Contents

• Contents
• Introduction
  • Muon Physics
• Introduction
  • Muon Physics
  • Overview of the muon catalyzed fusion cycle
    • Muonic atom formation
    • Cascade
    • Muonic atom collisions
    • Processes of excited muonic atoms
    • Formation of muonic molecules
    • Nuclear fusion
    • Sticking and stripping
  • Measurement of resonant molecular formation
    • Cycling measurements in D/T mixture
    • Epithermal molecular formation
• Theoretical aspects of $\mu$CF
  • Muonic molecule and the three body problem
    • The challenge
    • Three body coulomb problem
    • Adiabatic approaches
    • Variational approaches
    • Non-Coulombic corrections
  • Resonant molecular formation
    • The standard Vesman model
    • Subthreshold resonances
    • Condensed matter effects
• Experimental Apparatus
• Experimental Apparatus
  • Muon beam
  • Detection System
    • Overview
  • Detection System
    • Overview
  • Detection System
    • Overview
    • Trigger
    • Multi-wire proportional chambers
    • Silicon detector
    • Neutron detector
    • Germanium X-ray detector
    • Electron detection system
• Experimental Runs
• Experimental Runs
  • Run Series I
  • Run Series II
  • Histogramming and analysis tools
• Monte Carlo simulation codes
  • SMC Monte Carlo code
    • Muonic atom generation
• Monte Carlo simulation codes
  • SMC Monte Carlo code
    • Muonic atom generation
• Monte Carlo simulation codes
  • SMC Monte Carlo code
    • Muonic atom generation
    • Reaction selection
    • Time and position evolution
    • Muonic processes
    • Muon decay and imaging
  • Other simulation codes
    • Full muonic processes
    • Specific processes
• Analysis I - Absolute normalization
  • Effective target thickness
  • Effective target thickness
  • Silicon detector acceptance
  • Muon stopping fraction determination
  • Muon stopping fraction determination
  • Amplitude ratio method
    • Electron scintillator measurements
    • Electron telescope measurements
    • Corrections to $\overline {S}_H ^{AR}$ in the amplitude ratio method
  • Absolute amplitude method
  • Absolute amplitude method
    • Delayed electron lifetime
    • Delayed electron cuts efficiency
  • Discussion of stopping fraction
    • The discrepancy
    • A solution
• Analysis II - Emission of muonic tritium
  • MWPC imaging data
    • Cuts
  • MWPC imaging data
    • Cuts
    • Muonic tritium emission spectra
  • Measurement of the Ramsauer-Townsend effect
    • Monte Carlo parameter determination
  • Measurement of the Ramsauer-Townsend effect
    • Monte Carlo parameter determination
    • The Ramsauer-Townsend minimum energy
• Analysis III - Molecular formation
  • Si detector data
    • Si detector energy calibration
  • Si detector data
    • Si detector energy calibration
  • Si detector data
    • Si detector energy calibration
    • ADC dead time correction
    • Energy spectrum features
    • Time spectrum features
  • The $d\mu t$
    • Background subtraction
    • Yield measurements
    • Systematic effects
    • $d\mu d$ fusion
    • The yield results
    • Time-of-flight spectra
  • Monte Carlo analysis
    • Fusion yield analysis
    • Time-of-flight analysis
    • Monte Carlo uncertainties
    • Formation rate and resonance energy results
• Discussion and Conclusion
  • Muonic tritium scattering
    • The Ramsauer-Townsend effect
    • $\mu t+ d$ scattering
  • Condensed matter and subthreshold effects
  • Resonant molecular formation
  • Concluding remarks
    • Improvements and Future directions
    • Summary
• Abbreviations and notation
  • Abbreviations
• Abbreviations and notation
  • Abbreviations
  • Error notation
• Resonant scattering of $\mu t$
  • Effective formation model
    • Validity
    • Epithermal Collisions
    • Comparison with the explicit back decay model
  • Back-decayed $\mu t$ energy distribution
    • MMC recoil and thermalization
    • MMC ro-vibrational relaxation
    • Resonant excitation of DX molecule
    • Back-decayed $\mu t$ energy
  • Implications for our measurements
• Muon decay electron time spectrum fit
• Muon decay electron time spectrum fit
• Bibliography

Acknowledgments

I am most grateful to my research supervisor, and spokesperson of this experiment, Dr. Glen Marshall for his guidance and support he has given me throughout my years in Canada. Without his dedication to our experiment, this work would not have been possible. His high standard has helped me improve the quality of this thesis, while his warm support has encouraged me to think of new ideas and try new things.

I am most grateful to my research supervisor, and spokesperson of this experiment, Dr. Glen Marshall for his guidance and support he has given me throughout my years in Canada. Without his dedication to our experiment, this work would not have been possible. His high standard has helped me improve the quality of this thesis, while his warm support has encouraged me to think of new ideas and try new things.

I would like to thank my academic supervisor, Professor David Measday for his continuous support and advice on my studies at UBC and for valuable comments on this thesis. I am always inspired by his deep knowledge of physics as well as his broad interests in other areas of scholarship.

I wish to thank my local collaborators, Professors George Beer, Art Olin, and Ms. Tracy Porcelli for their invaluable input and criticism of this work, and always lively (and often heated) discussions at our weekly meetings. Contributions of Drs. Tom Huber, Francoise Mulhauser, and Paul Knowles, were also essential to this experiment, particularly in the design and the construction of our target system, and in the development of Monte Carlo programs, and I thank them immensely.

I would like to thank other member of Muonic Hydrogen Collaboration, Drs. John Bailey, Jack Beveridge, Roland Jacot-Guillarmod, Peter Kammel, S. K. Kim, Ray Kunselman, Jeff Martoff, Gren Mason, Claude Petitjean, and Hannes Zmeskal, and Ms. Maureen Maier and Jessica Douglas for their invaluable contributions. I am also grateful to my theoretical colleagues, Drs. Andrzej Adamczak, Mark Faifman, Valeri Markushin, Volodja Melezhik, and Jan Wozniak, for their theoretical input to the experiment, and for their taking time to answer my many (sometimes naive) questions. It has been a great pleasure to work in this collaboration, which consists of scientists from all over the world.

Thanks are due to my thesis committee members, Professors Jess Brewer, Elliot Burnell, Ken Crowe, Walter Hardy, Mike Hasinoff, and Anthony Merer. I appreciate their time for reading my thesis and giving me valuable comments and criticism, despite a stringent time constraint I imposed on them. Ray Kunselman also proofread my thesis.

I am much indebted to Professors Eiko Torikai and Ken Nagamine for introducing me to the excitement of muon physics, and for their continuous encouragement and support through out my studies.

My personal thanks go to my many friends and comrades I've met here, in particular, Andre, Ermias, Jennifer, and Sarah for making my life in Canada so special. Last but not least, I thank my family and friends in Japan, who have always supported me.

I acknowledge gratefully the financial support from the Rotary Foundation, the University of British Columbia, Government of Canada, Green College, Northern Telecom, and Westcoast Energy Inc.