In implantation experiments, the implanted particle is shot with a certain energy into the material and comes to rest at a site which may not correspond to the final position. The rearrangements of the surrounding atoms to accommodate the particle, i.e., the reaction with the host atoms may require some time and lead to delayed formation of the final states. In the case of the implantation of positive muons, this rearrangement process can be followed on a timescale of nanoseconds to microseconds. A delay is expected if an energy barrier inhibits the prompt reaction. We note that the barrier height may change during the rearrangement of the lattice, thus giving rise to a two-dimensional potential profile for the conversion process. The barrier model describes the reaction path of the muon in analogy to the passage over a mountain with a saddle point. The passing over the saddle point corresponds to the lowest energy trajectory. As an example, we discuss the application of the barrier model to solid ${\mathrm{Lu}}_2{\mathrm{O}}_3$.

• Received 9 June 2018
• Revised 31 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.115201