US yield

Figure 8.17 shows a comparison of the upstream fusion yields with the different Monte Carlo calculations. Only data from the same series of runs (ID=II-2, II-3, and II-4) are plotted to avoid a possible influence of the target conditions. Denoted MC(1) in the figure is our nominal physics input discussed above, with the possible variations in the yield due the layer thickness uncertainties, which are shown with dotted lines. Separate Monte Carlo runs with varied thickness inputs were performed for the latter. MC(2) is using the original $d\mu t$ formation from Ref. [133,70,71,72] without the low energy modification, while for MC(3) an energy independent rate s (also independent of F) was added to the nominal $d\mu t$ formation rates.

Our results are in rough agreement with the nominal MC, but using the original model of Faifman worsens the agreements at larger layer thicknesses. Many Monte Carlo calculations were performed in order to find a better agreement, varying the input such as formation rates and scattering cross sections and the transfer rates, but no simple scaling of any of these parameters allowed perfect agreement with the data.

A significant improvement is observed, however, when the constant rate is added. This is a phenomenological parameter motivated primarily by reproducing the experimental data, and its interpretation requires careful consideration, which we shall later come back to. The dependence of the fusion yield in thick layers on suggests the importance of, and our sensitivity to, the low energy processes in the solid state of hydrogen, but fortunately for our measurements of the epithermal molecular formation in thin layers, the low energy effects are expected to be rather small as we shall see.

In our nominal model, at low energy is already set to a considerably higher value than in the original Faifman's model, hence the main effect in the difference between MC(2) and MC(3) comes from the increase in the triplet formation rate. Indeed, increasing the singlet rate alone to =4000 $\mu$s^-1, while keeping the triplet rate at Faifman's value, does not change the fusion yield.