𝒆 − 𝒆 + Pair Production Using High Energy
- 1 Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia
- 2 Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia
- 3 Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia
Abstract
This work studies the energy distribution of pair production for 𝐵𝑒 4 9 and Al 13 25 using the Bethe-Heitler equation. We use the mathematics program “Mathematica” to compare the electromagnetic effects of photons interacting with beryllium and aluminum nuclei. We compare the impact of electric and magnetic cross-sections on pair generation. Using graphs, we investigate how electric and magnetic fields affect the production of 𝒆 − 𝒆 + . We also study the impact of atomic mass on 𝒆 − 𝒆 + emission. Our results indicate that harnessing magnetic interactions can produce 𝒆 − 𝒆 + with specific properties at high energies (MeV) and for lighter nuclei, the efficiency of electron-positron pair production increases significantly. We will now discuss this phenomenon in detail, illustrating the impact of energy and nuclear mass on pair production, as well as the role of multipole interactions in enhancing production efficiency. These ideas are crucial to PET technology, because regulated e − e + pair formation and annihilation are fundamental to imaging efficacy. These ideas are particularly relevant to positron emission tomography (PET), because regulated electron-positron pair formation and extinction are fundamental to imaging efficacy.
- Greiner, W. and Reinhardt, J. (2008) Quantum Electrodynamics. Springer Science & Business Media.
- Griffiths, D. (2020) Introduction to Elementary Particles. Wiley.
- Wu, B. (2023) Quantum Mechanics: A Concise Introduction. Springer Nature.
- Nishina, Y., Tomonaga, S. and Sakata, S. (1934) On the Photoelectric Creation of Positive and Negative Electrons. Institute of Physical and Chemical Research.
- Bethe, H. and Heitler, W. (1934) On the Stopping of Fast Particles and the Creation of Positive Electrons. Proceedings of the Royal Society A , 146, 83-112.
- Jaeger, J. and Hulme, H. (1936) On the Production of Electron Pairs. Proceedings of the Royal Society A , 153, 443-447.
- Sakharov, A.D. (1948) Interaction of an Electron and Positron in Pair Production. Journal of Experimental and Theoretical Physics , 18, Article 631.
- Hubbell, J.H. (2006) Electron-Positron Pair Production by Photons: A Historical Overview. Radiation Physics and Chemistry , 75, 614-623. https://doi.org/10.1016/j.radphyschem.2005.10.008
- Hubbell, J.H. and Seltzer, S.M. (2004) Cross Section Data for Electron-Positron Pair Production by Photons: A Status Report. Nuclear Instruments and Methods in Physics Research Section B : Beam Interactions with Materials and Atoms , 213, 1-9. https://doi.org/10.1016/s0168-583x(03)01524-6
- Alkhateeb, S. (2020) Effect of Nuclear Magnetic Distribution on the Photon Production of Longitudinally Polarized Lepton-Pairs in the Field of and Nuclei. Thermal Scie nce , 24, 139-147. https://doi.org/10.2298/tsci20s1139a
- Alkhateeb, S.A., Alshaery, A.A. and Aldosary, R.A. (2022) Electron-Positron Pair Production in Electro-Magnetic Field. Journal of Applied Mathematics and Physics , 10, 237-244. https://doi.org/10.4236/jamp.2022.102017
- Pardy, M. (2024) The Electron-Positron Pair Production in Modern Quantum Electrodynamics.
- Abuelhia, E.I. (2006) The Potential Use of Three Photon Positron Annihilation Processes as a New Imaging Modality for Positron Emission Tomography (PET). University of Surrey (United Kingdom).
- Zhu, W. (2020) Improved Bethe-Heitler Formula. Nuclear Physics B , 953, Article 114958. https://doi.org/10.1016/j.nuclphysb.2020.114958
- Obraztsov, I.V. and Milstein, A.I. (2021) Quadrupole Radiation and Pair Production in the Collision of Nonrelativistic Nuclei. Physics Letters B , 820, Article 136514. https://doi.org/10.1016/j.physletb.2021.136514