Formation rate and resonance energy results

We combine the values of scaling parameters and uncertainties to give the final results on the formation rate and the resonance energy for $d\mu t$muonic molecules. For the formation rate measurements, the best $S_{\lambda }$ from Series A and B disagree by more than the error bars as given in Table 8.16.

This discrepancy is curious. The difference in the run conditions, between the two series, in addition to the tritium concentration difference (i.e., $c_t=0.1\%$ vs. 0.2%), was the presence of a 500 T$\cdot l$ H₂substrate under the thin D₂ layer for Series A. Comparisons of two runs for other observables such as the US fusion yields and the pt transfer time suggest that there is no problem in the $\mu t$ production in the emission layer. There is also no evidence from our run record that there was a problem in target preparation for either run. One possible effect is that due to the presence of the thick H₂ substrate in Series A, $\mu t$which passed through a thin D₂ layer may thermalize in H₂, and may in turn be re-emitted back into the D₂ layer to form $d\mu t$ and fuse. In fact this effect was already taken into account in our analysis; using our Monte Carlo we estimated that the re-emission would increase the fusion yield by a factor of , where the uncertainty is estimated taking into account the lack of knowledge of formation rates as well as scattering cross section at very low energies. However, estimating these effects is difficult without proper solid state cross sections, and in light of our recent observation of emission from a pure H₂layer [216], it may still be underestimated. Note, however, that due to a high $p\mu t$ formation rate, low energy $\mu t$ emission from H₂ should be somewhat suppressed compared to .

Another possibility is the presence of some unaccounted errors in our values of and (the pt transfer rate and $p\mu p$ formation rate, respectively), which were measured with our solid targets [83]. There is no strong reason to doubt those values except perhaps that emission just mentioned was not considered at the time. Using the theoretical values from Refs. [17] and [51] would reduce the discrepancy significantly but not completely.

Accepting the discrepancy as a measure of an unaccounted systematic uncertainty in our measurement, we shall increase our errors in accordance with Particle Data Group's procedure [229,230]. Thus our final result for the resonant molecular formation rate is:

where the first error is the combined average error increased by a factor of 2.1, and the second error is due to the MC model uncertainty discussed in the previous section.

As for the resonance energy measurement, since the values from Series A and B agree within the error, we take the standard weighted average to obtain:

where similarly the first error is a combined measurement error and the second error is due to uncertainties in the MC modelling.