4 Muonium formation in Insulators

A great deal of the early work and a much smaller fraction of current work in the field of $\mu{\cal SR}$ deals with the question of what determines the final chemical state of the muon when it stops in a sample. This has been an important part of the development of $\mu{\cal SR}$ as a tool, and recent developments may have an impact on both the interpretation of $\mu{\cal SR}$ data in general and potential $\mu{\cal SR}$ related technology (such as ultra-slow muon beams) in the near future.

This chapter lays the groundwork by first discussing models of muonium formation and evidence from conventional $\mu{\cal SR}$ experiments that lead us to consider another mechanism - that electrons, stripped from atoms of the sample along the track of the muon, diffuse large distances through the sample to form muonium by recombination with the (positively charged) muon. Second, results from $\mu{\cal SR}$ experiments in which an electric field was applied to the sample are presented. These experiments unambiguously demonstrate that, at least in some cryocrystals, muonium formation depends on the electron transport properties of the sample. It is quite likely that this is at least part of the answer to a long-standing puzzle regarding the differentiation of muons into diamagnetic and muonium fractions in so many (electrically) insulating materials - solids, liquids and gases.

This chapter is not an exhaustive discussion of electric-field $\mu{\cal SR}$(EF-$\mu{\cal SR}$). It is intended only to re-examine muonium formation in light of new results from cryocrystals, introduce the technique of using an electric field in $\mu{\cal SR}$, and to show that the amount of muonium formed depends on the ability of radiolysis electrons, initially released by the muon much further from its final position than previously thought, to reach the stopped muon. Cryocrystals and cryoliquids have been instrumental in the discovery of this technique, so it is fitting that this be included in a thesis primarily concerned with muonium diffusion in cryocrystals.