Direct stop contribution at early time

The contributions from direct muon stops in the deuterium layer at early times are difficult to estimate experimentally from our data set, since at such times, an overwhelming $d\mu t$ signal is present in the spectrum. We therefore use the information from the cycling contribution and express the direct stop proton yield per GMU Y_p-fast^dir as:

where S_H=0.299 is the muon stopping fraction in the emission layer, = (14 T$\cdot l$)/(1000 T$\cdot l$) is the thickness fraction of the D₂ layer with respect to the emission layer, and is a phenomenological parameter which describes the ratio in the proton yields between $d\mu d$ fusion after dt cycling and the direct stop. If we assume the spatial distribution of cycled muons is the same as that of direct stop muons, the parameter simply accounts for the muon escape from the layer before stopping to form $\mu d$. Even if we allow a value as low as (i.e., up to 50% of muons escaping), the yield will be , which is only 0.46(26)% of the $\alpha$yield. Thus the uncertainty in is not serious for our purpose here. For thicknesses other than 14 T$\cdot l$, we estimate the yield by scaling to the thickness ratio. Table 8.12 summarizes the corrections due to protons from $d\mu d$ fusion. We shall apply the correction for the DS (estimated here for the time cut s) to the MOD measurements as well, ignoring some differences in the time cut.

 

Table 8.12: Summary of the correction due to protons from $d\mu d$ fusion. US is with the time cut of s and DS with s.

D2 target	Proton yield per $\alpha$ (%)
	Cycling	Direct	Total
US 20 T$\cdot l$	1.64 (94)	0.66 (37)	2.3 (10)
14 T$\cdot l$	ditto	0.46 (26)	2.1 (10)
6 T$\cdot l$	ditto	0.20 (11)	1.8 (9)
3 T$\cdot l$	ditto	0.10 (6)	1.7 (9)
DS 23 T$\cdot l$	1.64 (94)	1.10 (21)	2.8 (10)
20 T$\cdot l$	ditto	0.95 (18)	2.6 (10)
6 T$\cdot l$	ditto	0.64 (6)	2.3 (9)
3 T$\cdot l$	ditto	0.72 (6)	2.4 (9)