# Interaction of Electrons and Positrons with Protons Aligned in One-Dimension Line

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theory

_{i}= (q

_{ix}, q

_{iy}, q

_{iz}) and p

_{i}= (p

_{ix}, p

_{iy}, p

_{iz}). Figure 1 shows the schematic diagram of a two-proton system in colliding with electron projectiles.

_{z}velocities according to the initial energy. The v

_{x}and v

_{y}were set to be 0.

## 3. Results and Discussion

_{2}) with ground state helium. They plotted the projectile counts as a function of scattering angles, and they got two maxima. The cross sections of Murray et al. [33] as a function of the analyser angles show also two maxima. The work of both Zhou et al. [38] and Murray et al. [33] are equivalent to our two-proton system. In the case of electrons, the number of peaks is equal to the number of protons, but in the case of positrons, the number of peaks is equal to the number of protons plus one.

## 4. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Tőkési, K. The role of projectile double scattering in positron–atom collisions. Radiat. Phys. Chem.
**2007**, 76, 624–626. [Google Scholar] [CrossRef] - Afroz, S.; Haque, M.M.; Fazlul Haque, A.K.; Jakubassa-Amundsen, D.H.; Patoary, M.A.R.; Shorifuddoza, M.; Khandker, M.H.; Uddin, A.M. Elastic scattering of electrons and positrons from
^{115}In atoms over the energy range 1 eV–0.5 GeV. Results Phys.**2020**, 18, 103197. [Google Scholar] [CrossRef] - Makochekanwa, C.; Kawate, H.; Sueoka, O.; Kimura, M.; Kitajima, M.; Hoshino, M.; Tanaka, H. Total and elastic cross-sections of electron and positron scattering from C3H4 molecules (allene and propyne). Chem. Phys. Lett.
**2003**, 368, 82–86. [Google Scholar] [CrossRef] - Sueoka, O.; Makochekanwa, C.; Tanino, H.; Kimura, M. Total cross-section measurements for positrons and electrons colliding with alkane molecules: Normal hexane and cyclohexane. Phys. Rev. A
**2005**, 72, 042705. [Google Scholar] [CrossRef] - Horowitz, C.J. Parity violation in astrophysics. Eur. Phys. J. A
**2005**, 24, 167–170. [Google Scholar] [CrossRef] - Hossain, M.I.; Haque, A.; Patoary, M.A.R.; Uddin, M.A.; Basak, A.K. Elastic scattering of electrons and positrons by atomic magnesium. Eur. Phys. J. D
**2016**, 70, 41. [Google Scholar] [CrossRef] - Crooks, G.B.; Rudd, M.E. Experimental Evidence for the Mechanism of Charge Transfer into Continuum States. Phys. Rev. Lett.
**1970**, 25, 1599. [Google Scholar] [CrossRef][Green Version] - Kövér, A.; Szabó, G.; Gulyás, L.; Tőkési, K.; Berényi, D.; Heil, O.; Groeneveld, K.O. Electron emission at backward angles from He
^{2+}, He^{+}(2 mev) → He, Ne, Ar collision systems. J. Phys. Colloq.**1987**, 48, C9-289–C9-291. [Google Scholar] [CrossRef] - Kövér, A.; Szabó, G.; Gulyás, L.; Tőkési, K.; Berényi, D.; Heil, O.; Groeneveld, K.O. The electron loss process at backward observation angles in collision systems He
^{+}(2 MeV)-He, Ne, Ar. J. Phys. B At. Mol. Opt. Phys.**1988**, 21, 3231. [Google Scholar] [CrossRef] - Tőkési, K.; Mukoyama, T. Theoretical Investigation of the ECC Peak for Charged Particles with the CTMC Method. Bull. Inst. Chem. Res. Kyoto Univ.
**1994**, 72, 62–68. [Google Scholar] - Gagyi-Pálffy, A.C.; Barna, I.F.; Gulyás, L.; Tőkési, K. Angular Differential Cross-Section for Ionization of Helium in C
^{6+}Ion Collision. Chin. Phys. Lett.**2004**, 21, 1258. [Google Scholar] [CrossRef] - Tőkési, K.; Kövér, A. Existence of the electron capture to the continuum peak at positron impact. Nucl. Instrum. Methods Phys. Res. B Beam Interact. Mater. At.
**1999**, 154, 259–262. [Google Scholar] [CrossRef] - Tőkési, K.; Kövér, A.J. Electron capture to the continuum at 54.4 eV positron-argon atom collisions. Phys. B At. Mol. Opt. Phys.
**2000**, 33, 3067. [Google Scholar] [CrossRef] - Barna, I.F.; Tőkési, K.; Gulyás, L.; Burgdörfer, J. Total and angular differential cross sections of electrons emitted in collision between antiprotons and helium atoms. Radiat. Phys. Chem.
**2007**, 76, 495–498. [Google Scholar] [CrossRef] - Tőkési, K.; Sarkadi, L.; Mukoyama, T.J. Model calculation of the electron capture to the continuum peak at neutral projectile impact. Phys. B At. Mol. Opt. Phys.
**1997**, 30, L123. [Google Scholar] [CrossRef] - Hillenbrand, P.M.; Hagmann, S.; Groshev, M.E.; Banas, D.; Benis, P.E.; Brandau, C.; De Filippo, E.; Forstner, O.; Glorius, J.; Grisenti, R.E.; et al. Radiative electron capture to the continuum in U 89 + + N 2 collisions: Experiment and theory. Phys. Rev. A
**2020**, 101, 022708. [Google Scholar] [CrossRef][Green Version] - Nanos, S.; Quinto, M.A.; Madesis, I.; Laoutaris, A.; Zouros, T.J.M.; Rivarola, R.D.; Monti, J.M.; Benis, E.P. Subshell contributions to electron capture into the continuum in MeV/u collisions of deuterons with multielectron targets. Phys. Rev. A
**2020**, 105, 022806. [Google Scholar] [CrossRef] - Olson, R.E.; Salop, A. Charge-transfer and impact-ionization cross sections for fully and partially stripped positive ions colliding with atomic hydrogen. Phys. Rev. A
**1977**, 16, 531–541. [Google Scholar] [CrossRef] - Tőkési, K.; Hock, G. Double electron capture in collision up to 1500 keV/amu projectile impact. J. Phys. B
**1996**, 29, L119–L125. [Google Scholar] [CrossRef] - Olson, R.E.; Reinhold, C.O.; Schultz, D.R. High-Energy Ion-Atom Collisions. In Proceedings of the IVth Workshop on High-Energy Ion-Atom Collision Processes, Debrecen, Hungary, 17–19 September 1990. [Google Scholar]
- Tőkési, K.; DuBois, R.D.; Mukoyama, T. Interaction of positronium with helium atoms—The classical treatment of the 5-body collision system. Eur. Phys. J. D
**2014**, 68, 255. [Google Scholar] [CrossRef] - Tőkési, K.; Hock, G. Versatility of the exit channels in the three-body CTMC method. Nucl. Instrum. Meth. Phys. Res. B
**1994**, 86, 201–204. [Google Scholar] [CrossRef] - Tőkési, K.; Barna, I.F.; Burgdörfer, J. Ionization of helium in positron impact. Nucl. Instrum. Methods Phys. Res. B
**2005**, 233, 307–311. [Google Scholar] [CrossRef] - Kavčič, M.; Tőkési, K. Single and double K-shell ionization cross sections of silicon. Radiat. Phys. Chem.
**2007**, 76, 542–545. [Google Scholar] [CrossRef] - Ziaeian, I.; Tőkési, K. Interaction of Be
^{4+}and Ground State Hydrogen Atom—Classical Treatment of the Collision. Atoms**2020**, 8, 27. [Google Scholar] [CrossRef] - Atawneh, S.J.A.; Asztalos, Ö.; Szondy, B.; Pokol, G.I.; Tőkési, K. Ionization Cross Sections in the Collision between Two Ground State Hydrogen Atoms at Low Energies. Atoms
**2020**, 8, 31. [Google Scholar] [CrossRef] - Acebal, E.; Otranto, S. Influence of the projectile charge sign in light particle single ionization of H
_{2}O. Eur. Phys. J. D**2019**, 73, 91. [Google Scholar] [CrossRef] - Tőkési, K. Double electron excitation of helium by charged particle impact. Nucl. Instrum. Methods Phys. Res. B
**2019**, 233, 266–269. [Google Scholar] [CrossRef] - Oliveira, V.; Herbert, A.; Santos, A.; Tőkési, K. Electron capture and loss of O
^{+}projectile in collision with water near the Bragg Peak Energies. Eur. Phys. J. D**2019**, 73, 146. [Google Scholar] [CrossRef] - Tőkési, K.; Varga, D. Energy distribution of elastically scattered electrons from double layer samples. Nucl. Instrum. Methods Phys. Res. Sect. B Beam Interact. Mater. At.
**2016**, 369, 109–121. [Google Scholar] [CrossRef] - Sulik, B.; Tőkési, K. Accelerating Multiple Scattering of Electrons by Ion Impact: Contribution to Molecular Fragmentation and Radiation Damages. Adv. Quantum Chem.
**2007**, 52, 253–276. [Google Scholar] - Young, T. The Bakerian lecture: Experiments and calculations relative to physical optics. Philos. Trans. R. Soc.
**1804**, 94, 1–16. [Google Scholar] - Murray, A.J.; Hussey, M.J.; Kaiser, C.; Gao, J.; Madison, D.H. Electron impact ionization of molecules at low to intermediate energies—A search for Young’s double slit type interferences. J. Electron Spectrosc. Relat. Phenom.
**2007**, 161, 11–16. [Google Scholar] [CrossRef] - Steiger, T.D.; Stehr, J.; Griffin, H.C.; Rogers, J.H.; Skalsey, M.; Van House, J. Development of intense, long-lived positron sources. Nucl. Instrum. Methods M Phys. Res.
**1990**, A299, 255–260. [Google Scholar] [CrossRef] - Uesugi, Y.; Akagi, T.; Chehab, R.; Dadoun, O.; Furukawa, K.; Kamitani, T.; Kawada, S.; Omoric, T.; Takahashi, T.; Umemori, K.; et al. Development of an intense positron source using a crystal-amorphous hybrid target for linear colliders. Nucl. Instrum. Methods Phys. Res. B
**2014**, 319, 17–23. [Google Scholar] [CrossRef][Green Version] - Maekawa, M.; Wada, K.; Kawasuso, A. Development a new positron source for spin-polarized positron beam generation. Nucl. Inst. Methods Phys. Res. B
**2020**, 480, 49–55. [Google Scholar] [CrossRef] - Gossman, D.; Perez-Garcia, B.; Hernandez-Aranda, R.I.; Forbes, A. Optical interference with digital holograms. Am. J. Phys.
**2016**, 84, 508. [Google Scholar] [CrossRef][Green Version] - Zhou, H.; Perreault, W.E.; Mukherjee, N.; Zare, R.N. Quantum mechanical double slit for molecular scattering. Science
**2021**, 374, 960–964. [Google Scholar] [CrossRef] - Hecht, E. Interference. In Optics, 5th ed.; Borthakur, M., Tiwari, V., Eds.; Pearson Education Limited: Essex, UK, 2017; pp. 405–408. [Google Scholar]

**Figure 1.**Schematic diagram of our system for two protons case calculations mimicking the interaction between the projectile and the two protons. R

_{01}, R

_{02}and R

_{12}are the distances between electron–proton1, electron–proton2 and proton1–proton2, respectively. Distance between protons R

_{12}is constant during the simulation. L

_{1}is the vertical distance between electron source and protons, L

_{2}is the vertical distance between protons and the detector.

**Figure 2.**Trajectories of projectiles in three configurations of the target system, (

**a**) electrons with one proton, (

**b**) positrons with one proton, (

**c**) electrons with two protons, (

**d**) positrons with two protons, (

**e**) electrons with ten protons, (

**f**) positrons with ten protons. Blue solid lines: electrons with initial energy of 500 eV, red dashed lines: electrons with initial energy of 1000 eV, green solid lines: positrons with initial energy of 500 eV, black dashed lines: positrons with initial energy of 1000 eV, red circle shows positions of the protons.

**Figure 3.**Intensity distribution of projectiles at the detection plane: (

**a**) one-proton system, (

**b**) two-proton system, (

**c**) ten-proton system with electrons, (

**d**) ten-proton system with positrons. Vertical red line indicates the x-position of protons. Black solid line: 500 eV electrons, blue solid line: 1000 eV electrons, brown solid line: 500 eV positrons and green solid line: 1000 eV positrons.

**Figure 4.**Double differential intensity distribution of projectiles at the two-dimensional detection plane, one-proton system with (

**a**) 500 eV electrons, (

**d**) 1000 eV electrons, (

**g**) 500 eV positrons and (

**j**) 1000 eV positrons; two-proton system with (

**b**) 500 eV electrons, (

**e**) 1000 eV electrons, (

**h**) 500 eV positrons and (

**k**) 1000 eV positrons; ten-proton system with (

**c**) 500 eV electrons, (

**f**) 1000 eV electrons, (

**i**) 500 eV positrons and (

**l**) 1000 eV positrons. The small green circles indicate the position of the protons.

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**MDPI and ACS Style**

Al-Ajaleen, M.S.; Tőkési, K.
Interaction of Electrons and Positrons with Protons Aligned in One-Dimension Line. *Atoms* **2023**, *11*, 46.
https://doi.org/10.3390/atoms11030046

**AMA Style**

Al-Ajaleen MS, Tőkési K.
Interaction of Electrons and Positrons with Protons Aligned in One-Dimension Line. *Atoms*. 2023; 11(3):46.
https://doi.org/10.3390/atoms11030046

**Chicago/Turabian Style**

Al-Ajaleen, Musab S., and Károly Tőkési.
2023. "Interaction of Electrons and Positrons with Protons Aligned in One-Dimension Line" *Atoms* 11, no. 3: 46.
https://doi.org/10.3390/atoms11030046