Diffusion

The radial distribution for diffusion of $\mu p$ atoms is given in Fig. 6 of Ref. [1]. Fig. 18 in Ref. [3] shows the corresponding distribution for $\mu d$ atoms in protium for different time slices. Two disturbing effects arise from this $\mu d$ diffusion:

• If the muonic hydrogen atom diffuses more than the distance between muon stop point and electron decay point allowed by the event reconstruction, the event is lost in the analysis. As the diffusion range increases with time, this introduces a time dependent efficiency loss, faking a faster decay rate.
• If the diffusing atom hits a wall, transfer occurs quickly and the muon might disappear by capture on wall elements.

Diffusion of $\mu p$ is unavoidable, the effect of $\mu d$ diffusion depends on the isotopic purity achieved in the protium gas. The strategy to control this effect is similar to other impurities: Reduce the contamination as much as possible and measure the contamination quantitatively, by in situ monitoring. Then extrapolation to zero becomes possible.