Shown in Fig. 6.5 is an example of the electron time spectrum and fit with two exponential functions with a constant background. Plotted with error bars are the first electrons detected by electron pair scintillators for a target of 1000 T pure hydrogen, while the solid curve is a fit in the time interval of [0.02, 6] s.
The resulting fit amplitudes (A1/Q1, A2, and bkgd), normalized to GMU, and the lifetimes ( and ) are given in Table 6.6, for the fit from each detector (Ege, En1, and En2) as well as that from the first hit in the three detectors (1st). Also shown is the reduced muon stopping fraction in hydrogen ( ) derived from A2/(A1/Q1 + A2) with the Huff factor for Au of Q1=0.85. The data of runs 1650 and 1654, taken with the same conditions, were analyzed both separately and together.
Fits are mostly of satisfactory quality, but in some cases we observed rather low confidence levels. This could be in part due to beam related background which is correlated to the 23 MHz (43 ns) cyclotron RF cycle. This periodic background, when fitted with a straight line, would increase the total , but should not affect the fit parameters for the signals, since it is the average over the relevant time scale that affects the fit results.
Our fitted short lifetime is reasonably consistent with 74.31.5 ns for gold given by Suzuki, Measday and Roalsvig , but the long lifetime is somewhat shorter than 2.195 s for hydrogen .
In the single hit mode, if the detection efficiency is high, there could be a distortion in the recorded accidental background, since the detector is more likely active at earlier time. But the individual detector fits and the fit to the first hit among them (``1st'') are consistent with each other, indicating that the effect of accidental background in distorting the fit is negligible (``1st'' can be considered as one single-hit detector with an efficiency three times as large as a single detector, hence if an efficiency dependent effect was important in the fit, it would show up as the difference between the 1st and other detectors). In fact, fits with explicitly non-constant backgrounds were tried, but the stopping fraction was found rather insensitive to the background model.
The dependence of the derived stopping fraction was tested by changing the fit region from [0.02;6] s to [0.02; 9.5] s. While the H2 component lifetime was slightly increased (%), the variation in stopping fraction was negligible.
We have also fitted the later time t>1 s, at which the gold signal is negligible, to a single exponential and a background. In these fits, in which 100 ns bin size was used (averaging out the RF structure), a lifetime of 2.11(1) s was obtained with a confidence level of 8%, a lifetime closer to, yet still significantly smaller than, the literature value for muons in hydrogen. An exponential background was also tried, giving s with a background lifetime of 0.0829 s with a confidence level of 11%. The amplitude for the hydrogen component thus derived is somewhat smaller than the ones in Table 6.6, but by no more than 3%.
Alternatively, fits were tried with the lifetime fixed to 2.195 s and with a constant background (varying the amplitude) or an exponential background (varying the lifetime and the amplitude). Neither background gave a satisfactory fit, suggesting that the deviation of the lifetime is unlikely due to a trivial error in modeling the background, thus pointing to the existence of one or more muon loss mechanisms. This could include a small amount of non-hydrogenic contamination in the target, which would not affect the extraction of the stopping fraction, as long as it is well approximated with an exponential function. Emission of muonic protium from the solid layer, recently observed by our collaboration for the first time , could be partly responsible for the discrepancy also. According to Wozniak , several percent of muonic protium atoms may be emitted back to the gold foil, whereby the muon transfers and is captured by the gold nucleus.
The sensitivity of to the shift of the time zero definition ( ) was also investigated. An example for the first electron spectrum is given in Table 6.7. The fit to the individual detectors as well as to individual runs gives similar trends. The error 4 ns is a rather conservative estimate of the shift, and it is more likely to be less than 2 ns. The variation in the amplitude for the hydrogen component in this time scale is, nevertheless, completely negligible, hence the change in comes from that in the gold component. In any case, this alone cannot explain the 20% difference between method 1 and method 2, as will be discussed later.
While for Ege and En1 are consistent with each other, there is a systematic difference between En2 and the others, with En2 being relatively lower by nearly 10%. This discrepancy will be addressed later in relation to the acceptance difference for the upstream and downstream targets.
We note that agreement between Ege and En1, which were symmetrically located across the target (beam-left and beam-right, respectively), exclude the possible effects of polarized muon precession about the vertical axis.