The first part of this work presented results from
experiments in which the muon and muonium asymmetries
in insulators were measured in the presence of an
externally applied electric field.
These experiments have found that an
electric field can, in some insulators, influence the fraction
of muons that form muonium atoms.
Furthermore, the amount of muonium formed depends also on the
orientation of the electric field with respect
to the initial momentum of the muon.
These results imply that there is an
anisotropic spatial distribution of electrons
with respect to the muon. and that the electric field influences
the probability of forming muonium by drifting these electrons
either away from or toward the muon.
It can be concluded that muonium is formed, at least sometimes, from electrons that move considerable distances through the sample to the site of the muon. A modest electric field having any effect at all implies that the electron spends some time (between being stripped from an atom and finding the muon) in a low-field region far from these charged ions. Previously it had been thought that muonium formed when an electron was stripped from at atom and promptly captured by the passing muon, which then thermalized with no further ionization. In this scenario the bare electron would never be sufficiently far from the muon or the ion left behind that an external electric field could compete with the Coulomb fields of their positive charges. It is likely that in most insulators that both mechanisms occur to varying degrees. For example, in solid nitrogen the magnetic field dependence of the muonium amplitude showed that at least 22% of the muonium was formed by the delayed mechanism, the remaining muonium fraction being formed rapidly would include hot (prompt) muonium.
One way for the delayed process to come about is by a hot muonium atom, after moving away from the last ion from which the electron came, undergoing a collision with a neutral atom, ionizing the muonium and putting the electron back into the lattice with a fraction of the muonium kinetic energy. The muon sometimes would continue on, still with the last few electron-volts of its initial kinetic energy, and eventually thermalize further downstream. In this picture neither the electron or muon are left in the immediate vicinity of any other ion. The electron is in an otherwise undisturbed region of the lattice where the magnitude of the Coulomb field of the muon can be comparable to the externally applied field, so the external field can affect the electron's subsequent trajectory. Most importantly, this electron is the closest one to the muon and therefore is the one that reaches the thermal muon first. The asymmetry of the electron distribution also implies that the direction of travel of the muon, at the very end of the track, is still predominantly in the direction of the muon beam.
Currently, one technology being developed for producing beams of spin polarized muons with kinetic energies of a few eV relies on cryogenic insulating materials, such as the solid rare gases, as moderators.[29,30] A good understanding of low energy end-of-track processes of charged particles in general - which is still lacking - will be valuable in selecting materials that should minimize muonium formation, and maximize the probability of these slow muons escaping the moderator surface.