Multi-electronic Processes in Collisions Involving Charged Particles and Photons with Atoms and Molecules E-Book
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- Herausgeber: Bentham Science Publishers
- Kategorie: Wissenschaft und neue Technologien
- Serie: Frontiers in Nuclear and Particle Physics
- Sprache: Englisch
This volume describes the advanced research on the behavior of electrons in ionized atoms and molecules. Readers will learn about relevant techniques used and experimental results for different electron and molecular theories. The information presented in
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Veröffentlichungsjahr: 2018
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Frontiers in Nuclear and Particle
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Antônio Carlos Fontes dos Santos
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FOREWORD
This e-book explores some of the most exciting frontiers of atomic, molecular and nuclear physics. Written and illustrated in a simplified manner, this e-book aims to provide insight to its readers how electrons play a major role in the atomic and nuclear collision processes. Indeed, this book contains a wealth of theoretical information and variety of fascinating experiments to unravel the fundamental mechanisms positron, negative, ion, photons, protons, and antiprotons which makes the readers visualize different types of collisions and the physics behind. Each of the nine chapters in this bool are written by prominent scientists from atomic and molecular physics including Prof. R. D. DuBois and A. C. F. Santos.
This eBook covers several essential aspects of multiple interaction processes between electrons, nucleus, atoms and molecules. It addresses exciting applications of these fundamental processes, and gives insights in the recent experimental and theoretical developments of leading research groups of these areas. It will provide the researchers of this field a valuable overview of this broad and rapidly evolving field. The various contributions, mostly from Latin-American research groups, show the dynamism of this community in the area of basic molecular processes. The forthcoming facility "Syrius Project" in Brazil will benefit from the expertise of this community and allow the realization of ground-breaking experiments. We hope that this eBook will promote interactions between the researchers of this area and provoke many passionate discussions.
PREFACE
This eBook contains nine contributions, covering a diversity of subject areas in atomic, molecular and nuclear physics. Robert (Bob) DuBois surveys the ionization by antiparticles and particles. He compares fully to total differential ionization cross sections and finds where the differences are. His contribution concentrates on the progress and methods used in particles and antiparticles based studies of inelastic atomic interactions. This chapter shows how new experimental techniques are critical in advancing experimental studies from total or integral cross section measurements to highly differential investigations that are now being performed. The primary emphasis is on ionization of atoms and simple molecules by low-energy positrons and in showing similarities and differences between positron, electron and proton impact data. Experimental techniques associated with the generation, moderation, and transport of low-energy positron beams summarizing existing experimental studies are provided. Comments with respect to future studies and directions, plus how they might be achieved, are presented.
The chapter by Alcantara et al. deals with photoionization of an important atmospheric molecule, the dichloromethane. Chemical processes are of significant importance in determining the equilibrium distribution of ions in planetary ionospheres. Photoionization and impact ionization are responsible for the initial creation of the electron-ion pairs. Thus, the knowledge of the chemical processes taking place in the Earth`s atmosphere is necessary for the understanding of ionospheric structure and behavior. Thus, the chapter by Alcantara et al. presents the centre of mass kinetic energy release distribution spectra of ionic fragments, formed through dissociative single and double photoionization of CH2Cl2 at photon energies around the Cl 2p edge, which were extracted from the shape and width of the experimentally obtained time-of-flight distributions. The authors report that the kinetic energy distributions spectra exhibit either smooth profiles or structures. In the particular case of double ionization with the ejection of two charged fragments, the kinetic energy distributions present own characteristics compatible with the Coulombic fragmentation model. Intending to interpret the experimental data singlet and triplet states at Cl 2p edge of the CH2Cl2 molecule, corresponding to the resonant transitions, were calculated at multiconfigurational self-consistent field level and multireference configuration interaction. Minimum energy pathways for dissociation of the molecule were additionally calculated aiming to support the presence of the ultra-fast dissociation mechanism in the molecular break-up.
Paulo Limão-Vieira and colleagues revisit electron transfer processes yielding negative ion formation in gas-phase collisions of fast neutral potassium atoms (electron donor) and biomolecular target molecules (electron acceptor) in a crossed molecular-beam arrangement. The negative ions formed in the interaction region are time-of-flight (TOF) mass analysed as a function of the collision energy. Selective site and bond excision in the unimolecular decomposition of the transient negative show clear dependence on the collision energy.
The chapter by Santos and Almeida aims to the study of electron correlation in atoms, which is a significant but difficult study subject to its many-body interactions, nevertheless it may be the main process to describe the absolute electron impact cross section for the ionization of atoms and molecules. The outer-shell double photoionization of a multi-electron target is usually a weak process in comparison to single photoionization and it is determined completely by electron-electron interaction. The main scope of this chapter has been upon a review of the recently found relationship between shake-off probabilities and target atomic number and electron density. By comparing the saturation values of measured double-to-single photoionization ratios from the literature, a simple scaling law was found, which allows us to forecast the shake-off probabilities for several atomic elements up to xenon within a factor two. The electron shake-off probabilities accompanying valence shell photoionization have been scaled as a function of the target atomic number, and static polarizability.
Claudia Montanari analyzes the multiple ionization by the impact of singly charged projectiles: electrons, positrons, protons and antiprotons. This comparison allows to study the mass and charge effects on the ionization processes. To that end Dr. Montanari includes the theoretical description given by the continuum distorted wave eikonal initial state, and a detailed compilation of the experimental data available for particle (proton and electron) and antiparticle (antiproton and positron) multiple ionization of the heaviest rare gases. The multiple ionization results include the Auger-type post-collisional contribution, which enhances the number of emitted electrons. For heavy projectiles, this is important at high energies. For light projectiles such as electrons and positrons, the Auger-type processes dominate the highly-charged ion production in the whole energy range, even close to the energy threshold. For this reason, the theoretical calculation of multiple ionization values requires good description of the deep-shell contributions.
In a work involving researchers from USA, Canada and Brazil, the fragmentation of the tetrachloromethane molecule, following core-shell photoexcitation and photoionization in the neighborhood of the chlorine K-edge is presented by using time-of-flight mass spectroscopy and monochromatic synchrotron radiation. Branching ratios for ionic dissociation were derived for all detected ions, which are informative of the decay dynamics and photofragmentation patterns of the core-excited species. In addition, the absorption yield has been measured, with a new assignment of the spectral features. The structure that appears above the Cl 1s ionization potential in the photoionization spectrum, has been ascribed in terms of the existing connection with electron-CCl4 scattering through experimental data and calculations for low-energy electron-molecule cross sections. In addition, the production of the doubly ionized Cl2+ as a function of the photon energy has been analyzed in the terms of a simple and appealing physical picture, the half-collision model.
Tőkési and Varga present a theoretical description of the spectra of electrons elastically scattered from various samples. The analysis is based on very large scale Monte Carlo simulations of the recoil and Doppler effects in reflection and transmission geometries. Besides the experimentally measurable energy distributions the simulations give many partial distributions separately, depending on the number of elastic scatterings (single, and multiple scatterings of different types). Furthermore, they present detailed analytical calculations for the main parameters of the single scattering, taking into account both the ideal scattering geometry, i.e. infinitesimally small angular range, and the effect of the real, finite angular range used in the measurements. The effect of the multiple scattering on intensity ratios, peak shifts and broadening, is shown. The authors show results for multicomponent and double layer samples. Our Monte Carlo simulations are compared with experimental data.
Ginette Jalbert et al present a contribution that relates molecular and atomic physics with the fundamental of quantum mechanics. This chapter reports the accomplishment of successful measurements in detecting two metastable atoms H(2s) metastable atoms arriving from the dissociation of the same hydrogen molecule induced by electron impact. Two detectors, placed close to the collision center, measure the neutral metastable H(2s) through a localized quenching process, which mixes the H(2s) state with the H(2p), leading to a Lyman-α detection. The data show the accomplishment of a coincidence measurement which proves for the first time the existence of the H(2s) + H(2s) dissociation channel. These results may stimulate theoretical computations regarding the production of H(2s)+ H(2s) coming from the doubly excited states, by electron impact, of the molecular hydrogen. In addition, an emerging pair of atoms with mean lifetime of the order of 0.1 s and with polarized angular momentum (polarized spin or polarized total angular momentum) may provide a new manner to obtain insight into the complex field of the molecular interactions, from the short-distance to the long-distance domain of interactions between moving atoms. Besides, the authors present a proposal to test the spin coherence of molecular dissociation processes. Clearly, the H(2s) + H(2s) dissociation channel has a great potential as a coherent twin-atom source.
Finally, most of the knowledge of the atomic nucleus was obtained from experimental data involving stable nuclei or nuclei in the vicinity of the stability line. Since the 1980s, several intermediate energy laboratories in the world started to produce nuclei out of the stability line, Rare Ion Beams. Many new interesting phenomena related to these nuclei have been discovered so far. Light nuclei far away from the stability line such as 6,8He, 11Be, 11Li, 22C, 24O and others have been produced in laboratory. Some of these nuclei present a pronounced cluster structure formed by a core plus one or more loosely bound neutrons forming a kind of low density nuclear matter around the core (nuclear halo). Most of the research involving RIB was developed at intermediate energies, from 30 up to hundreds of MeV/nucleon, and more recently, some facilities are producing secondary beams to perform scattering experiments at energies around the Coulomb barrier. Heavy ion elastic scattering angular distributions at incident energies close to the Coulomb barrier, when plotted as a ratio to the Rutherford cross section, frequently exhibit a typical Fresnel type diffraction pattern, with oscillations in the forward angle region. This behaviour is a consequence of the interference between the Coulomb and nuclear scattering amplitudes. Due to the low binding energies of exotic projectiles, the coupling between the elastic channel and the breakup states of the projectile is very important and strongly affects the elastic angular distributions, with a damping of the Fresnel oscillations and the complete disappearance of the Fresnel peak in some cases. To describe the effect of the breakup of the projectile in the elastic scattering, new theoretical approaches have been developed. Viviane Morcele and colleagues present elastic scattering angular distributions at energies a little above the Coulomb barrier. The angular distributions have been analyzed by Continuum-DiscretizedCoupled-Channels calculations to take into account the effect of the 6He breakup on the elastic scattering. Two different approaches were used to describe the structure of the projectile. One considering the 6He as a three-body system consisting of an alpha particle and two neutrons which, in addition to the target, form a four-body problem. To compare, in a second approach, the projectile is described as a two-body cluster formed by an alpha particle plus a di-neutron. A new kind of effect due to the projectile breakup in the elastic scattering angular distributions is reported.
I would like to thank the authors for their contributions and cooperation in assembling this ebook.
List of Contributors
Antimatter-Matter and Matter-Matter Atomic Interactions: Their Similarities and Differences
R.D. DuBois*Abstract
Total and differential cross sections for positron and electron impact on argon atoms are compared in order to show their similarities and differences. These comparisons provide information as to how antimatter-matter atomic interactions are like, or different from, matter-matter interactions that are normally encountered. Plus such comparisons provide information about how simply changing the direction of the coulomb field in atomic interactions influences the interaction probabilities and the kinematics. Data taken from the literature are used for these comparisons. The selected data are considered to be the most reliable available and representative of the many studies performed to date.
INTRODUCTION
Many types of atomic interactions take place as charged atomic particles impact on or travel through gases, liquids and solids. These range from elastic scattering, where only the projectile momentum is altered, to highly inelastic processes, where a significant amount of the projectile kinetic energy and momentum can be transferred to one or more target electrons. Beginning over a century ago, many electron beam studies have been performed to investigate such processes. With the discovery of the positron, new possibilities became possible. These include the ability to enhance our understanding of matter-matter interactions since for positron impact certain interactions such as electron exchange are prohibited. Thus, comparing electron and positron impact data can show the importance of this process. Also, comparison of positron and electron impact data can provide
information about how simply reversing the Coulomb forces alters various interaction probabilities and reaction kinematics. Such information can be used to test and improve existing theoretical models of matter-matter interactions. In addition, comparison of positron and electron induced processes provides insight into the similarities and differences of antimatter-matter and matter-matter interactions.
Here, we will compare positron and electron impact data for interactions with argon atoms using a range of experimental information currently available. The primary reason for choosing interactions with argon atoms is because many positron based studies with argon have been performed. Another reason is that any similarities and differences observed for argon should also be representative of interactions involving other multi-shell, medium size atoms, thus a somewhat broader picture can be obtained.
Fig. (1) shows a simple schematic picture of how positrons and electrons behave differently as they approach, pass by, and depart an atom. There are two major differences, both of which are associated with the sign of the projectile charge. One difference is a trajectory effect, where because the coulomb force between the projectile and partially screened nucleus is attractive/repulsive for electrons/positrons, the impact parameter will be smaller/larger for otherwise equivalent incoming particles. This means that the probability of interaction as well as the interaction kinematics will differ. Another trajectory effect occurs post-collision. Depending on the sign of the projectile charge, the scattered particle and the ejected electron will either be attracted to or repelled from each other.
The other major difference is a polarization effect where again because of the opposite direction of the coulomb forces, the target electron cloud is attracted to or pushed away from the interacting particle. Again, this will influence the interaction probabilities and to some extent the final kinematics. Please note that for antimatter-matter lepton ionizing interactions, e.g., for positron impact, the outgoing particles are distinguishable. Thus the kinematics can be studied in detail. In contrast, for matter-matter ionizing interactions by leptons, e.g., for electron impact, kinematic arguments must be used to “identify” the outgoing particle. Other differences, not shown in Fig. (1) but easy to visualize, include the presence or absence of certain channels such as electron exchange (present only for electron impact) or capture (present only for positron impact).
Fig. (1)) Schematic showing target polarization and trajectory effects for positron and electron impact.From a theoretical viewpoint, the attractive/repulsive trajectory effects are associated with scattering from the target core potential. This results in a repulsive force for positrons and an attractive force for electrons. This core scattering term must be combined with a polarization term which is attractive for positrons and repulsive for electrons. At low impact energies these terms tend to cancel for positron impact and add for electron impact whereas at sufficiently high energies, the polarization term becomes unimportant and only the static core interaction remains. These imply larger interaction cross sections for electron impact at low energies and identical cross sections at high energies.
Using a physical picture, the polarization and trajectory effects mean that the nuclear charge is more effectively screened for positron impact than it is for electron impact. Thus, one would expect a smaller elastic scattering cross section for positrons but a higher probability for inelastic interactions because more of the electron cloud is closer. However, the probability of electron exchange or capture must be added to obtain an overall picture. For electron impact electron exchange will further enhance both the elastic and inelastic cross sections. For positron impact, electron capture (Ps formation) should be significant at low energies because of the longer time that the positron and bound electrons are in close proximity of each other. Ps formation will greatly increase the overall inelastic cross section but will also rob available flux from the ionization channel. Thus, at lower energies physical arguments imply smaller elastic and ionization cross sections for positron impact. On the other hand, at significantly high impact energies the cross sections should be identical because the transverse forces leading to trajectory effects will be negligible compared to the incoming momenta and because the electron cloud does not have time to polarize.
Finally, theories using a perturbative expansion predict differences in cross sections due to the opposite signs of the projectile which influences certain terms. This is most evident for a 2nd Born expansion where the cross term scales as the third power of the product of the projectile and bound electron charges. This term is negative for positron impact and positive for electron impact. Thus, the double ionization cross section should be larger for electron impact as compared to positron impact, something that has been confirmed by many experimental studies. The reader is referred to Charlton et al. [1] for an example of this.
In the following sections, we will illustrate the influence of these features using total and differential data. As will be seen, under certain conditions there is little or no difference in how antimatter (positrons) and matter (electrons) interact with matter whereas for other conditions, large differences are seen. The data used in making these comparisons are taken from the literature and were selected to be representative or the most reliable data available. But the reader should keep in mind that the cross sections were measured using different techniques and in many cases were placed on absolute scales by normalizing to other measurements. Thus, agreement or disagreement within a 15-20% level should be viewed with caution as comparisons on the absolute level are subject to which set of normalization data was used. If a more detailed analysis than provided here is required, the reader should visit the references quoted.
TOTAL CROSS SECTION COMPARISONS
The first comparison we make is on the total (integral) cross section level. Cross sections for the various interaction channels associated with positron and electron impact on argon are shown in Fig. (2). For positron impact, the uppermost (black) curve is the total cross section for elastic plus inelastic interactions. This curve is a combination of the values recommended by Chiari and Zecca [2] and the measurements of Dababneh et al. [3]. Note that the early unpublished measurements of Coleman et al. [4] as quoted in Joachain et al. [5] are consistent with the later, more extensive, measurements of Dababneh et al. For inelastic interactions, the Ps production (electron capture) channel cross sections are shown by the blue curve. These data are also the recommended values of Chiari and Zecca [2]. The ionization (red) curve is from the combined measurements of Van Reeth et al. [6], Jacobsen et al. [7], Moxom et al. [8], Mori and Sueoka [9] and Kauppila et al. [10]. Lastly, the elastic cross section (magenta) curve is obtained via subtraction of the inelastic (ionization plus Ps production) cross sections from the total elastic plus inelastic cross section curves. For display purposes, the elastic cross section data for energies less than 7 eV have been shifted slightly downward.
Fig. (2)) Measured total cross sections for positron (left figure) and electron (right figure) -argon interactions. Positron impact: Total elastic plus inelastic (black curve), recommended values of Chiari and Zecca [2] and data of Dababneh et al. [3]; Ps production (blue curve), recommended values of Chiari and Zecca [2]; ionization (red curve), data of Van Reeth et al. [6], Jacobsen et al. [7], Moxom et al. [8], Mori and Sueoka [9], Kauppila et al. [10]. The elastic cross section curve (magenta) is obtained via subtraction with the data for energies less than 7 eV being shifted slightly downward for display purposes. Electron impact: Total elastic plus inelastic (black curve): suggested values from Gargioni Grosswendt [11]; total ionization (red curve): suggested values from Gargioni and Grosswendt [11], data of Straub et al. [12], Sorokin et al. [13], Wetzel et al. [14], Rapp and Englander-Golden [15] and Kauppila et al. [10]. Elastic (magenta curve): suggested values from Gargioni and Grosswendt [11], data of Gibson et al. [16], Iga et al. [16], Panajotović et al. [18], Srivastava et al. [19], Furst et al. [20] and DuBois and Rudd [21].The right portion of the figure shows cross sections for electron impact. Here the total elastic plus inelastic cross sections (black curve) are the suggested values from Gargioni and Grosswendt [11]. The ionization cross sections are the combined values also suggested by Gargioni and Grosswendt [11] plus measurements of Straub et al. [12], Sorokin et al. [13], Wetzel et al. [14], Rapp and Englander-Golden [15] and Kauppila et al. [10]. The elastic scattering cross sections (magenta curve) are a combination of the suggested values by Gargioni and Grosswend [11] and the measurements of Gibson et al. [16], Iga et al. [17], Panajotović et al. [18], Srivastava et al. [19], Furst et al. [20] and DuBois and Rudd [21].
Before discussing comparisons between positron and electron impact, let us look at the overall characteristics of each. For both projectiles, elastic interactions dominate below 100 eV, more so in the case of electron impact than for positron impact. At high impact energies, the probabilities for elastic and inelastic interactions are comparable for positron impact but, for electron impact elastic collisions remain more probable. That the elastic and ionization cross sections are comparable for positron impact can be attributed to the reduced probability of elastic scattering due to the extra screening of the nuclear charge plus the increased probability of inelastic interactions due to the closer proximity of more of the electron cloud, as illustrated in Fig. (1). That elastic scattering tends to dominate for electron impact can be attributed to the same reasons. But for electron impact the screening is reduced, thus enhancing the elastic cross section. Ionization is also reduced because fewer electrons are near the projectile as it passes by. The other thing to note in Fig. (2) is that for positron impact the overall inelastic cross section, i.e., the sum of the Ps formation and ionization channels, is significantly larger at low energies compared to the inelastic channel for electron impact. This is consistent with the picture where polarization causes more of the electron cloud to be near the positron as it passes by.
In Fig. (3) the same curves are plotted in order to compare the cross sections for positron (dashed curves) and electron impact (solid curves). The Ps formation curve is included in order to illustrate that this channel both decreases the threshold energy and significantly increases the cross section for inelastic interactions at lower energies for positron impact. Except at the very lowest energies shown, the cross sections for elastic scattering are significantly larger for electron impact than for positron impact.
Fig. (3)) Comparison of total cross sections for positron (dashed curves) and electron (solid curves) impact on argon. Data are the same as in Fig. (2).This is consistent with the theoretical and physical arguments discussed in the introduction. Only at the very highest impact energies shown, do the elastic interaction probabilities seem to merge. Merging at higher energies occurs much sooner for ionizing interactions. At lower energies, namely below 100 eV, ionization of argon resulting in electron emission by electron impact is more probable than for positron impact. This is again in accordance with arguments discussed in the introduction. One should also note that the ionization cross sections deviate from each other in the same region where Ps formation is important.
This illustrates how the loss of flux to the capture channel aids in reducing the probability of direct emission of target electrons. Looking at the total elastic plus inelastic cross sections, the data imply that they still have not merged, even for impact energies two orders of magnitude larger than the ionization energy. Whether this indicates an overall normalization error, most likely for the positron impact data, or that the merging occurs at still higher energies is uncertain from data available at this time.
CROSS SECTION COMPARISONS FOR SINGLE AND DOUBLE ELECTRON REMOVAL
Let us now look a bit closer at the ionization channel. In Fig. (4) the cross sections for single (filled symbols) and double (open symbols) electron removal from argon by positrons (circles) and electrons (triangles and solid and dashed curves) are shown. Note that the double ionization cross sections include direct removal of two outer shell electrons plus removal of an inner shell electron followed by an Auger decay transition. The positron data are those of Jacobson et al. [7] and Bluhme et al. [22]. The Bluhme et al. data for impact energies less than 100 eV are not shown as their measurements include contributions from the Ps formation channel. The electron data are those of McCallion et al. [23] (solid and dashed curves) and Rejoub et al. [24] (filled and open triangles). These two data sets agree well for single ionization but for double ionization the McCallion et al. cross sections (the dashed curve) are about 15% larger than those reported by Rejoub et al. (the open triangles).
With regard to the differences in absolute cross sections, the general method of obtaining double ionization cross sections is to measure double to single cross section ratios and normalize these data using total ionization cross sections. Depending on the source used for the total cross sections, differences on the order of 10-15% in the absolute cross sections can result. However, from the many studies of double ionization (see ref [1], for example), the consensus is that the probability for removing a single target electron at high energies is the same for positron and electron impact while it is roughly twice more as likely that electron impact will result in double ionization. Thus, in Fig. (4) the dashed curve probably provides the best comparison with the positron double ionization data which are shown by the open circles. Also, with regard to the double ionization comparison, at energies about ~250 eV, L-shell ionization followed by an Auger decay contributes to the cross sections shown. Inner shell ionization cross sections have not been measured for positron impact so interpreting differences above this energy should be done with caution. Below approximately 100 eV, single electron removal by electron impact is more likely whereas there is little or no difference in the probability of double electron removal by positron or electron impact. Since single ionization dominates, the differences noted in Figs. (3 and 4) for single and total electron removal mimic each other.
Fig. (4)) Total cross sections for single and double ionization of argon by positrons (filled and open circles) and electrons (filled and open triangles plus solid and dashed curves). Positron data are from Bluhme et al. [22] and Jacobsen et al. [7]. Electron data are from McCallion et al. [23] (solid and dashed curves) and Rejoub et al. [24] (filled and open triangles).SINGLE AND DOUBLE DIFFERENTIAL CROSS SECTION COMPARISONS
Fig. (3) showed that the probabilities for ionizing argon by positron and electron impact are maximum and nearly identical around 100 eV. Also, at this energy and above the elastic and inelastic scattering probabilities have similar magnitudes. Because of this and since lepton beam experiments can be easily performed in the few hundred eV energy range, several types of differential studies have been performed in this region for positron impact. These data can be compared with the multitude of electron impact data available in order to gain greater insight into the kinematic similarities and differences associated with the sign of the projectile charge.
The first example of these kinematic features is shown in Fig. (5). Here differential cross sections for elastic scattering as a function of scattering angle are shown for 100 and 300 eV electron impact (the blue dashed curve and the filled stars and solid curve, respectively). The 100 eV data are those of DuBois and Rudd [21] while the 300 eV data are a combination of the measurements of Williams and Willis [25] and Jansen s [26]. These are compared to the positron impact data of Dou et al. [27] and Falke et al. [28]. Here, the Falke et al. data have been placed on an absolute scale by normalizing to the average value of integrated doubly differential cross sections for the sum of positron scattering plus electron emission reported by Kövér et al. [29] at a 30o observation angle.
Fig. (5)) Singly differential cross sections for elastic scattering from argon by positrons and electrons. 100 eV impact: dashed curve for electron impact, DuBois and Rudd [21]; solid curve for positron impact, Dou et al. [27]. 300 eV impact: filled squares and solid curve for positron impact, Falke et al. [28] normalized as described in the text; filled stars and solid curve, electron impact from Williams and Willis [25] and Jansen et al. [26].As seen, the differential cross sections for forward scattering angles, e.g., less than 60o, are very similar for positron and electron impact. But, at larger angles the probability that a positron scatters elastically decreases monotonically whereas electron elastic scattering has significant structure. In particular, there is a marked increase for electron scattering in the backward direction. In contrast, a similar behavior is totally absent when the projectile has the opposite charge.
Going back to Fig. (1) the differences in the backward direction can be attributed to an incoming electron being attracted toward the positively charged nucleus whereas a positron will be pushed further away. Thus, when the incoming particle (the electron) is closer there is a distinct possibility that it will be deflected completely around the nucleus and end up exiting in the backward direction. With regard to the differences in the total elastic cross sections, Fig. (5) shows that is primarily associated with scattering in the forward direction, which from the physical arguments presented in the introduction, is probably due to the differences in screening of the nuclear charge by the polarized electron cloud combined with trajectory deviations as the incoming lepton passes by the argon atom.
Turning our attention to the inelastic channel, Fig. (6) shows single differential cross sections for an incoming lepton to be scattered or a bound argon electron to be ejected at a specific angle. Shown are electron impact data measured at 100 eV [30] compared to positron impact data measured at 90 and 120 eV [28]. The positron data have again been placed on an absolute scale by normalizing the integrated double differential cross sections provided in reference [29].
Fig. (6)) Singly differential cross sections for projectile scattering plus electron emission for electron and positron impact ionization of argon. Solid squares: 100 eV electron impact data from DuBois [30]; open and filled circles: 90 and 120 eV positron impact data of Falke et al. [28] placed on an absolute scale as described in the text.As was seen in the previous figure for elastic scattering, the probabilities for electron and positron impact are very nearly the same in the forward direction. A following figure will show that the contributions in the forward direction are primarily due to the scattered projectile. But, the probabilities differ significantly in the backward direction. Again, for positron impact the cross sections decrease monotonically with angle whereas for electron impact the probabilities reach a minimum value and then increase in the backward direction. Only looking at Fig. (6), the differential data in the forward direction implies an overall higher probability for ionizing interactions for positron impact at 100 eV. However, this is in conflict with the measured values that were shown in Fig. (3).
Fig. (7) clarifies this apparent discrepancy. Here the differential cross sections shown in Fig. (6
