Dynamics of Twisted Electron Impact Ionization of CH4 and NH3 Molecule
Abstract
1. Introduction
2. Theory
2.1. “Twisted” Electron Ionization Cross Section
2.2. Average over the Impact Parameter
2.3. Superposition of Two Bessel Beams
3. Results and Discussions
3.1. Ionization from Orbitals of p-Type Character of the Targets
3.2. Ionization from Orbitals of s-Type Character of the Targets
3.3. Angular Profiles for the (TDCS) for the Macroscopic Molecular Targets
3.3.1. (TDCS) from Orbitals of p-Type Character of the Targets
3.3.2. (TDCS) from Orbitals of s-Type Character of the Targets
3.4. TDCS from the Coherent Superposition of Bessel Beams
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Torres, J.P.; Torner, L. Twisted Photons: Applications of Light with Orbital Angular Momentum; John Wiley & Sons: Hoboken, NJ, USA, 2011. [Google Scholar]
- Molina-Terriza, G.; Torres, J.P.; Torner, L. Twisted photons. Nat. Phys. 2007, 3, 305–310. [Google Scholar] [CrossRef]
- Bliokh, K.; Ivanov, I.; Guzzinati, G.; Clark, L.; Van Boxem, R.; Béché, A.; Juchtmans, R.; Alonso, M.; Schattschneider, P.; Nori, F.; et al. Theory and applications of free-electron vortex states. Phys. Rep. 2017, 690, 1–70. [Google Scholar] [CrossRef][Green Version]
- Lloyd, S.M.; Babiker, M.; Thirunavukkarasu, G.; Yuan, J. Electron vortices: Beams with orbital angular momentum. Rev. Mod. Phys. 2017, 89, 035004. [Google Scholar] [CrossRef][Green Version]
- Larocque, H.; Kaminer, I.; Grillo, V.; Leuchs, G.; Padgett, M.J.; Boyd, R.W.; Segev, M.; Karimi, E. ‘Twisted’ electrons. Contemp. Phys. 2018, 59, 126–144. [Google Scholar] [CrossRef]
- Ivanov, I.P. Promises and challenges of high-energy vortex states collisions. Prog. Part. Nucl. Phys. 2022, 127, 103987. [Google Scholar] [CrossRef]
- Bliokh, K.Y.; Bliokh, Y.P.; Savel’ev, S.; Nori, F. Semiclassical Dynamics of Electron Wave Packet States with Phase Vortices. Phys. Rev. Lett. 2007, 99, 190404. [Google Scholar] [CrossRef][Green Version]
- Uchida, M.; Tonomura, A. Generation of electron beams carrying orbital angular momentum. Nature 2010, 464, 737–739. [Google Scholar] [CrossRef]
- Verbeeck, J.; Tian, H.; Schattschneider, P. Production and application of electron vortex beams. Nature 2010, 467, 301–304. [Google Scholar] [CrossRef]
- Mafakheri, E.; Tavabi, A.H.; Lu, P.H.; Balboni, R.; Venturi, F.; Menozzi, C.; Gazzadi, G.C.; Frabboni, S.; Sit, A.; Dunin-Borkowski, R.E.; et al. Realization of electron vortices with large orbital angular momentum using miniature holograms fabricated by electron beam lithography. Appl. Phys. Lett. 2017, 110, 093113. [Google Scholar] [CrossRef][Green Version]
- Tavabi, A.H.; Rosi, P.; Roncaglia, A.; Rotunno, E.; Beleggia, M.; Lu, P.H.; Belsito, L.; Pozzi, G.; Frabboni, S.; Tiemeijer, P.; et al. Generation of electron vortex beams with over 1000 orbital angular momentum quanta using a tunable electrostatic spiral phase plate. Appl. Phys. Lett. 2022, 121, 073506. [Google Scholar] [CrossRef]
- Juchtmans, R.; Béché, A.; Abakumov, A.; Batuk, M.; Verbeeck, J. Using electron vortex beams to determine chirality of crystals in transmission electron microscopy. Phys. Rev. B 2015, 91, 094112. [Google Scholar] [CrossRef][Green Version]
- Juchtmans, R.; Verbeeck, J. Local orbital angular momentum revealed by spiral-phase-plate imaging in transmission-electron microscopy. Phys. Rev. A 2016, 93, 023811. [Google Scholar] [CrossRef][Green Version]
- Thirunavukkarasu, G.; Thirunavukkarasu, G.; Yuan, J.; Babiker, M. Observation of gold nanoparticles movements under sub-10 nm vortex electron beams in an aberration corrected TEM. In Proceedings of the 15th European Microscopy Congresss; Stokes, D., Hutchison, J., Eds.; Royal Microscopical Society: Manchester, UK, 2012. [Google Scholar]
- Jesacher, A.; Fürhapter, S.; Bernet, S.; Ritsch-Marte, M. Shadow Effects in Spiral Phase Contrast Microscopy. Phys. Rev. Lett. 2005, 94, 233902. [Google Scholar] [CrossRef]
- Serbo, V.; Ivanov, I.P.; Fritzsche, S.; Seipt, D.; Surzhykov, A. Scattering of twisted relativistic electrons by atoms. Phys. Rev. A 2015, 92, 012705. [Google Scholar] [CrossRef][Green Version]
- Dhankhar, N.; Choubisa, R. Electron impact single ionization of hydrogen molecule by twisted electron beam. J. Phys. B At. Mol. Opt. Phys. 2020, 54, 015203. [Google Scholar] [CrossRef]
- Gong, M.; Cheng, Y.; Zhang, S.B.; Chen, X. Twisted-electron-impact single ionization of an H2O molecule by multicenter distorted-wave calculations. Phys. Rev. A 2022, 106, 012818. [Google Scholar] [CrossRef]
- Bartschat, K.; Kushner, M.J. Electron collisions with atoms, ions, molecules, and surfaces: Fundamental science empowering advances in technology. Proc. Natl. Acad. Sci. USA 2016, 113, 7026–7034. [Google Scholar] [CrossRef][Green Version]
- Dunn, W.B. Chapter two—Mass Spectrometry in Systems Biology: An Introduction. In Methods in Systems Biology; Methods in Enzymology; Jameson, D., Verma, M., Westerhoff, H.V., Eds.; Academic Press: Cambridge, MA, USA, 2011; Volume 500, pp. 15–35. [Google Scholar] [CrossRef]
- Girazian, Z.; Mahaffy, P.; Lillis, R.J.; Benna, M.; Elrod, M.; Fowler, C.M.; Mitchell, D.L. Ion Densities in the Nightside Ionosphere of Mars: Effects of Electron Impact Ionization. Geophys. Res. Lett. 2017, 44, 11248–11256. [Google Scholar] [CrossRef]
- Kynienė, A.; Kučas, S.; Masys, Š.; Jonauskas, V. Electron-impact ionization of Fe8+. A&A 2019, 624, A14. [Google Scholar] [CrossRef][Green Version]
- Caleman, C.; Ortiz, C.; Marklund, E.; Bultmark, F.; Gabrysch, M.; Parak, F.G.; Hajdu, J.; Klintenberg, M.; Tîmneanu, N. Radiation damage in biological material: Electronic properties and electron impact ionization in urea. EPL (Europhys. Lett.) 2009, 85, 18005. [Google Scholar] [CrossRef][Green Version]
- Yavuz, M.; Okumus, N.; Ozer, Z.N.; Ulu, M.; Dogan, M.; Sahlaoui, M.; Benmansour, H.; Bouamoud, M. Double Differential Cross Sections for Methane Molecules at Intermediate Energies. J. Phys. Conf. Ser. 2014, 488, 052031. [Google Scholar] [CrossRef][Green Version]
- Yavuz, M.; Ozer, Z.N.; Ulu, M.; Champion, C.; Dogan, M. Experimental and theoretical double differential cross sections for electron impact ionization of methane. J. Chem. Phys. 2016, 144, 164305. [Google Scholar] [CrossRef]
- Tachino, C.A.; Monti, J.M.; Fojón, O.A.; Champion, C.; Rivarola, R.D. Single electron ionization of NH3 and CH4 by swift proton impact. J. Phys. Conf. Ser. 2015, 583, 012020. [Google Scholar] [CrossRef]
- Tóth, I.; Nagy, L.; Campeanu, R.I. Triple-differential cross sections for the ionization of NH3 by positron impact. Eur. Phys. J. D 2016, 70, 170. [Google Scholar] [CrossRef]
- Lahmam-Bennani, A.; Naja, A.; Casagrande, E.M.S.; Okumus, N.; Cappello, C.D.; Charpentier, I.; Houamer, S. Dynamics of electron impact ionization of the outer and inner valence (1t2 and 2a1) molecular orbitals of CH4 at intermediate and large ion recoil momentum. J. Phys. B At. Mol. Opt. Phys. At. Mol. Opt. Phys. 2009, 42, 165201. [Google Scholar] [CrossRef]
- Mir, R.E.; Casagrande, E.M.S.; Naja, A.; Cappello, C.D.; Houamer, S.; Omar, F.E. Triple differential cross sections for the ionization of the valence states of NH3 by electron impact. J. Phys. B At. Mol. Opt. Phys. 2015, 48, 175202. [Google Scholar] [CrossRef]
- Mouawad, L.; El Bitar, Z.; Osman, A.; Khalil, M.; Hervieux, P.A.; Dal Cappello, C. Triply Differential Ionization Cross Sections of atomic and molecular targets by single electron impact. EPJ Web Conf. 2018, 170, 01012. [Google Scholar] [CrossRef][Green Version]
- Bouchikhi, A.; Sahlaoui, M.; Lasri, B.; Sekkal, A.; Bouamoud, M. Electron-impact ionization of the CH4 and NH3 molecules in coplanar symmetric and asymmetric geometries. J. Phys. B At. Mol. Opt. Phys. 2018, 52, 015201. [Google Scholar] [CrossRef]
- Nixon, K.L.; Murray, A.J.; Chaluvadi, H.; Ning, C.; Madison, D.H. Low energy (e,2e) studies from CH4: Results from symmetric coplanar experiments and molecular three-body distorted wave theory. J. Chem. Phys. 2011, 134, 174304. [Google Scholar] [CrossRef] [PubMed][Green Version]
- Ali, E.; Granados, C.; Sakaamini, A.; Harvey, M.; Ancarani, L.U.; Murray, A.J.; Dogan, M.; Ning, C.; Colgan, J.; Madison, D. Triple differential cross sections for electron-impact ionization of methane at intermediate energy. J. Chem. Phys. 2019, 150, 194302. [Google Scholar] [CrossRef][Green Version]
- Nixon, K.L.; Murray, A.J.; Chaluvadi, H.; Ning, C.; Colgan, J.; Madison, D.H. Low energy (e,2e) coincidence studies of NH3: Results from experiment and theory. J. Chem. Phys. 2013, 138, 174304. [Google Scholar] [CrossRef] [PubMed]
- Tóth, I.; Nagy, L. Triple-differential cross-section calculations for the ionization of CH4 by electron impact. J. Phys. B At. Mol. Opt. Phys. At. Mol. Opt. Phys. 2010, 43, 135204. [Google Scholar] [CrossRef]
- Lin, C.Y.; McCurdy, C.W.; Rescigno, T.N. Theoretical study of (e,2e) from outer- and inner-valence orbitals of CH4: A complex Kohn treatment. Phys. Rev. A 2014, 89, 052718. [Google Scholar] [CrossRef]
- Castro, C.M.G. Application of Generalized Sturmian Basis Functions to Molecular Systems. Ph.D. Thesis, Université de Lorraine, Metz, France, 2016. [Google Scholar]
- Granados-Castro, C.M.; Ancarani, L.U. Electron impact ionization of the outer valence orbital 1t2 of CH4. Eur. Phys. J. D 2017, 71, 65. [Google Scholar] [CrossRef]
- Gong, M.; Li, X.; Zhang, S.B.; Liu, L.; Wu, Y.; Wang, J.; Qu, Y.; Chen, X. Theoretical study of (e,2e) processes for valence orbitals of CH4 using a multicenter distorted-wave method. Phys. Rev. A 2017, 96, 042703. [Google Scholar] [CrossRef]
- Houamer, S.; Chinoune, M.; Cappello, C.D. Theoretical study of (e, 2e) process of atomic and molecular targets*. Eur. Phys. J. D 2017, 71, 17. [Google Scholar] [CrossRef][Green Version]
- Mir, R.E.; Kaja, K.; Naja, A.; Casagrande, E.M.S.; Houamer, S.; Cappello, C.D. New investigation of the electron-impact ionization of the intermediate valence state of ammonia. J. Phys. B At. Mol. Opt. Phys. 2020, 54, 015201. [Google Scholar] [CrossRef]
- Harris, A.L.; Plumadore, A.; Smozhanyk, Z. Ionization of hydrogen by electron vortex beam. J. Phys. B At. Mol. Opt. Phys. 2019, 52, 094001. [Google Scholar] [CrossRef][Green Version]
- Plumadore, A.; Harris, A.L. Projectile transverse momentum controls emission in electron vortex ionization collisions. J. Phys. B At. Mol. Opt. Phys. 2020, 53, 205205. [Google Scholar] [CrossRef]
- Dhankhar, N.; Choubisa, R. Triple-differential cross section for the twisted-electron-impact ionization of the water molecule. Phys. Rev. A 2022, 105, 062801. [Google Scholar] [CrossRef]
- Dhankhar, N.; Banerjee, S.; Choubisa, R. Twisted electron impact single ionization coincidence cross-sections for noble gas atoms. J. Phys. At. Mol. Opt. Phys. At. Mol. Opt. Phys. 2022, 55, 165202. [Google Scholar] [CrossRef]
- Mandal, A.; Dhankhar, N.; Sébilleau, D.; Choubisa, R. Semirelativistic (e,2e) study with a twisted electron beam on Cu and Ag. Phys. Rev. A 2021, 104, 052818. [Google Scholar] [CrossRef]
- Moccia, R. One-Center Basis Set SCF MO’s. I. HF, CH4, and SiH4. J. Chem. Phys. 1964, 40, 2164–2176. [Google Scholar] [CrossRef]
- Moccia, R. One-Center Basis Set SCF MO’s. II. NH3, NH4+, PH3, PH4+. J. Chem. Phys. 1964, 40, 2176–2185. [Google Scholar] [CrossRef]
- Champion, C.; Hanssen, J.; Hervieux, P.A. Influence of molecular orientation on the multiple differential cross sections for the (e,2e) process on a water molecule. Phys. Rev. A 2005, 72, 059906. [Google Scholar] [CrossRef][Green Version]
- Karlovets, D.V.; Kotkin, G.L.; Serbo, V.G.; Surzhykov, A. Scattering of twisted electron wave packets by atoms in the Born approximation. Phys. Rev. A 2017, 95, 032703. [Google Scholar] [CrossRef][Green Version]
- Khajuria, Y.; Tripathi, D.N. Geometry effects on the (e,2e) triple differential cross sections of Li+, Na+, and K+. Phys. Rev. A 1999, 59, 1197–1207. [Google Scholar] [CrossRef]
- Surzhykov, A.; Seipt, D.; Serbo, V.G.; Fritzsche, S. Interaction of twisted light with many-electron atoms and ions. Phys. Rev. A 2015, 91, 013403. [Google Scholar] [CrossRef]
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Dhankhar, N.; Neha; Choubisa, R. Dynamics of Twisted Electron Impact Ionization of CH4 and NH3 Molecule. Atoms 2023, 11, 82. https://doi.org/10.3390/atoms11050082
Dhankhar N, Neha, Choubisa R. Dynamics of Twisted Electron Impact Ionization of CH4 and NH3 Molecule. Atoms. 2023; 11(5):82. https://doi.org/10.3390/atoms11050082
Chicago/Turabian StyleDhankhar, Nikita, Neha, and Rakesh Choubisa. 2023. "Dynamics of Twisted Electron Impact Ionization of CH4 and NH3 Molecule" Atoms 11, no. 5: 82. https://doi.org/10.3390/atoms11050082
APA StyleDhankhar, N., Neha, & Choubisa, R. (2023). Dynamics of Twisted Electron Impact Ionization of CH4 and NH3 Molecule. Atoms, 11(5), 82. https://doi.org/10.3390/atoms11050082