With an energy cut in the second detector of
2701<E<3100 ch to select
proton events, we obtained the coincidence rates with two different time
s, and (b)
is the time
difference between the proton and the
candidate events. The yield
with time cut (b) was corrected for the cut efficiency assuming the fusion disappearance rate of 34 s-1 given by the hyperfine
transition rate in the kinetics model , as well as the
average time-of-flight difference between the 3 MeV proton and 3.5 MeV ,
while the cut (a) required no time corrections.
The conditional solid angle for the protons given an
could be different from the solid angle singles events, since the detection biases the proton distribution towards the first detector ( i.e., away from the proton detector). This effect was estimated using
a Monte Carlo  taking into account the geometrical
correlation of the two detectors, and found to give about 10% (relative)
reduction in the second detector. Using the coincidence solid angle,
yield with the energy cut
/GMU, and the time cut
for cut (a) (
cut (b)), we obtain the proton yield per dt fusion from cycling,
The inconsistency between the results from the two time cuts can be due either to the time cut efficiency or possible presence of a prompt background (such as decay electron). For example, if the fusion disappearance rate is different in a thin layer from 34 s-1 measured in bulk solid targets, the time correction made is not appropriate. As well, with limited statistics, it is difficult to estimate the prompt background contribution. Given the uncertainty, we take the average of the two cuts, and quote an error covering two extremes of the error bars. Thus we have as the contribution from cycling. In our analysis below, we assume the cycling proton yield per dt to be independent of the D2 layer thickness, which is sufficient for the accuracy required here.
We note that at late time s, the coincidence yield is more than an order of magnitude smaller than at early times, hence the slow lifetime component of (observed in bulk solid and other targets) appears nearly absent from cycled fusion in a thin layer.
The value of here should be compared with our earlier estimate with the kinetics model given by (Eq. 8.3), which is significantly higher. It is interesting to note, however, that our value is more or less consistent with the estimated fast component yield in the kinetics model ( ). One possibility is that the muonic deuterium in the lower hyperfine state ( ) escapes from the layer before fusion takes place, since the low rate of non-resonant fusion ( s), which is responsible for the slow component, implies a rather long interaction length. Another possibility, of course, is that the muon escapes from the layer before stopping to form muonic deuterium . Physics of the muon cycling and the transport in thin layers is a very interesting topic on its own, indeed.