the whole final momentum distribution. A great variety of experimental conditions allowed by changing the projectile charge and velocity constitute a stringent test for theory. The continuum-distorted-wave eikonal-initial-state (CDW-EIS) approximation model has emerged as a reliable method to compute cross sections for different projectile/target combinations from intermediate to high non-relativistic impact energies. This model is of the first order in a distorted-wave series. It takes into account the long-range behaviour of the Coulomb potential and includes the distortion of the target states in both the initial and final channels. In the present work, the single different cross sections (SDCS), double different cross sections (DDCS), and total cross sections for single ionization of 1s, 2s and 2p shell of Ne atom by impact of proton are calculated in the framework of continuum-distorted-wave (CDW) method and the CDW-EIS approximation model, respectively. The influence of the eikonal-initial-state on the cross section, and the mechanism of the proton-atom collision ionization are discussed in detail. Moreover, the structures of the SDCS and DDCS of each shell are studied and the ionization mechanism of soft collision, electron capture to the continuum state, binary encounter collision are demonstrated. Our results show that for the 2p shell of Neon, as the incident proton energy increases, the region of the SDCS becomes larger and the soft ionization turns dominant in the low energy region. The eikonal-initial-state effect on the cross section is obvious in the lower energy region, yet smaller as the incident energy increases. These effects on the DDCS are greater than on the SDCS. The present CDW-EIS and CDW results are compared with the experimental data available in the energy range of 1-5000 keV/u for H+ on Ne in the literature, showing that they are quantitatively in good agreement. In general, the CDW-EIS describes well the multiple ionization above 50 keV/u, showing a clear tendency to coalesce with the CDW at high energies.

Intra- and intercycle interference of electron emissions in laser-assisted XUV atomic ionization

We study the ionization of atomic hydrogen in the direction of polarization due to a linearly polarized XUV pulse in the presence a strong field IR. We describe the photoelectron spectra as an interference problem in the time domain. Electron trajectories steming from different optical laser cycles give rise to intercycle interference energy peaks known as sidebands. These sidebands are modulated by a grosser structure coming from the intracycle interference of the two electron trajectories born during the same optical cycle. We make use of a simple semiclassical model which offers the possibility to establish a connection between emission times and the photoelectron kinetic energy. We compare the semiclassical predictions with the continuum-distorted wave strong field approximation and the ab initio solution of the time dependent Schr\"odinger equation. We analyze such interference pattern as a function of the time delay between the IR and XUV pulse and also as a function of the laser intensity.

Comparison of experimental and theoretical fully differential cross sections for single ionization of the2sand2pstates of Li byO8+ions

This paper presents a full three-dimensional (3D) comparison between experiment and theory for 24 MeV ${\mathrm{O}}^{8+}$ single ionization of the $2s$ ground state of lithium and the $2p$ excited state. Two theoretical approximations are examined: the three-body continuum distorted-wave (3DW) and three-body continuum distorted-wave--eikonal initial state (3DW-EIS). Normally, there is a significant difference between these two approaches and the 3DW-EIS is in much better agreement with experiment. In this case, there is very little difference between the two approaches and both are in very good agreement with experiment. For the excited $2p$ state, the 3D cross sections would exhibit a mirror symmetry about the scattering plane if all three magnetic sublevels were excited in equal proportions. For the present experiment, the $2{p}_{+1}\phantom{\rule{4pt}{0ex}}(m=+1)$ sublevel is dominantly excited (quantization axis is the incident beam direction) and for this case there is a magnetic dichroism which is observed both experimentally and theoretically.

Electron emission in collisions of fast highly charged bare ions with helium atoms

We have studied the electron emission from ground state helium atom in collision with fast bare heavy ions at intermediate and high incident energies. In the present study, we have applied the present three-body formalism of the three Coulomb wave (3C-3B) model and the previously adopted four-body formalism of the three Coulomb wave (3C-4B). To represent the active electron in the helium atom in the 3C-3B model, the initial bound state wavefunction is chosen to be hydrogenic with an effective nuclear charge. The wavefunction for the ejected electron in the exit channel has been approximated to be a Coulomb continuum wavefunction with same effective nuclear charge. Effectively the continuum-continuum correlation effect has been considered in the present investigation. Here we have calculated the energy and angular distribution of double differential cross sections (DDCS) at low and high energy electron emission from helium atom. The large forward-backward asymmetry is observed in the angular distribution which is explained in terms of the two-center effect (TCE). Our theoretical results are compared with available experimental results as well as other theoretical calculations based on the plain wave Born approximation (PWBA), continuum-distorted wave (CDW) approximation, continuum-distorted wave eikonal-initial state (CDW-EIS) approximation, and the corresponding values obtained from the 3C-4B model [S. Jana, R. Samanta, M. Purkait, Phys. Scr. 88, 055301 (2013)] respectively. It is observed that the four-body version of the present investigation produces results which are in better agreement with experimental observations for all cases.

Coulomb Three-Body Effects in the Single Ionization of Helium by 16MeV $O^{7+}$ Impact

Three-Coulomb-wave (3C)model is applied to study the single ionization of helium by 16MeV O7+ impact in the scattering plane. Fully differential cross sections (FDCS) is presented for the different momentum transfers. Our theoretical results are compared with the recent experimental data and the results of continuum distortedwave eikonal-initial-state (CDW-EIS). It is shown that the 3C calculations qualitatively reproduce the experimental peak structure, especially at smaller momentum transfers. PACS: 34.80.Dp

CDW and CDW-EIS calculations of simultaneous ionization in collisions between dressed projectiles and atomic targets

SynopsisThe role of simultaneous electron emission in collision between dressed ions and atoms is discussed. Methods of calculations within quantum-mechanical Continuum-Distorted- Wave (CDW) and Continuum-distorted Wave-Eikonal-Initial-State (CDW-EIS) models are revisited and improved within a semiclassical probabilistic approach.

Relativistic effects in electron-capture to the continuum in 90 MeV/u U88+ +N2 collisions

SynopsisThe Continuum Distorted Wave (CDW) model is used to describe electron-capture to continuum cusp in 90 MeV/u U88+ + N2 collisions. Relativistic effects are studied considering Lorentz transformations on the electron kinematics.

How include properly the dynamic-screening into the post-version of the Continuum Distorted Wave model

SynopsisThe post-version of the Continuum Distorted Wave (CDW) model neglects a part of the active electron- residual target interaction which has been shown to play a major role in obtaining the doubly differential cross sections (DDCS) for electron ionization. In this work we properly include the dynamic screening into the CDW model showing its influence over the ionization DDCS for several collision systems.

Production of excitons in grazing collisions of protons with LiF surfaces: An onion model

In this work we evaluate the production of excitons of a lithium fluoride crystal induced by proton impact in the intermediate and high energy regime (from 100 keV to 1 MeV). A simple model is proposed to account for the influence of the Coulomb grid of the target by dressing crystal ions to transform them in what we call onions. The excited states of these onions can be interpreted as excitons. Within this model, total cross section and stopping power are calculated by using the first Born and the continuum distorted-wave (CDW) eikonal initial-state (EIS) approximations. We found that between 7 and 30 excitons per incident proton are produced in grazing collisions with LiF surfaces, becoming a relevant mechanism of inelastic transitions.

Non-statistical population of 1s2s2p4PJ states by charge transfer into multiply charged ions

The experimentally observed enhancement of (1s2s3s)ml4P to (1s2s3S)ml2P populations in collisions of He-like ions with H2 and He targets is discussed and explained by a state-selective cascade feeding mechanism. Continuum Distorted Wave (CDW) and Classical Trajectory Monte Carlo (CTMC) calculations show that large populations of higher lying (1s2s 3S)nℓ2'4L Rydberg states for ℓ = L = 0, n-1 and n = 2 - 8 can be formed in 0.25-2 MeV/u collisions by direct capture to metastable F7+(1s2s3S) ions. These states subsequently decay through a cascade sequence of radiative or Auger transitions dictated by angular momentum and spin selection rules. All radiative (E1) and Auger transitions for n = 5 were evaluated using the Cowan package for Hartree-Fock calculations. The (1s2s3S)ml2L doublets were found to Auger decay rapidly to the 1s2 level allowing for negligible cascade feeding of lower lying doublets including the 1s2s2p2P±. Alternatively, Auger decay of the (1s2s3S)ml4L quartets is blocked by spin selection rules. Decay can proceed, however, through dipole transitions, but only to other quartets, including the lowest lying 1s2s2p4P state, which in this way acts as an "excited ground state" eventually collecting most cascade flux. This selective cascade feeding mechanism thus leads to the non-statistical enhancement of the 1s2s2p4P quartet population over those of the 1s2s2p2P± doublet populations providing an alternative explanation to the recently suggested novel mechanism of dynamical Pauli exchange.

CDW theoretical description of the single ionization of argon by positron and electron impact

In this work, we consider the single ionization of Ar by 200eV positron and electron impact. The quantum mechanical continuum distorted wave (CDW) model is used in the one-active electron approximation. Parametrizations of Hartree–Fock potentials by Garvey et al. are used to represent the interaction of the light particles with the Ar+ ion. The post collisional interaction (PCI) between the emitted electron and the receding projectile is naturally considered by the present model. Comparison with recent experimental data for very asymmetric geometries is made. The role of the PCI is studied by analyzing the differences in the angular distributions for positron and electron impact predicted by the CDW model and the first Born approximation.

Production of 1s2s2p4P states by transfer-loss cascades in O5+ collisions with he and H2 targets

Single differential cross-sections for transfer-loss (TL) leading to the production of O5+(1s2s3S)nl4L states were computed for 0.2-1.2 MeV/u collisions of O5+(1s22s) ions with He and H2 targets. At these collision energies, 1s loss is significant and electron transfer to n = 3-4 levels is dominant. Furthermore, due to spin conservation, quartet states can only be populated by TL. Within the independent particle model (IPM), the probability of 1s electron loss from O5+(1s22s) projectiles was calculated using the semi-classical approach, while the probability for electron transfer to the O5+(1s2s3S)nl4L states (n > 2) was computed using the continuum distorted wave (CDW) approximation. The majority of states with n > 2 can be assumed to have sufficient time to eventually decay with an almost 100% probability to the long-living metastable 1s2s24P level via a much faster sequence of electric dipole transitions, thus establishing an upper limit to such cascade contributions. The inclusion of this cascade feeding is found to lead to a strong enhancement in the production of the 1s2s2p4P states, particularly for collisions with the H2 target, thus reducing dramatically the existing two-order of magnitude discrepancy between older TL calculations (for n = 2 only) and existing zero-degree Auger projectile electron spectroscopy measurements.

Total and single differential cross sections for simple resonant collisions using a fully orthonormal continuum-distorted-wave basis

Simple electron capture processes are studied using an orthonormal two state continuum-distorted-wave (CDW) basis. The suitability of the basis set is tested by comparing predictions for total and differential cross sections with available experimental data. Overall good agreement is obtained and the authors conclude that a relatively small CDW basis set may be suitable to model a wide variety of low-energy collisions if the members of this extended set are astutely chosen.

Influence of the electron binding energy in the distortion of the initial state in ion-atom collisions

In this work, we propose a modified continuum distorted wave (CDW) theory for ion-atom ionization that incorporates an electron effective-mass model for the bound electron-projectile distortion in the entrance channel. Distorted wave theories have been shown to be adequate when the projectile impact energy is high enough but, as the projectile velocity decreases, both CDW and continuum distorted wave--eikonal initial state (CDW-EIS) approximations exhibit remarkable discrepancies when compared with the available experimental data, in particular for highly charged ion impact. Our modified CDW approximation incorporates the active electron binding energy in the distorted wave description of the initial state. We found very good agreement with experimental data in a single ionization doubly differential cross section for multiply charged projectiles and impact energies as low as 50 keV∕amu.