Si detector energy calibration

The energy scales of the two silicon detectors were calibrated with ²⁴¹Am sources, which were attached to the diffuser and hence could be removed during the muon beam measurements.

    

Figure: Silicon (Si2) energy spectra taken with ²⁴²Am source (peak energy 5.486 MeV). One ADC channel is close to 1 keV. Si1 had similar spectra.

Figure 8.1 illustrates the calibration spectra for one of the silicon detector (Si2) taken with the source. Measurement with no target present in the system is shown in Fig. 8.1(a) which had a full width half maximum resolution of about 40 keV. This is partly due to the resolution of the source itself, and the detector resolution may be better. The spectrum in Fig. 8.1(b), on the other hand, was taken with 2 T$\cdot l$, or about 6.8 Ci of tritium present (Target II-14 in Table 4.4 in page ). The effect of tritium caused the peak width to be about 65 keV, due to the decay background.

Since energy spectroscopy is not the purpose of our experiments, the absolute energy scale was not very crucial. However, as we found in the thickness measurements in Section 3.3, the change in the detector temperature could cause significant variation in the energy gain, hence frequent calibration was performed to ensure the relative stability of the energy scale. In addition, the fusion signal itself, whose energy is well known, could provide the calibration information.

  

Figure: Centroid values of ADC for ²⁴¹Am peak for different calibration runs, showing the stability of the system.

Figure 8.2 shows the position of the centroid of the peak corresponding to ²⁴¹Am for different calibration runs. The centroid value was determined by Eq. 3.1 (page ) in a similar manner to the thickness measurements described in Section 3.3 with the lower and upper cut off values 5300 ch and 5600 ch, respectively. The error bars in the figure indicate statistical uncertainties in the centroid. Changing the lower cut off value to 5200 ch caused less than 3 ch change in the centroid, indicating the systematic uncertainty in the calibration. The average of the measured centroid values is 5486.9 ch (4.7 ch) for Si1 and 5473.5 ch (3.4 ch) for Si2, respectively with the values in parentheses being the standard deviation of 14 measurements. These should be compared to the weighted average of 3 alpha lines of ²⁴¹Am, 5491 keV (note that the peak energy for the strongest line is 5486 keV). Assuming there is no significant offset, which was confirmed by a test using a pulse generator, the calibration is very close to 1 ch = 1 keV for both detectors.