The most suitable background run for the series (BG6 in Table 8.2, Page ) had rather limited statistics with about 1/9 of GMUs of the production run. Performing our standard background subtraction procedure using BG6, illustrated in Fig. 8.9, exhibited two potential systematic effects: (a) a Si1 to Si2 detector ratio of up to about 30% was observed in the yield using BG6 for 3 T (see values with in Table 8.6), which appear to be due mostly to asymmetry in the background BG6, not the signal, and (b) there appears to be low energy tails in the background subtracted spectra down to 2 MeV (2000 ch) (see Fig. 8.9, and Table 8.6).

Using instead BG5, which does not have DS 500 T
H** _{2}** under the DS
deuterium layer, makes the Si1/Si2 ratio consistent with 1. However, the
lack of the H

Another possible run to be used for background subtraction is BG7, which
had an emission target with ** c_{t}=0.2**%, and no H

Given this situation for the 3 T
measurement in the series, we made several different background subtractions, and compared
them to see the systematic effects. Method 1 is the standard procedure
using BG6, but with a wide energy cut (
**2.5 < E < 3.7** MeV) to account for
the possibility that the lower energy tails are due indeed to real particle events, which gave the Si averaged yield of
/GMU.

The energy spectra obtained with Method 1 had nonzero counts even at
energies much higher than the fusion signal, where we expect an average of
counts consistent with zero. In Method 1-b, taking into account the
possibility that this is due to a potential error in the relative
normalization (although the ADC blocking effect in Si detectors was
corrected carefully in Section 8.1.2), we fitted the region
between 4000 and 8000 ch with a constant base line, and subtracted that
from the yield from Method 1 above to obtain
.
Using a line with a slope or exponential curve in the fit gave
a larger base line yield (hence smaller fusion yield), but we use the
value
** Y_{meth1-b}** as our upper limit in calculating the average later.

Method 2 used the entire background data set available (sum of BG5, BG6,
and BG7) to make a first order background subtraction (see bottom in
Fig. 8.10). But keeping in mind some differences in the
conditions, we made an additional, second order correction from the above
background. From the narrowly defined signal region (denoted SG,
**3.1 < E<
3.7** MeV), the average of counts from the region below (shown as B-LO,

The systematics in Method 2 were checked for the manner in which the additional correction was made; the background cut, B-LO, might contain the signal, which, together with the narrow cut for SG, might lead to over-subtraction of background. We present two more systematic checks of Method 2, in which the second order additional correction was done in a different way, while keeping the first order the same as Method 2.

Method 2-b is simply to use a wider signal region of
**2.7 < E< 3.7** MeV, with
B-L0

In Method 2-c, illustrated in Fig. 8.11, we have fitted
the residual background obtained in Fig. 8.10 with an
exponential function. The fit was performed simultaneously in the regions
B-LO (
**2.0 < E<2.4** MeV) and B-HI (

The Si yield for 3 T
in TOF Series A (), using different
background subtraction methods, are summarized in
Table 8.7. Energy cut width dependent corrections, *i.e.*, the energy cut efficiency and the ** dd** proton contribution, which
will be discussed in detail in Sections 8.2.4 and 8.2.3, are
applied here.

As can be seen, Method 2, 2-b, 2-c, which all used combined background BG5+6+7 but had different methods of residual background subtraction, gave consistent results, giving some confidence at least in the residual background subtraction procedure. In comparison with Method 1, Method 1-b appears more reliable since it takes into account the possible relative normalization error by subtracting a constant base line. Note that in Series B, the constant term was consistent with zero, as expected. Discarding Method 1, we chose the two extreme values in (Method 1-b and Method 2-c) as representative of the deviations due to the background subtraction procedure. Since these measurements are not completely independent, determining the average and its error is somewhat tricky. Obviously, since the two values are incompatible within in the quoted error, simply taking a weighted mean and combining the error would underestimate the total uncertainty.

Here we adopt a procedure used by the Particle Data
Group [229,230], which scales the error bar
to give
.
In our case, with the numbers
of points and the free parameter being 2 and 1 respectively (hence ** dof=1**),
we scale the error by a factor 1.9 and obtain
/GMU.

As for other TOF series A measurements (with ), the statistics of the production runs and the standard background run (BG6) are comparable, and the accuracy is not limited by the background statistics. Also because of a better signal-to-background ratio, effects of the background are not as serious. Furthermore, the Si1/Si2 asymmetry in Si yields are at the 10% level for the most part. Thus, we shall use BG6 for our background subtraction. Using other backgrounds in fact gives consistent results for a reasonable range of the energy cuts (Table 8.6).