The disappearance rate of delayed electrons enters in the determination of stopping fraction (6.26), directly in the branching ratio and indirectly in the time cut efficiency . The rate was determined by fitting the time t_{del}  t_{Si}, i.e., the time between the silicon event in Si1 or Si2 and the first electron (telescope) event following the Si event, with a single exponential function. In order to ensure accurate determination of , cuts were made on both energy and time of the Si events.
A cut on t_{Si} (Si time with respect to muon entrance time t_{0}) of 0.02 < t_{Si} < 0.5 s was applied to select prompt fusion events from the upstream D_{2} moderator overlayer (where the signaltobackground ratio is most preferable), and to ensure a uniform time efficiency of the Del cuts. Since the event gate was open for a finite width ( s) after the muon entrance, the efficiency for the Del cuts for the Si events occurring late (with respect to t_{0}) is reduced, due to the smaller time window for the detection of delayed electrons^{}.
Two different energy cuts were applied. The nominal [2000, 3700] ch^{} cut (noted as Energy cut ``'' in Tables 6.14, 6.15) covered a good portion of the fusion peak, while the lower energy cut [2000, 3000] ch (noted as ``l'' in Tables 6.14, 6.15) avoided the fusion events which occurred near the surface of the D_{2} overlayer. The latter cut was implemented to test a possible systematic effect which depends on the depth of the fusion event in the layer, such as or escaping from the layer. The energy of the is related to the event depth thanks to energy loss in the layer.
Tables 6.14 and 6.15 give the fitted results of for Dele and Delt time spectra, respectively. Two different series of runs, (A) Runs 167183^{}, and (B) Runs 170930^{}, were used for the fit. While a thick hydrogen layer (500 T) was present in the downstream target for Run A, there was no (Target II13) or only a very thin (II14) layer in the downstream target for Run B.
For the delayed electron (Table 6.14), the use of a constant background term was necessary to obtain reasonable fits. This was not the case for the delayed telescope (Table 6.15) where the background was smaller, and fits both with and without the constant term were tried to check the consistency.


As shown in Tables 6.14 and 6.15, for Si1, Runs A and B give a consistent value of for both Dele and Delt, while for Si2, Run B gives a smaller value than Run A by 2 to 3 . If Runs A and B are averaged, however, Si1 and Si2 give consistent . The averages over Si1 and Si2 as well as over Runs A and B were thus taken and are presented in Table 6.16. We note the following. First, Dele and Delt are for the most part consistent with each other. Second, not including the constant background term increases the value of fitted . Though not shown in the tables, this holds true for the Dele fits as well. Third, the energy cut l gives a that is 24 lower than the cut in all cases in Table 6.16. Our determination of is thus limited by systematic effects, which are possibly due to the finite thickness of our layer. Taking the average of the two extreme values in Table 6.16 we assign s with the error covering the two extremes. Thus we have the time cut efficiency, , and the electron branching ratio, , which combine to give the factor for Eq. 6.26. Note that the errors are correlated.

