Diffusion

Diffusion of atoms in hydrogen has been extensively studied in theory by A. Adamczak [26], and results of detailed MC calculations were presented in our main proposal (ch. 4.2 and Figs. 5,6 in [1]). The effects are confined to a few mm and, therefore, should not affect our muon decay time distribution.

Quite the opposite is true once a muon is transferred to a deuterium nucleus to form a $\mu d$ atom. Due to the famous "Ramsauer-Townsend" minimum in elastic -p scattering, these atoms can travel easily several cm in 10 bar hydrogen. Some fractions even leave the sensitive volume of the chamber, especially at late times after muon stop. Therefore, the -e time distribution can get significantly distorted toward a steeper slope simulating a larger capture rate. This is the principal reason why it is necessary to use protium which is strongly depleted from any deuterium.