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Positron-Atom Interactions Studied Using Configuration Interaction Methods POSITRON-ATOM INTERACTIONS STUDIED USING CONFIGURATION INTERACTION METHODS Michael William James Bromley A thesis for the degree of Doctor of Philosophy at the Faculty of Science, Information Technology and Education Northern Territory University, Australia Submitted on September 12, 2002. Declaration I hereby declare that the work herein is the result of my own investigations, and all references to ideas and research of others have been specifically acknowledged. I certify that the work embodied in this thesis has not already been accepted in substance for any degree, and is not being currently submitted for any other degree. Abstract The non-relativistic configuration interaction (CI) method is applied to the study of positron interactions with either one or two valence electron atoms possessing a positron-atom bound state. Although the binding energy and other atomic properties are slowly convergent with respect to the angular momenta of the single particle orbitals used to construct the CI wavefunctions, the calculations are sufficiently large to give usefully accurate descriptions of the positronic atom structures. Calculations of the accurately known positron-atom bound states; positronic cop- per (e+Cu), positronic lithium (e+Li), and positronium hydride (PsH) systems were undertaken to develop and refine the numerical procedures. CI calculations confirmed the stability of three other systems; positronic beryllium (e+Be), positronic magnesium (e+Mg), and positronic zinc (e+Zn). The e+Mg calculations independently resolves the disagreement between the University of New South Wales group and a previous computational approach of the Northern Territory University group. Further CI calcu- lations demonstrated the stability of four systems; positronic calcium (e+Ca), copper positride (CuPs), positronic strontium (e+Sr) and positronic cadmium (e+Cd). These predictions are all rigorous with respect to the underlying model Hamiltonians. CI convergence issues are examined in detail, with trends used to give estimated binding energies (in units of Hartree) of 0.037795 (PsH), 0.000886 (e+Li), 0.003083 (e+Be), 0.016151 (e+Mg), 0.016500 (e+Ca), 0.005088 (e+Cu), 0.014327 (CuPs), 0.003731 (e+Zn), 0.010050 (e+Sr) and 0.006100 (e+Cd). The CI program used for the structure calculations was adapted to perform scat- tering calculations via the imposition of plane-wave boundary conditions within the Kohn variational formalism. Test calculations of model potential and low-energy elastic positron-hydrogen scattering reveal that in practice, the effects of ’Schwartz’ singular- ities are insignificant. CI-Kohn calculations of low-energy (k = 0 0.2 a−1) elastic → 0 positron-copper scattering gave a scattering length of +13.7 a0 and a threshold Zeff of 69.3, explicitly demonstrating that Zeff is not overly large for such a metal vapour. These investigations demonstrate the feasibility of using single particle orbitals centred on the nucleus to reliably describe certain classes of positronic systems with one or two valence electrons. ii List of Publications As of the 30th March 2003, the following papers with contributions from the results presented in this thesis have been published, or are under review: 1. Configuration interaction calculations of positronic atoms and ions. M W J Bromley, J Mitroy and G G Ryzhikh. Nucl. Inst. Methods. B, (2000) 171 47-59. 2. Positron binding to calcium, a configuration interaction study. M W J Bromley and J Mitroy. J. Phys. B, (2000) 33 L325-L331. 3. Positronic Atoms J Mitroy, M W J Bromley, and G G Ryzhikh. Pages 199-221 in New Directions in Antimatter Physics and Chemistry. C M Surko and F A Gianturco, Eds. Kluwer Academic Publishers, The Netherlands, 2001. 4. Configuration interaction calculations of PsH and e+Be. M W J Bromley and J Mitroy. Phys. Rev. A, (2002) 65 012505. 5. Configuration interaction calculations of positron binding to group II elements. M W J Bromley and J Mitroy. Phys. Rev. A, (2002) 65 062505. 6. Configuration interaction calculations of positron binding to Zn and Cd. M W J Bromley and J Mitroy. Phys. Rev. A, (2002) 65 062506. 7. Positron and positronium binding to atoms and ions. J Mitroy, M W J Bromley, and G G Ryzhikh. J. Phys. B, (2002) 35 R81-R116 (Topical review). 8. Positron and positronium interactions with Cu. M W J Bromley and J Mitroy. Phys. Rev. A, (2002) 66 062504. iii 9. Variational calculations of positron-atom scattering using Configuration Interac- tion type wave functions M W J Bromley and J Mitroy. Phys. Rev. A, (2003) 67 (in press). The following papers contain contributions from M W J Bromley that are not reported in this thesis. Except for the first paper, the contributions consisted of using the programs developed as part of this thesis to perform calculations that were essential to the published research. 1. The elastic scattering of positrons from beryllium and magnesium in the low energy region. M W J Bromley, J Mitroy and G Ryzhikh. J. Phys. B, (1998) 31 4449-4458. 2. Positron binding to a model alkali atom. J Mitroy, M W J Bromley and G G Ryzhikh. J. Phys. B, (1999) 32 2203-2214. 3. Asymptotically exact expression for the energies of the 3Se Rydberg series in a two-electron system. I A Ivanov, M W J Bromley and J Mitroy. Phys. Rev. A, (2002) 66 042507. 4. Use of Orthogonalising Pseudo-Potentials in electronic scattering calculations I A Ivanov, J Mitroy M W J Bromley. Comp. Phys. Commun., (2003) 152 9-24. 5. Comment on Positronium Scattering by Ne, Ar, Kr and Xe in the Frozen Target approximation. J Mitroy and M W J Bromley. J. Phys. B, (2003) 36 793-795. 6. Positronium Scattering from Kr and Xe at low energies J Mitroy and M W J Bromley. Phys. Rev. A, (2003) 67 034502. iv Acknowledgements This is a thesis spanning four years, two cities, many bottles of Australian red, and there are many to thank... Professor Chojnacki for being kind enough to provide the exact input of their CI calculations, which allowed me to verify my program right from the outset! Huge thanks to Dr. Jim Mitroy for teaching me with patience how to do → ∞ relentless computational physics, Dr. Gregory Ryzhikh for much initial help, and Dr. Sergey Novikov for a final critical thesis reading. Many thanks to Dr. Bill King and Dr. Jenny Blackwood for providing copies of their thesii. Thanks to the NT Solar Energy Society and NT Power and Water Authority for their awards (and cash ;). The Queens’ Trust for Young Australians for their project support to send me to Can- berra; Prof. Buckman, Prof. McEachran and the crew of the good-ship AMPL for the hospitality. Thanks to NTU for still existing, and the various IT techos; Prasad Gunatunge, Shane Nuessler, Bronwyn Allan and J-C Nou for happily maintaining the workstations used to perform the calculations. Also the GNU/Linux/g77 free-sourced-nerds, with- out whom this thesis would not have happened at NTU (to this extent). The beautiful CAPA/NTUPSA peoples for taking time out of their lives and daring to question the ways things are heading (and how they are now). Best wishes to the following exquisite friends who all helped to keep me sane... Sparkles&Julieanne, J2T, travellingKat, Emma H-W, Luscious Lari, Shane-e, will&dani, Lauraζ, (Matt, Dan, Mary), Asco Gordon, Jenny Blackwood, Neutrino Girl and the McKeddieans, Que-bit, Sandra Thibodeaux, Mont´eand Greg, Hoges, Harri B, Bruce Rock, QueenJ, Dr. Kate, Groover Gill, and Iam&Grant&Jasper. Ups to the Jim Henson, Towards 2000, Quantum, NTU Revue, NEo, and Nude2000 crews for their Bubbles of Reality. Thanks to my wonderful family for all things principled, financial and culinary. Dedicated to my niece Caitlin; may she always smile, and the world upon her. v Contents 1 Introduction 1 1.1 Positron-electroninteractions . ..... 2 1.1.1 Applications and implications of positron annihilation ...... 4 1.2 Positron-atominteractions. ... 6 1.3 Nomenclatureandunits ........................... 8 1.4 Positronbindingtoneutralatoms . 9 1.4.1 Positroniumbindingtoneutralatoms . 15 1.4.2 WhyCI? ............................... 17 1.5 ChapterOutlines ............................... 19 2 Modelling Atomic Structures 21 2.1 Hartree-Fock and configuration interaction ansatz . ......... 22 2.2 Treatmentoffrozen-coreelectrons . 24 2.2.1 Core-direct and core-exchange interactions . ...... 25 2.2.2 Core-polarisationinteraction . 26 2.2.3 Orthogonalitywiththecoreelectrons . 29 2.3 Choiceofbasisfunctions. 29 2.3.1 Diagonalisation of the one-electron atoms . 31 2.3.2 Choice of two-electron configurations . 32 2.3.3 Determinationofdissociationlimits . 32 2.4 Oscillator strengths, sum rules and αd ................... 33 2.5 Atoms..................................... 34 2.5.1 Li and Li− .............................. 35 2.5.2 Be+ andBe.............................. 36 2.5.3 Mg+ andMg ............................. 39 vi 2.5.4 Ca+ andCa.............................. 42 2.5.5 Cu................................... 44 2.5.6 Cu− .................................. 45 2.5.7 Zn+ andZn.............................. 48 2.5.8 Sr+ andSr .............................. 50 2.5.9 Cd+ andCd ............................. 53 2.6 Summary ................................... 56 3 Positron Binding to one-Electron Systems 57 3.1 CI method for one-electron positronic systems . ....... 58 3.1.1 Subsetbasis.............................. 59 3.2 Electron-positronannihilation . ..... 60 3.3 Partial-wave convergence and extrapolation . ....... 61 3.4 Previous CI calculations of e+Li and e+Cu ................ 62 3.5 e+Liresults.................................. 63 3.6 e+Curesults ................................. 66 3.7 e+Li and e+Cupartial-waveconvergence. 69 3.8 Summary ................................... 74 4 Positron Binding to Simple two-Electron Systems 75 4.1 CI method for two-electron positronic systems . ....... 76 4.2 Choice of two-electron-positron configurations . ......... 77 4.3 ResultsforPsH................................ 78 4.3.1 Convergence of Ps-H scattering calculations . ..... 82 4.4 e+Beresults.................................. 84 + 4.5 Lint = 3 calculations of PsH and e Be................... 88 4.6 Chaptersummary .............................. 89 5 Positron Binding to Group II and IIB Atoms (and CuPs) 93 5.1 Positron binding to alkaline-earth atoms .
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