The subject of this thesis is the study of the evolution of a negative muon captured in an atom and the formalism of energy loss associated with the muonic atom. The principal goals are to calculate reliably the muon x-ray intensities, given .the initial population of the muonic orbits, to invert the problem and deduce the initial distribution from the x-ray intensities, to provide the experimentalist with a reasonably simple and convenient tool to correlat·e his observations, and finally, to systematize some questions of theoretical interest. The early part of the history of the muon in matter, including the atomic capture and classical phase of the atomic cascade are reviewed. In the quantal treatment of the transition rates, both radiative and electron Auger transitions are considered. In general, multipolarities up to E3 and K, L, and M electronic shells are fully investigated. Multipole radiation is treated in the conventional way and presents no special problems . Magnetic type transitions between states with different principal quantum numbers are shown to be small. Auger electron ejection rates are more complicated and several approximations have been adopted. The basic results have been computed in terms of elementary functions. The relativistic retardation effect is significant at high transition energies, where Auger rates are unimportant. Similarly, the effect of the electron screening of the muon has no significant influence on the results. The calculation of the penetration makes the transition rates reliable . In the Auger transitions we have shown that magnetic multipoles can be safely neglected. The relative sizes of the rates corresponding to different multipoles are systematically studied. The E1 Auger rates are generally largest, but the E0 and E2 transitions are also substantial. Penetration usually decreases rates, being mostly important for transitions with small continuum electron momentum. A comparison of our results is made with atomic photoelectric effect data and with the nuclear internal conversion coefficients. A general agreement is found, except around shell thresholds. The existing data of muonic x-ray intensities in iron and thallium are analyzed in a systematic way. The data are fitted with an initial Z-distribution and some other derived physical parameters. The quality of the fits is good. It is found that for Fe the initial Z-distribution is almost flat, whereas that for T1 is weighted toward s the high Z values, sharper than statistical. As a result of the investigations and in order to make our findings usable, a computer program has been developed. This program is superior to the present standard one, including more precise calculation of transition rates , wider choice of parameters, and a flexible input/output section.
