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Theoretical Study of the Effects of Di-Muonic Molecules on Muon-Catalyzed Fusion Eugene V

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Theoretical Study of the Effects of Di-Muonic Molecules on Muon-Catalyzed Fusion Eugene V Air Force Institute of Technology AFIT Scholar Theses and Dissertations Student Graduate Works 3-22-2012 Theoretical Study of the Effects of Di-Muonic Molecules on Muon-Catalyzed Fusion Eugene V. Sheely Follow this and additional works at: https://scholar.afit.edu/etd Part of the Nuclear Engineering Commons Recommended Citation Sheely, Eugene V., "Theoretical Study of the Effects of Di-Muonic Molecules on Muon-Catalyzed Fusion" (2012). Theses and Dissertations. 1190. https://scholar.afit.edu/etd/1190 This Dissertation is brought to you for free and open access by the Student Graduate Works at AFIT Scholar. It has been accepted for inclusion in Theses and Dissertations by an authorized administrator of AFIT Scholar. For more information, please contact [email protected]. THEORETICAL STUDY OF THE EFFECTS OF DI-MUONIC MOLECULES ON MUON-CATALYZED FUSION DISSERTATION Eugene V. Sheely, Lieutenant Colonel, USA DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY AIR FORCE INSTITUTE OF TECHNOLOGY Wright-Patterson Air Force Base, Ohio DISTRIBUTION STATEMENT A; APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED The views expressed in this thesis are those of the author and do not reflect the official policy or position of the United States Air Force, the Department of Defense, or the United States Government. This material is declared a work of the US Government and is not subject to copyright protection in the United States. AFIT/DS/ENP/12-M02 THEORETICAL STUDY OF THE EFFECTS OF DI-MUONIC MOLECULES ON MUON-CATALYZED FUSION DISSERTATION Presented to the Faculty Department of Engineering Physics Graduate School of Engineering and Management Air Force Institute of Technology Air University Air Education and Training Command In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Nuclear Engineering Eugene V. Sheely, BS, MS, PhD Lieutenant Colonel, USA 8 March 2012 DISTRIBUTION STATEMENT A; APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED AFIT/DS/ENP/12-M02 Abstract This document presents a theoretical study di-muonic hydrogen and helium molecules that have the potential of enhancing the muon-catalyzed fusion reaction rate. In order to study these di-muonic molecules a method of non-adiabatic quantum mechanics referred to as a General Particle Orbital (GPO) method was developed. Three mechanisms that have the possibility of enhancing the muon-catalyzed fusion rate were discovered. Two involve the formation of di-muonic hydrogen molecules, and the other uses di-muonic molecules to liberate muons stuck to 3He nuclei. The effects of muon spin on di-muonic hydrogen molecules was studied. The nuclear separation in di-muonic hydrogen molecules with parallel muon spin is too great for the molecules to have a fusion rate which can enhance the fusion yield. The possibility of these molecules transitioning to single muon molecules or triatomic oblate symmetric top molecules which may fuse faster is examined. Using two muons to catalyze 3He-3He fusion is shown to be impractical; however, using two muons to catalyze 3He-d fusion is possible. While studying the physical properties of di-muonic hydrogen and helium molecules some unique properties were discovered. Correlation interactions in these molecules result in an increase in the calculated nuclear bond length. v To my wonderful family vi Table of Contents Abstract ................................................................................................................................v List of Figures ......................................................................................................................x List of Tables ..................................................................................................................... xii I. Introduction ....................................................................................................................1 II. Background ...................................................................................................................5 2.1 Muons ....................................................................................................................5 2.2 Muon-Catalyzed Fusion .........................................................................................8 2.2.1 History ............................................................................................................8 2.2.2 Single-Muon Catalyzed Fusion Process .......................................................10 2.3 Muon-Catalyzed Fusion Yield .............................................................................19 2.3.1 Muon Production ..........................................................................................19 2.3.2 Increasing the number of fusions per muon .................................................20 2.3.2.1 Muonic-molecular reaction rates ............................................................20 2.3.2.2 Muon Sticking to Fusion Products ...........................................................21 2.3.2.3 Muon Scavenging .....................................................................................22 2.4 Applications of Muon-Catalyzed Fusion with Currently Obtainable Yields ..................................................................................................................23 2.5 Conclusions ..........................................................................................................24 III. Novel Muon-Catalyzed Fusion Reaction Paths ...........................................................34 3.1 Addition of Positive Muons and Positrons ..........................................................34 3.2 A Novel Approach to Decrease Muon Loss Due to Sticking ..............................35 3.3 Two-Muon Catalyzed-Fusion ..............................................................................40 3.4 Enhance Fusion Yields with Electromagnetic Radiation.....................................42 3.5 Conclusions ..........................................................................................................43 IV. General Multi-Configurational HF-SCF/CI Method to Model Molecules Made of Multiple Types of Quantum Particles .......................................................46 4.1 Introduction ..........................................................................................................46 4.2 Theory ..................................................................................................................50 4.2.1 GPO Hartree-Fock Method .........................................................................50 4.2.2 Configuration Interaction ............................................................................56 4.2.3 Basis Set Development ...............................................................................59 4.3 Applications .........................................................................................................62 4.3.1 Contributions to the CI Energy ...................................................................62 4.3.2 Bi-Muo Hydrogen Molecules .....................................................................66 vii 4.4 Conclusions ..........................................................................................................70 V. Correlation Interactions in Di-Muonic Hydrogen Molecules .....................................79 5.1 Introduction ..........................................................................................................79 5.2 Methods................................................................................................................80 5.3 Results ..................................................................................................................82 5.4 Conclusions ..........................................................................................................85 VI. Di-Muonic Helium Molecules ...................................................................................89 6.1 Introduction ..........................................................................................................89 6.2 Methods................................................................................................................91 6.3 Results and Discussion ......................................................................................100 6.3.1 3He+3He ....................................................................................................100 6.3.2 3He+d ........................................................................................................102 6.4 Conclusions ........................................................................................................107 VII. Reacion Paths of pμμp(T) and pμpμp(T)....................................................................111 7.1 Introduction ........................................................................................................111 7.2 Methods..............................................................................................................112 7.3 Results and Discussion ......................................................................................115 7.4 Conclusions ........................................................................................................124 VIII. Di-muonic Hydrogen Reaction Kinetics ...............................................................128 8.1 Introduction ........................................................................................................128
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