Sticking and stripping

Sticking is a process in which the muon becomes attached to a positively charged fusion product such as an $\alpha$ particle. The probability of the process, denoted by $\omega _{s}$, imposes a more stringent limit on the efficiency of $\mu$CF than the short lifetime of the muon itself, hence it has attracted much attention, but discrepancy between experiments and theory persists, motivating further investigation.

Sticking takes place in two distinct steps:

where $\mu \alpha ^{*}$ refers to the muonic helium ion in a bound state n,l recoiling with kinetic energy 3.46 MeV. The initial sticking $\omega _{s}^{0}$ is the intrinsic branching ratio of the sticking reaction channel immediately after the fusion, while stripping can occur during the slowing down of the $\mu \alpha$, that is the muon is detached from the $\alpha$ with probability R, in collisions with the neighbouring atoms. Hence the final sticking $\omega _{s}$is:

$$\omega _{s} = \omega _{s}^{0} (1-R).$$ (12)

  

Figure 1.3: Summary of experimental results of the final sticking $\omega _{s}$ as a function of the target density $\phi$, plotted with theoretical predictions, where $\phi =1$ is the liquid hydrogen density ( $4.25\times 10^{22}$ atoms/cm³).

The experimental results on sticking have been in disagreement with theory and, sometimes, with each other. The challenge lies in its low branching ratio and in the handling of tritium. Figure 1.3 summarizes the previous measurements of final sticking plotted against target density $\phi$. Apart from a longstanding discrepancy on the density dependence between two major experimental groups at PSI and LAMPF, in which the analysis of the latter now appears to be unreliable at low densities, most experimental values are systematically and substantially smaller than the theoretical prediction, even though different methods have been used. For a recent review, see Ref. [60].