Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Engineering Physics

First Advisor

Larry W. Burggraf, PhD.


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 dimuonic 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.

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