====== Performance and Contamination of 14 GAGG wafers ======

The data storage is referred to https://wiki.sites.lngs.infn.it/doku.php?id=gagg-nd:gagg_wafer_measurement_campaign

Reminder: T represents a standard wafer, which is the same type as the prototype; CF has a low light yield but fast time response; HL has a high light yield but slow time response 

=== Decay time constant ===

The decay time constant can be resolved into two components. The fast component with a decay time constant of a few nanoseconds is attributed to the recombination from activation centers, and a slow one that extends to few hundred nanoseconds is associated with the recombination due to trapping. The slow component has a small intensity relative to the fast one. 

The decay time constants can be determined from the recorded waveforms. A waveform typically includes the rising slope followed by a decay curve. To describe these features, a double-exponential decay function and a delta function are used:
 
f = A<sub>1</sub> exp(-(x-0.47e-6)/τ<sub>f</sub>)*((x>0.46e-6)?1:0) + A<sub>2</sub> exp(-(x-0.47e-6)/τ<sub>s</sub>)*((x>0.46e-6)?1:0)，

where τ<sub>f</sub> and τ<sub>s</sub> are the respective decay time constant for the fast and slow components. The A<sub>1</sub> and A<sub>2</sub> denote the corresponding amplitudes, with A<sub>1</sub> + A<sub>2</sub> =1 in the case of the normalization.

The fit to the average pulse (gamma events) is presented in the following figure. 

^ Averaged gamma waveforms recorded by the standard wafer one with background data (left) and with calibration data using a 241Am source (right). ^ 
{{:gagg-nd:t1_bk_ap.png?400|}}  {{:gagg-nd:t1_calib_ap.png?400|}}

For each wafer, the fit is performed for each background data file. As there are fluctuations, outliers are rejected from the obtained fitting values. One example is shown in the figure below. The mean value is taken as the decay time constant. The result is summarized in the table below. 

^Extracted fast decay time constant of the standard wafer one from each data file ^
{{:gagg-nd:mean_tao.png?400|}} 


The "CF" type wafer should have a faster time response than other ones, which is observed in CF2, but not in CF1 (check the time response of T4, T5 and CF1). As expected, the "HL" wafers indeed have a slower time response compared to other wafers.


=== Energy resolution determined with the 241Am calibration data ===

The energy resolution at 59.6 keV is given in the table for each wafer. The "HL" type wafer is expected to have a better energy resolution than other wafers due to its high light yield. However, the difference in the detector performance is not prominent. For reference, the large GAGG detector has an energy resolution of 31.92% at 59 keV.

=== Low-energy alpha (147Sm) contamination ===

From the previous experience, we know that the prominent low-energy alpha peak is contributed by <sup>152</sup>Gd and <sup>147</sup>Sm contamination. According to the calculation, the count rate from <sup>152</sup>Gd is 0.02 per second for each wafer given a mass of 25.9 g. If the total count rate is above this value, then the remaining events are contributed by <sup>147</sup>Sm.  

The selection of low-energy alpha events is performed with the "nSigmaBetaGamma" branch in the "gaggpsd" tree and the energy cut. More specifically, nSigmaBetaGamma is less than -3, and the integral is in the range of 4500 to 10000. These values are applied to all the wafers. The count rate of low-energy alpha events is shown in the figure below. 
The wafer T6 (black dot) and CF2 (red square) have the highest and lowest event rates, respectively. All the values are given in the table below. It can be clearly seen from the psd plots that there are many events at around integral=10000 for T6, whereas CF has almost none. After checking the baseline property of these events, they do not belong to noise.

^ PSD(relativeamplitude) versus Integral for T6 ^ Count rate of low-energy alphas for all wafers ^ PSD(relativeamplitude) versus Integral for CF2 ^
{{:gagg-nd:psd_T6.png?400|}} | {{:gagg-nd:lowE_alphas.png?400|}} | {{:gagg-nd:psd_CF2.png?400|}}


(Note that the psd parameters in few files of T2 are not well reconstructed. The mean value ("relativeamplitude" branch in the "chi2_gammafreq" tree) is somehow not normalized to be one. These files are rejected.)


=== High-energy alpha contamination with delayed coincidence ===

The high-energy alpha events contributed by natural decay chains are selected by defining the PSD parameter "nSigmaBetaGamma <= -4 && Integral > 10000". The count rate is calculated for each wafer and presented in the table and the plot below.

{{:gagg-nd:highE_alphas.png?400|}} 


As a reference, the prototype has a total count rate of 0.031/s for high-energy alphas. In comparison, the wafer has a much lower contamination.

 
Delayed coincidences are used to look for short-lived decays. However, due to a low number of events, only few coincident events are found. 

^High-energy alpha background spectrum of T9 ^ Events spectrum used for delayed coincidences analysis ^
{{:gagg-nd:highE_alphas_T9.png?400|}} | {{:gagg-nd:dc_alphas_T9.png?400|}} 

The two prominent peaks shown in the left figure are from the early part of Th and U decay series.

One decay process being searched for is the Rn->Po->Pb of the Th decay chain with a half-life of 0.145 s. The selected energy interval for Po decay is [32000, 37000], and the interval for Rn decay is [27000, 32000]. The reconstructed time difference distribution is shown below.

{{:gagg-nd:Rn_Po_Th_wafer.png?400|}} 

The fastest decay of <sup>235</sup>U chain with a half-life of 1.78 ms is not found so far.

=== Summary ===


^  Wafer  ^  τ<sub>f</sub> [10<sup>-8</sup> s]  ^ τ<sub>s</sub> [10<sup>-7</sup> s]  ^ Ratio(A<sub>1</sub>/A<sub>2</sub>) ^ FWHM [%] ^ low-energy α count rate [per s] ^ <sup>147</sup>Sm contamination [per s] ^  high-energy α count rate [per s]^
| T1  | (8.32 ± 0.05)   | (4.59 ± 0.09)  | 12.93 ± 0.19| 39.90 |(0.0207 ± 0.0002) | (0.0007 ± 0.00004)| (0.0084 ± 0.0001) |
| T2  | (8.52 ± 0.03)   | (4.67 ± 0.05)  | 13.08 ± 0.23|38.63 | (0.0220 ± 0.0001)| (0.0020 ± 0.00003) | (0.0098 ± 0.0001)|
| T3  | (8.51 ± 0.05)  | (4.69 ± 0.05)  | 13.16 ± 0.26|43.23 |((0.0212 ± 0.0002) | (0.0012 ± 0.00004) | (0.0087 ± 0.0001)|
| T4  | (8.01 ± 0.02)   | (4.08 ± 0.05)  |13.01 ± 0.21|41.84 |( 0.0232 ± 0.0002)| (0.0032 ± 0.00007) |(0.0159 ± 0.0002)|
| T5  | (8.04 ± 0.03)  | (4.08 ± 0.02)  | 13.03 ± 0.11|41.19| (0.0205 ± 0.0001) | (0.0005 ± 0.00002)|(0.0109 ± 0.0001)|
| T6  | (8.36 ± 0.03)   | (4.62 ± 0.05)  | 12.72 ± 0.20|42.49|(0.0237 ± 0.0002)| (0.0037 ± 0.00008)| (0.0134 ± 0.0001)|
| T7  | (8.39 ± 0.03)   | (4.64 ± 0.06)  | 12.82 ± 0.18|41.23|(0.0216 ± 0.0002) | (0.0016 ± 0.00004)| (0.0085 ± 0.0001)|
| T8  | (8.46 ± 0.02)   | (4.69 ± 0.06)  | 13.03 ± 0.22|39.88|(0.0216 ± 0.0001) |(0.0016 ± 0.00003)| (0.0086 ± 0.0001) |
| T9  | (8.34 ± 0.03)  | (4.65 ± 0.05)  | 13.04 ± 0.20|40.32 |(0.0224 ± 0.0001) |(0.0024 ± 0.00002)|(0.0093 ± 0.0001) |
| T10  | (8.30 ± 0.03)   | (4.63 ± 0.07)  |13.02 ± 0.18|40.70|(0.0211 ± 0.0001) |(0.0011 ± 0.00003)|(0.0085 ± 0.00001)|
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| CF1  | (8.34 ± 0.03)  | (4.63 ± 0.05)  | 12.89 ± 0.18|38.92 |(0.0218 ± 0.0002) |(0.0018 ± 0.00005)|(0.0088 ± 0.0001)|
| CF2  | (7.99 ± 0.02)  | (4.07 ± 0.06)  | 13.03 ± 0.02|38.41 |(0.0202 ± 0.0002) |(0.0002 ± 0.00002) |(0.0085 ± 0.0001)|
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| HL1  | (10.1 ± 0.06)  | (4.96 ± 0.09)  | 10.39 ± 0.16|38.98 |(0.0210 ± 0.0001) |(0.0010 ± 0.00003)| (0.0021 ± 0.00005)|
| HL2  | (9.62 ± 0.04)  | (4.29 ± 0.02)  | 10.09 ±0.08 |37.46|(0.0216 ± 0.0001) |(0.0016 ± 0.00004)|(0.0020 ± 0.00005)|