⇦Chinese Physics Letters, 2016, Vol. 33, No. 7, Article code 073401 Signature of Single Binary Encounter in Intermediate Energy He$^{2+}$–Ar Collisions * Yong Gao(高永)1,2, Xiao-Long Zhu(朱小龙)1, Shao-Feng Zhang(张少锋)1, Rui-Tian Zhang(张瑞田)1, Wen-Tian Feng(冯文天)1, Da-Long Guo(郭大龙)1, Bin Li(李斌)1, Dong-Mei Zhao(赵冬梅)1, Han-Bing Wang(汪寒冰)1,2, Zhong-Kui Huang(黄忠魁)1,2, Shun-Cheng Yan(闫顺成)1, Dong-Bin Qian(钱东斌)1, Xin-Wen Ma(马新文)1** Affiliations 1Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000 2University of Chinese Academy of Sciences, Beijing 100049 Received 3 June 2016 Supported by the National Basic Research Program of China under Grant No 2010CB832902, the National Natural Science Foundation of China under Grants Nos U1332128 and 11274317, 10979007 and 11004202.
**Corresponding author. Email: x.ma@impcas.ac.cn Citation Text: Gao Y, Zhu X L, Zhang S F, Zhang R T and Feng W T et al 2016 Chin. Phys. Lett. 33 073401 Abstract We experimentally observe the signature of electron emission resulting from a single binary encounter mechanism in the intermediate collision energy regime of 30 keV/u He$^{2+}$ on argon. Electron emission spectra in the transfer ionization are obtained and compared with classical calculations from a two-step model considering the initial electron velocity and re-scattering of the binary encounter electron in the recoil potential. Although the present reaction is actually a four-body problem, the model starting from a binary encounter gives out surprisingly good agreement with the experimental data. Our studies show that orbital velocities of the electron affect the emission patterns of ionized electrons significantly. DOI:10.1088/0256-307X/33/7/073401 PACS:34.50.-s, 34.70.+e © 2016 Chinese Physics Society Article Text Electron emission occurring in ion–atom collisions is one of the simplest, and thus most fundamental, dynamical few-body problems. In fast collisions $v_{\rm p}\gg v_{\rm i}$, where $v_{\rm p}$ is the projectile velocity, and $v_{\rm i}$ is the orbital velocity of the active electron, results of perturbation theories already exhibit impressive agreement with experimental data where the binary and recoil peaks are distinct from each other (for an overview see Refs. [1–3] and references therein). Meanwhile, in sufficiently low velocity collision regime where $v_{\rm p} \ll v_{\rm i}$, the projectile can barely directly knock out the electron. Under such circumstance, electrons evolve adiabatically in the presence of both the slowly moving projectile and the recoil potentials, and electron emission patterns can be, though yet far from satisfactory, interpreted by quasi-molecular treatment.[4-8] However in the junction zone where $v_{\rm p} \approx v_{\rm i}$, i.e., in the so-called intermediate energy collisions, the projectile moves at the velocity comparable with that of the active electron, collision dynamics still remains the least understood so far.[2] The knowledge of intermediate energy ion–atom collisions is demanding not only in the fundamental aspects but also in the relevant fields such as the life science, the nuclear energy science, the aeronautical and space technologies. For instance, the flourishing ion–tumor therapy techniques need detailed information on electron emission in this energy regime to determine the precise energy deposition in tissues.[9-11] The relevant knowledge concerns detailed information about the electron emitting angles, its energies and the corresponding cross sections, however, the prerequisite for building up proper models for academic predictions relies on the fact that the collision dynamics has been fundamentally understood. Thus experimentally discriminating and isolating fundamental processes occurring in the complex system in this velocity regime are of practical importance in advancing the relevant knowledge in the field. In single ionization of atoms by fast projectiles, the well-known 'binary' and the 'recoil' peaks are two characteristics of electrons of small energies. The binary peak results from the mechanism in which the electron is directly knocked out of the atom by a binary encounter (BE) interaction with the projectile, and its polar angle represents the momentum transfer direction. Meanwhile, the recoil peak represents the case when the BE electron undergoes a further re-scattering on the recoil ion and changes its direction opposite to the momentum transfer. In 2002, triple, even quadruple, scattering of ionized target electrons between the projectile and the target cores were also experimentally confirmed in fast collision regime.[12] As the collision velocity decreases to the intermediate collision energy regime, characteristics of BE processes gradually disappear whereas quasi-molecular patterns start to emerge. Only in the very specific situation when the active electron originally belongs to the projectile, re-scattering of the BE electron can be identified experimentally. In 1996, Suárez et al. reported the first re-scattering evidence of the projectile electron in collisions of 30 keV/u H$^0$ on He.[13] There the hydrogen electron experienced the first binary encounter with the target core and gained a backward velocity of $-v_{\rm p}$. In the next step, this electron was re-scattered on its parent core and was ejected in the forward direction with the final velocity of $3v_{\rm p}$. However, other processes also produce comparable cross sections at this velocity. As a consequence, the re-scattering evidence can be confirmed only via the normalization of the experimental data to the first Born calculations (see Ref. [13] for details). Even though the above-mentioned higher order BE mechanisms have already been confirmed experimentally in intermediate energy ion–atom collisions, which implies that the first order BE must exist, electron emissions from single-BE scattering between the projectile nucleus and target electrons have not been reported or even predicted yet. The difficulties are from the fact that these single-BE electrons have low kinetic energies, thus are easily involved in higher order processes (for instance, the projectile/residual recoil post collision interactions, that is, PCIs). In this Letter, we report an observation of the single-BE electrons in the transfer ionization (TI) process, that is, one electron ionized with simultaneous one electron captured, in collisions of 30 keV/u He$^{2+}$ on argon, $$\begin{align} {\rm He}^{2+}+{\rm Ar} \rightarrow {\rm He}^{1+}+{\rm Ar}^{2+}+e,~~ \tag {1} \end{align} $$ by considering the post-collisional interactions (PCIs) between the recoil ion and the emitted electron. An intuitive two-step collision model starting from the BE scattering between the projectile nucleus and the target electron is proposed, and our explanations are in good agreement with the forward electron distributions, which paves the way for understanding intermediate-energy collision processes. The experiment was performed by using the reaction microscope located at the 320 kV platform for multi-discipline research with highly charged ions at the Institute of Modern Physics, CAS.[14] Briefly, He$^{2+}$ ions produced in the electron cyclotron resonance ion source were accelerated, charge analyzed, and then transported to the reaction chamber. There a 30 keV/u well-collimated He$^{2+}$ ion beam intersected with a supersonic argon gas jet of spectrometer. After reaction, the projectiles with different charge states were further analyzed by another electrostatic deflector downstream of the collision center. After that, He$^{+}$ ion was directed to the position sensitive detector, and the remaining primary beam was collected by a Faraday cup. Meanwhile, the momenta of the target fragments were obtained via the reaction microscope. Triple coincident measurements among the recoil ion, the electron and the projectile were employed to distinguish the reaction channels. In ion–atom collisions the impact parameter $b$, defined by the transverse distance between the projectile and target nuclei, is a key factor to determine how strong the collision would be. However, such a parameter is not an observable. In this circumstance, resorting to the transverse momentum transfer or transverse recoil ion momentum is an alternative to statistically characterize how close the collisions are.[4] In the following the mechanisms of the electron emissions are investigated differentially in transverse recoil ion momentum.
cpl-33-7-073401-fig1.png
Fig. 1. (Color online) Electron triple differential cross sections of the polar angle $\theta$, of the energies $E_{\rm e}$, and of the transverse recoil ion momentum $P_{{\rm re},\perp}$. (a)–(d) The transverse recoil momentum ranges of 0–4, 4–8, 8–15, and 15–30 a.u., respectively. In (a), the dashed curve indicates Auger electrons from the projectiles.
In Fig. 1 the measured triple differential cross sections are shown as functions of the electron energy $E_{\rm e}$, the electron polar angle $\theta$ (the angle between the direction of the initial projectile and that of the emitted electron), and of the transverse recoil ion momentum $P_{{\rm re},\perp}$. One can see from the spectra that low-energy electrons ($E_{\rm e}\lesssim$5 eV) are dominant in all four transverse recoil momentum regimes. In these spectra, a 'mountain'-like structure was observed in forward directions where electron energies exceed 20 eV. As the transverse recoil ion momentum increases, this structure gradually disappears and electrons tend to distribute evenly in all directions. In intermediate collision energy regime, electrons with longitudinal velocities smaller than the projectile have profound signatures of the molecular orbital promotion.[4-8] However, these electrons of a speed larger than the projectile's cannot be explained via the molecular orbital promotion model. In the following we will focus on these electrons and a classical model will be given to understand the origin of these electrons.
cpl-33-7-073401-fig2.png
Fig. 2. (Color online) Schematic diagram of collision mechanisms at different impact parameters $b$: (a) at large impact parameter; (b) at small impact parameter. Here e: target electron, N: target nucleus, p: incoming projectile.
The fact that a considerable amount of electrons in the spectra are of longitudinal velocities larger than the projectile velocity is a strong hint that they undergo hard collisions with the projectile. It is thus reasonable to assume that, in the collision, the initial bound electron experiences a binary encounter with the incoming projectile. Let us define $\theta_{\rm m}$ as the resulting polar angle with respect to the incident projectile direction. In the second step, the BE electron escapes from the target with the angle $\theta_{\rm m}$ and its kinetic energy is inhibited by the residual recoil ion (the PCI between the emitted electron and the recoil ion, whereas the PCI between the emitted electron and the projectile ion is already included in the binary collision processes and thus the inhibiting effects from the projectile are not considered here). Here we further assume that the final polar angle is not affected by either the projectile or target nuclei, that is, $\theta=\theta_{\rm m}$. We note that this assumption is valid when electrons are emitted in the forward direction and the velocities are larger than that of the projectile (see Fig. 2(a)). We can then write down the final electron energy as a function of the polar angle, $$\begin{align} E_{\rm e}(\theta)=\,&\frac{m}{2}(v_{\rm p}\cos\theta+\sqrt{v_{\rm p}^2\cos^2\theta +v_{\rm i}^2-2v_{{\rm i},\parallel}v_{\rm p}})^{2}\\ &-\frac{1}{2}mv_{\rm i}^2+E_{\rm b},~~ \tag {2} \end{align} $$ where $m$ is the electron mass, $v_{\rm i}$ is the orbital velocity, $v_{{\rm i},\parallel}$ is the corresponding longitudinal component, and $E_{\rm b}$ is the binding energy. Different from the BE model routinely used in swift collisions where $E_{\rm e}=2mv_{\rm p}^2\cos^2\theta$, Eq. (2) takes the influences of the residual target nucleus into account by adding in kinetic parameters of the initial electronic state, that is, in terms of $v_{\rm i}$ and $E_{\rm b}$. In fast collisions where $v_{\rm p} \gg {v_{\rm i}}$, Eq. (2) naturally degenerates into the swift form by ignoring these three terms. In the model, the sudden approximation was employed to simplify the complexity, i.e., at the instance of the BE collision we assume that the electron actually does not change in position. For a certain orbital electron velocity $v_{\rm i}$, the electron longitudinal velocity $v_{{\rm i},\parallel}$ can be derived from Eq. (2) for each $[E_{\rm e},\theta]$ set. These parameters are used as further inputs of the Rutherford scattering formula, and the cross section information for predefined coordinates $[E_{\rm e},\theta]$ can be calculated. It was already concluded that in collisions of He$^2+$ on Ar, the ionization process is independent of the capture procedure.[15,16] In fact, processes of independent ionization with electron capture are not limited to the rich-electron target. In the swift collisions of 1 MeV/u O$^{7+}$ on He, Schneider et al. observed the binary peak in electron spectra for TI processes which consist of the independent ionization assumption.[17] Further studies also show that the ionization is prior to the capture during the collision in the present reaction channel.[16] The ionization process in TI thus can be treated as the single ionization of Ar by He$^{2+}$.
cpl-33-7-073401-fig3.png
Fig. 3. (Color online) Calculated energy-$\theta$ spectra. Cross sections are generated according to the two-body elastic Rutherford scattering formula which takes our model (Eq. (2)) into account. (a) For the single orbital velocity $v_{\rm i}$=0.3 a.u.; (b) for the single orbital velocity $v_{\rm i}$=0.6 a.u.; (c) for the orbital velocity $v_{\rm i}$ integrated from 0 to 3 a.u.; (d) the same as (c) but 10% of the electrons are randomly deflected by the recoil ion; and (e) the same as (c) but 80% of the electrons are randomly deflected by the recoil ion.
Figure 3 shows the calculated spectra of the same dimensions as those in Fig. 1. For the single ionization of Ar (i.e., $E_{\rm b}=-0.58$ a.u.), Fig. 3(a) gives out cross sections for collisions on electrons of the orbital velocity $v_{\rm i}$=0.3 a.u. circulating around the residual target core, and those of $v_{\rm i}$=0.6 a.u. are shown in Fig. 3(b). The spectrum (Fig. 3(c)) can thus be obtained by integrating over different orbital velocities with proper weightings taken from Ref. [18]. For each single $v_{\rm i}$, simulation shows that BE electrons produce 'band'-type distributions (see Figs. 3(a) and 3(b)). The band width varies on absolute values of $v_{\rm i}$. In Fig. 3(a), the dashed line marks the BE ridge predicted by $E_{\rm e}=2mv_{\rm p}^2\cos^2\theta$, i.e., by the swift collision assumption. Apparently, our model reveals more details and it is evident that the orbital velocity is non-negligible in the intermediate energy range. In the convoluted spectrum of Fig. 3(c), our simulations qualitatively predicate the 'mountain'-like structure in Fig. 1. From the experimental spectra, one can also conclude that the mountain peak in the forward direction gradually vanishes as the transverse recoil ion momentum increases to the regime of 15–30 a.u., and electrons of energies larger than 20 eV tend to distribute evenly in all directions. In small transverse recoil ion momentum collisions (for instance, 0 a.u. $\leq P_{{\rm re},\perp}\leq 4$ a.u. in Fig. 1(a)), the impact parameter $b$ is so large that BE electrons in forward polar angles are less affected by the recoil nucleus and the initial scattering angles are thus conserved (see Fig. 2(a)). As the transverse recoil ion momentum becomes larger (a smaller impact parameter is needed), the recoil ion is not only inhibiting the emission electron but also changes the direction of the BE electron significantly as indicated in Fig. 2(b). Such re-scattering processes are random, which may result in redistributions of the emitted electrons. Although such re-scattering processes have been confirmed in swift collisions (for instance, see Ref. [19]), it is rarely discussed in the intermediate energy ion–atom collision system. To test our speculations, we further investigate triple differential cross sections of the ejected electron, i.e., $d^3\sigma/d\phi dE_{\rm e} dP_{{\rm re},\perp}$, where $\phi$ is the azimuthal angle of the electron with respect to the direction of the transverse recoil ion momentum. In Fig. 4, such cross sections with electron energies larger than 20 eV are presented as a function of the azimuthal angle, where 0$^\circ$ is the direction of the transverse recoil ion momentum and 180$^\circ$, the opposite direction, is the direction of the scattered projectile ion. Electrons in these spectra concentrate mainly on these two directions and form two distinct peaks. In swift collisions, these two peaks are the so-called binary peak ($\phi= 0^\circ$) and recoil peak ($\phi= 180^\circ$),[2,20] respectively. We will use the same notations for these two peaks in the following. In the regime of 0 a.u$\leq P_{{\rm re},\perp}\leq$4 a.u. as shown in Fig. 4(a), the binary peak dominates over the recoil peak. As transverse recoil ion momentum increases, i.e., the impact parameter $b$ becomes smaller, more and more electrons were deflected by the residual recoil ion and the recoil peak steadily increases. Eventually, intensities of the recoil peak and the binary peak flip at about $P_{{\rm re},\perp}\approx8$ a.u. (see Figs. 4(b) and 4(c)). Such phenomena confirm the assumption as illustrated in Fig. 2. As a further test, we simulate the re-scattering processes with implementation of a random $\theta$ generator in our code. For the rescattering events, $\theta$ is randomly chosen after the BE process. Our results show that a similar spectrum as Fig. 1(a) can be achieved by assuming 10% of the electrons deflected by the recoil ion, which corresponds to the larger impact parameter collisions (Fig. 3(d)). As this amount increases to 80% (the close collision situation), the mountain-structure almost vanishes (compared Fig. 3(e) with Figs. 1(c) and 1(d)).
cpl-33-7-073401-fig4.png
Fig. 4. Azimuth angle distributions for electrons of energies larger than 20 eV. In the spectra only statistical errors are given.
Auger electron emissions are important processes in collisions involving rich electron atoms.[21,22] In our work, such auto-ionizing phenomena are also observed in the spectra. The dashed line in Fig. 1(a) marks the regime where Auger electrons are ejected from the excited projectile after double electron capture from the target atom, i.e., auto-ionization of He$^*$ ($2lnl'$, $n\geq2$). In the rest frame of the projectile these electrons are of constant energies above 33 eV, while in the laboratory frame their kinetic energies are a function of the polar angle $\theta$ (indicated by the dashed curve). The Auger electron emissions are not included in our model. It should be noted that, although our model is purely classical which ignores interference effects, it can still reproduce the structures emerging in highly differential electron spectra qualitatively. The classical model, with adoption of orbital velocity $v_{\rm i}$ as well as the binding energy $E_{\rm b}$ into the swift BE formula, uncovers detailed information about collisional dynamics. In summary, we have experimentally investigated the transfer ionization in collisions of 30 keV/u He$^{2+}$ on Ar. It is found that when the transverse recoil momentum is small, electrons of energies larger than 20 eV are emitted mainly in the forward directions. As the transverse recoil momentum becomes larger, these electrons tend to redistribute in all directions. The distributions can be explained by a two-step model: the electron firstly experiences a projectile-electron binary encounter, and in the next emitting procedure the energy is inhibited in the residual recoil potentials with/without angular deflections depending on whether the impact parameter $b$ is relatively small or not. Combined with the Rutherford elastic scattering cross sections our model reveals experimental observations qualitatively. Although the present reaction is actually a four-body problem, our studies show that electron emissions from the rich-electron system actually originate from the fundamental binary encounter process. We would like to thank the engineers to operate the 320-kV platform for their assistance in running the ECR ion source. References STUDIES OF THE FEW-BODY PROBLEM IN ATOMIC BREAK-UP PROCESSESRecoil-ion and electron momentum spectroscopy: reaction-microscopesThree-dimensional imaging of atomic four-body processesImaging of Saddle Point Electron Emission in Slow p − H e CollisionsObservation of an impact-parameter window in low-velocity ionizing collisions of Ne + on Ne proceeding through quasimolecular statesMomentum Images of Continuum Electrons from He + and He 2 + on He: Ubiquity of π Structure in the ContinuumImaging of continuum states of the He 2 2 + quasimoleculeDynamics of electron-capture-to-continuum (ECC) formation in slow ion–atom collisionsAngular and Energy Distributions of Electrons Produced in Arbitrary Biomaterials by Proton ImpactSite-Specific Dissociation of DNA Bases by Slow Electrons at Early Stages of IrradiationDissociative Electron Attachment to Phosphoric Acid Esters: The Direct Mechanism for Single Strand Breaks in DNAEvidence for Fermi-Shuttle Ionization in Intermediate Velocity C + + X e CollisionsDouble Scattering Effects in the Ionization Spectrum Produced by Single Energetic Atomic CollisionsElectron emission from single-electron capture with simultaneous single-ionization reactions in 30-keV/u He 2 + -on-argon collisionsCusp-electron production due to transfer ionization in 25–250 keV/amu He2+ + Ar collisionsPicturing electron capture to the continuum in the transfer ionization of intermediate-energy He 2 + collisions with argonRole of Projectile Coherence in Close Heavy Ion-Atom CollisionsSatellite structure in the argon valence shell by electron-momentum spectroscopyIntra-atomic Double Scattering of Binary Encounter Electrons in Collisions of Fast Heavy Ions with Atoms and MoleculesCold Target Recoil Ion Momentum Spectroscopy: a ‘momentum microscope’ to view atomic collision dynamicsEnergy Levels of Doubly Excited States in ArgonDouble capture into autoionizing states in low-energy He 2 + -, Li 3 + -, and B 5 + -H 2 collisions
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