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The Calculation of Electron Collisions with Atoms and Molecules

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The Calculation of Electron Collisions with Atoms and Molecules The Calculation of Electron Collisions with Atoms and Molecules Thomas Meltzer A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy of University College London. August 10, 2020 2 I, Thomas Meltzer, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the work. Abstract In this thesis electron collisions are studied under two different scattering energy regimes. Firstly, low energy electron-molecule collisions are considered. These typically occur in interstellar medium, planetary atmospheres or industrial plasmas. Under these conditions the electrons cannot be treated classically and so a quan- tum mechanical approach is used. Using R-matrix theory two targets are studied: nitric oxide (NO) and molecular hydrogen (H2). Owing to new developments in the UKRMol+ code the boundaries of previous R-matrix calculations are pushed to new limits in order to produce accurate cross-sections for electron-impact elec- tronic excitation of H2. This includes the use of a B-spline continuum basis, a triply-augmented target basis and a box size of 100 a0. NO is used as a prototypical example of an open-shell molecule that exhibits mixed Rydberg-like and Valence states. Systems like this are typically difficult to solve using standard quantum chemistry approaches, and so the R-matrix with pseudo-states method is employed to produce a set of improved potential energy curves, capable of being used in fur- ther scattering calculations. In the second regime, high energy electron-atom collisions are investigated. These types of collision take place in strongly-driven systems, e.g., atoms in in- tense laser fields. In this case, the scattering electron is provided by the neutral parent atom as it is ionised by the external field. The specific focus of this work is the phenomena of non-sequential double ionisation. A semiclassical Monte-Carlo method is used based on the three step model, which fully accounts for two active electrons, the Coulomb potential and the magnetic-field. Using this model the role of magnetic-field effects in strong-field physics are investigated. Impact Statement The research conducted in this thesis concerns mostly fundamental physics. There- fore, the impact to society is somewhat less immediate. Nevertheless, this research has implications for the academic community that will no doubt influence society further along the line. Electron collisions are important for understanding the world around us, whether they occur in natural environments, such as, planetary aurora, lightning strikes or interstellar medium. Or whether they occur in man-made environments like those found in the plasma etching industry, lasers or nuclear fusion reactors. Furthermore, research conducted in the strong-field regime has already revolu- tionised physics by providing access to high intensity, ultrafast laser pulses. Now it is possible to observe electrons, atoms and molecules with unprecedented levels of accuracy and detail. The R-matrix calculations presented in this thesis are intended as a proof-of- concept. They push the limits of previous R-matrix studies and provide an example of the capabilities of the new UKRMol+ code. It is hoped that many more calcula- tions like these will be carried out in future for a wide range of molecules, to satisfy the demand for accurate cross-section data. Finally, the studies of non-sequential double ionisation, presented in this thesis, have identified important magnetic-field effects that were previously assumed to be negligible. This body of work predominantly focussed on linearly-polarised laser fields but given the flexibility of the theory it could be readily adapted to describe more intricate experiments, such as those that employ two-colour lasers or pump- probe beam experiments. Acknowledgements When I sat down to write this thesis, I had no idea that it would actually be harder to thank all of the people that helped me get here in the first place. To that end, I want to start first and foremost with my family. Mum and Dad, thanks for all of your unending support, encouragement and love – I would not be here without you. To my twin Betty, thanks for putting me in my place on numerous occasions. Without you telling me to stop playing video games I would probably have never made it past my A-levels. It was a privilege to share my progress through education with you every step of the way. To my brother Pete, you have been a constant source of inspiration to me, your dedication to learning and your ability to do anything you put your mind to has never ceased to amaze me. To my sister Issy, thanks for showing me that there’s more to life than physics. Your appreciation of art, music and pottery painting have most definitely rubbed off on me over the years. To my partner Emma, you have taken the rough end of the stick over the last four and a half (nine?) years and I cannot thank you enough. You have selflessly supported me in all of my endeavours, no matter what. You have helped me navigate the rocky and emotional terrain of PhD research, and you have never once complained about it – for that, I am eternally grateful. PhD supervisors can be good, bad and ugly. It turns out I lucked out with my supervisor, Prof Jonathan Tennyson, and the ExoMol group. Jonathan leads by example and in doing so he has crafted generations of successful academics. It is both intimidating and inspiring to see just how successful his mentoring has been – whilst former students and postdocs merit their own success, clearly Jonathan is doing something right. Personally, his ability to provide just the right amount Acknowledgements 6 of guidance has allowed me to develop self-confidence and independence, whilst ensuring I never strayed too far from the path. Thank you for taking me in. I would like to thank all of my collaborators throughout the PhD, in particular Dr Zdenekˇ Masˇ´ın for allowing me to use his DCS code and for his helpful sugges- tions with the UKRMol+ code. I would also like to thank Dr Mark Zammit, Liam Scarlett, Prof Dmitry Fursa and Prof Igor Bray for providing their MCCC data and useful discussions on the molecular hydrogen project. I thank Prof Paul Corkum for his insightful contributions to our non-dipole recollision gating project. Ad- ditionally, I thank Jakub Benda for his valuable help in debugging the UKRMol+ code. I would like to thank all of the past and present members of ExoMol for wel- coming me into the group and making me feel at home, with special thanks to: Sergey Yurchenko for his enthusiasm and constant supply of memes; Tony Lynas- Gray for his infectious kindness and Friday evening whiskies; and Victoria Clark for being the heart of the ExoMol group and a great friend. I would also like to thank the members of my former group, whom without, I would have given up long before the end, i.e., Harry Banks, Arnau Casanovas and Ahai Chen. I would like to thank all my former office mates for helping the days fly by: Carlo Sparaciari, Tom Galley, Lorenzo Catani, Mike Staddon, Alex Paraschiv and Eryn Spinlove. In addition, I also want to thank everyone who made UCL special for me including: Jacob Lang, Erika Aranas, Andy Maxwell, Katy Chubb, Diana Serbanescu and Duncan Little. Finally, thanks to my “physics friends”: Simon Hind, Tom Vice (Kennelly) and Josh Kettlewell*. *also a mini shout-out to Bram Moolenaar et al. for making my life easier – vim <3 Publications 1. A. Emmanouilidou and T. Meltzer. Recollision as a probe of magnetic-field effects in nonsequential double ionization. Phys. Rev. A, 95:033405, 2017. doi:10.1103/PhysRevA.95.033405. 2. A. Emmanouilidou, T. Meltzer, and P. B. Corkum. Non-dipole recollision- gated double ionization and observable effects. J. Phys. B: At. Mol. Opt. Phys., 50:225602, 2017. doi:10.1088/1361-6455/aa90e9. 3. T. Meltzer, J. Tennyson, Z. Masˇ´ın, M. C. Zammit, L. H. Scarlett, D. V. Fursa, and I. Bray. Benchmark calculations of electron impact electronic excitation of the hydrogen molecule. J. Phys. B At. Mol. Opt. Phys., 53:145204, 2020. doi:10.1088/1361-6455/ab8c58. Contents 1 Introduction 15 1.1 Overview . 15 1.2 Low Energy Scattering . 17 1.3 Intermediate Energy Scattering . 20 1.4 High Energy Scattering . 21 1.5 Outline of the Thesis . 24 I Low to Intermediate Energy Electron Collisions with Molecules 25 2 R-matrix Theory 26 2.1 Fixed Nuclei Approximation . 29 2.1.1 Outer Region . 29 2.1.2 Inner Region . 31 2.1.3 Asymptotic Region . 34 2.2 Adiabatic Nuclei Approximation . 35 2.3 Scattering Models . 36 2.4 UKRMol+ Code . 38 2.4.1 UKRMol+ Inner . 38 2.4.2 UKRMol+ Outer . 39 3 Benchmark Calculations of Electron Impact Electronic Excitation of the Hydrogen Molecule 41 Contents 9 3.1 Introduction . 41 3.2 Method . 43 3.2.1 R-Matrix . 43 3.2.2 Molecular convergent close-coupling . 51 3.3 Results . 53 3.3.1 Fixed-Nuclei Cross-Sections . 54 3.3.2 Adiabatic-Nuclei Cross-Sections . 78 3.3.3 Including Higher Partial Waves . 79 3.4 Conclusion . 84 4 Intermediate Energy Collisions 86 4.1 Introduction . 86 4.2 Method . 89 4.2.1 R-matrix with Pseudostates . 90 4.2.2 Mixed Rydberg and valence states . 92 4.3 Results . 94 4.4 Conclusion and Further Work . 100 II High Energy Electron Collisions with Atoms in Strong Laser Fields 102 5 Strong-Field Theory 103 5.1 Three Step Model .
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