Protons from fusion in the deuterium layer can cause a background in the measurements depending on the energy cut (recall that the proton energy is 3 MeV). They can come from two different sources: (a) direct stopping of muons in the deuterium layer, or (b) recycled muons, i.e., the muons released after the fusion reaction (with the probability , where is the sticking probability). For both cases, because of solid state effects and finite thickness, estimating the proton yield is difficult, and there is yet no satisfactory theoretical model. The use of the Monte Carlo is untested in these conditions, and its reliability is questionable without solid state effects included in the input.
Nonetheless, we first make an analytical estimate using the two node
kinetics model which successfully, if accidentally, described the time
fusion in a
bulk solid deuterium . According to this kinetics
approximation, with an assumption of an infinite target and ignoring
fusion yield per muon
can be obtained as:
This level of proton yield would give a non-negligible contribution in the yield measurements, when the direct stops and the recycling components are combined. However, a proton yield at the 10% level relative to can be excluded by comparing the expected peak shape, simulated with an energy loss Monte Carlo program , with experimental energy spectra. Recall that the dd proton, with an energy of 3 MeV, has energy loss much smaller than a 3.5 MeV , by a factor of roughly , hence a 10% proton yield would appear as a sharp peak in the Si energy spectra, which is absent from the data. Given the inconsistency with this simple analytical approach, we pay closer attention to our data set to extract the proton contribution in the sections which follow.