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
tdel - tSi, 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 tSi (Si time with respect to muon entrance time t0) of
0.02 < tSi < 0.5 
s was applied to select prompt fusion events
from the upstream D2 moderator overlayer (where the signal-to-background
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 t0) is reduced, due to the smaller
time window for the detection of delayed electrons![[*]](foot_motif.gif)
.
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 D2 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 Del-e and Del-t time spectra, respectively.
Two different series of runs, (A) Runs 1671-83, and (B) Runs 1709-30, 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 II-13) or only a very thin (II-14) 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.
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As shown in Tables 6.14 and 6.15,
for Si1, Runs A and B give a consistent value of
for both Del-e and Del-t, 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, Del-e and Del-t 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 Del-e fits as well. Third, the energy cut l gives a
that is 2-4
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.
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/dof
,
the absolute electron detection efficiency,
,
and the muon stopping fraction,
SFABSH determined from
the absolute yield method. Run A is the same as that in
Table