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# Silicon detector acceptance

The silicon detector acceptance depends both on the geometry and the distribution of the beam (which determines the distribution of the particle source). The Monte Carlo method was used to determine the acceptance. We define our Si acceptance as the average of two silicon detectors (Si1 and Si2), as this quantity is much less sensitive to the beam position shift as we shall see.

The position of the silicon detectors is rather well defined, since they are mounted on the thermal shield box made of gold plated copper. A copper collimator sheet (aperture of 13.90.2 mm 500.2 mm at room temperature) in front of the detector, further defined the acceptance. Thermal contraction, for both the thermal shield box and the collimator sheet, is taken into account using the values given in Ref. [214] and is estimated to give a combined relative correction of about 1.3% to the Si acceptance. Uncertainties due to the possible variations in the geometry are summarized in Table 6.4, where the total uncertainty is given as a quadratic sum of the all the uncertainties. Note that shifting the beam with respect to the target centre in the Xdirection always increases the solid angle (the two detectors are symmetric to the beam on the X axis), while shifting in the Y direction always reduces it. The variations of the silicon detector acceptance due to the beam distribution and its parameterizations were already given in Tables 6.1 and 6.2, for the upstream layers and the downstream layers, respectively.

Table 6.4: Variations in Si acceptance due to uncertainties in the geometry.
 Source Uncertainty Relative change in Si Acceptance beam X position shift mm + 2.7 % beam Y position shift mm - 0.9 % Si distance -0.5 mm + 2.1 % Si distance +0.5 mm - 1.9 % Si Z position shift -1 mm -2.4 % Si Z position shift +1 mm +1.7 % collimator width -0.2 mm -1.4 % collimator width +0.2 mm +1.5 % +4.1 % Total uncertainty -3.5 %

Except for the case of the US beam of size 1515 mm which appears inconsistent with the electron imaging data (Fig. 6.3), the variations of the Si acceptance due to the beam parameters are found to be less than 1%.

Given in Table 6.3 are the changes in the Si acceptance due to varying the upstream overlayer thicknesses, in which about 2% relative difference is found between 14 T overlayer and no overlayer.

Table 6.5 summarizes the final values and their uncertainties for the effective thickness and Si acceptance for all the target arrangements used in this thesis. The uncertainties for the thickness include the ones due to the beam parameterization, the scaling factor for the diffuser distance (DS only) and the stopping power, which were added quadratically. Uncertainties for are due to the geometry and the beam parameterization, also added in quadrature.

Table 6.5: Summary of effective average thickness and Si acceptance for all the target arrangements used in this thesis.
 Target Effective thickness (gcm-2 (T)-1) (%) US 2.375 + 0.100-0.086 DS (0 T US) 2.512 +0.105-0.090 DS (3 T US) 2.486 +0.104-0.089 DS (6 T US) 2.474 +0.103-0.089 DS (14 T US) 2.461 +0.103-0.088

Next: Muon stopping fraction determination Up: Analysis I - Absolute Previous: Effective target thickness