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Calibration files
Data was taken on August 22. We used a Th232 source and for every file the measurement time is 2 minutes. The voltage was varied from 1500V to 1200V with steps of 50V. The files used for this analysis are listed below.

LaBr3_H2431_1500V_UG_Th_20240822_165354.root
LaBr3_H2431_1450V_UG_Th_20240822_171420.root
LaBr3_H2431_1400V_UG_Th_20240822_171708.root
LaBr3_H2431_1350V_UG_Th_20240822_172040.root
LaBr3_H2431_1300V_UG_Th_20240822_172315.root
LaBr3_H2431_1250V_UG_Th_20240822_172554.root
LaBr3_H2431_1200V_UG_Th_20240822_172829.root

Data analysis for calibration
When the high voltage was set too high the digitizer was saturating around the signal of the alphas, for this reason we decreased the HV. In the figures below I plotted the scatter plot amplitude vs integral: on the left the HV was set at 1500 V, and we can clearly see a cut on the alpha signal; on the right the HV was set at 1200 V, at which the digitizer saturates at around 10 MeV (and so it is not visible), which corresponds to the end of the ROI for the GAGG.

Because the saturation doesn't affect the gamma spectrum for every file I fitted the gamma peaks in the spectrum. In this way I was able to perform an energy calibration, and characterize the energy resolution at different voltages. The peaks were fitted with a gaussian plus a linear background centered at the mean of the peak, plus a costant background and the error function. I report for example the spectrum with some fitted peaks obtained with the HV set at 1500V (left) and at 1200V (right).

The first two peaks present in the left image are probably x-rays at around 80 and 90 keV and we can clearly see that they disappear when the voltage is set too low. In the table below I report the other peaks that were fitted, excluding the x-rays:

By plotting the mean amplitude extrapolated from the fit against the energy of the peaks one can obtain a calibration curve with the fitted gamma peaks. Here the image is obtained with HV 1500 V, I also plot the residuals (energy reconstructed-nominal energy).

Finally I plot the energy resolution obtained with HV 1500 V. To do this I used only the highest and isolated peak in the spectrum, corresponding to ²¹²Pb 238.6 keV, ²²⁸Ac 338.3 keV, ²⁰⁸Tl 583.2 keV and ²⁰⁸Tl 2614.5 keV. The energy resolution was fitted using a function of the type: a/√E +b.

This was done also for the other data, which had different voltage, so in this way I was able to compare the energy resolution obtained using different HV. In the images below are plotted the energy resolution functions obtained for the different voltages, with a focus on the low and high energy (respectively bottom left and right).

In theory we expected that the energy resolution would be better with a higher voltage, given the fact that the gain would also be higher. Instead we see that at higher energies the energy resolution is better with lower voltages, while in the low energy region the opposite is true. To investigate this more I plotted the energy resolution of the four peaks used in function of the applied voltage, here I report the case of ²⁰⁸Tl at 2614.5 keV.

One can see that the resolution is nearly compatible for all the voltages, and so the take away is that the error is too large to see the effect of different voltages on the energy resolution. This can be seen also if one plots the different theoretical curve with 1 sigma band, in fact they are all overlapped.

Next steps
The next step is to try to work at higher voltages using an attenuator, in this way the problem of saturation regarding the alphas would not be present and in theory the resolution should be better.

Edit: data with attenuator
On August 30 we took more calibration data (Th232), this time the HV was set at 2000V, 2500V and 3000V. For the 2000V data we used an attenuator of 20dB, while when the HV was at 2500, 3000 V we used two attenuators (20dB and 10dB) placed in series. The data files are:

LaBr3_H2431_2000V_20dB_UG_Th_20240830_120036.root
LaBr3_H2431_2500V_UG_Th_20240830_112353.root
LaBr3_H2431_3000V_UG_Th_20240830_113001.root

At 2500 V, 3000 V this time we have the problem that the PMT is saturating, and so the response is not linear (this is what happened with the first PMT used with LaBr3). This effect doesn't happen at 2000 V, and so I was able to characterize the energy resolution by following the method reported above. The curve obtained is overlapped with the other ones. For reference the energy resolution (FWHM) of ²⁰⁸Tl at 2614.5 keV is (2.83±0.03)%, compatible with most of the others. By having investigated the range of HV [1200, 2000] V we can conclude that changing the voltage doesn't affect the energy resolution curve, which remains stable (around 2.9 % at 2615 keV , 7 % at 238 keV).

Background analysis
We took background for 30 minutes at 1250 V, and for 11 hours and 30 minutes at 2000 V (with 20dB attenuator):
LaBr3_H2431_1250V_UG_bkg_20240826_104833.root

I checked the possibility to discriminate between alphas and gammas, defining the PSD=chi2.amplitude/integral.integral and plotting against the integral. Below I report the figures for HV 1250 V (left) and 2000 V (right):

Here we can see that at 1250 V we can discriminate pretty well, while this is not the case at 2000 V. One possible explanation for this is that the attenuator is distorting the signal in some way, and so the distintion beetween alphas and gammas is not possible. This effect, combined with the same energy resolution at 1250 V, leads me to the conclusion that the best way to operate this PMT with the LaBr3 crystal is near 1250 V. This value also represent the highest voltage possible (without attenuator) that we can use if we want the saturation of the digitizer to happen at around 10 MeV. Nevertheless we see that the discrimination is worse compared to the GAGG, and this happens because the signal generated in the LaBr3 crystal is similar for gammas and alphas, as we can see in the two figures below (HV=1250 V).

The fact that the integral is similar for the alphas and the gammas causes the proximity of the two bands.
In the end we notice that if we take the background with HV=1250 V, even if we set a stringent discrimination parameter like PSD=0.05, there are already some events beyond the line of ²⁰⁸Tl at 2614.5 keV (around 49500 [a.u.]). This means that the contamination of the LaBr3 crystal is too high and so it can't be coupled with the GAGG to detect the γ from neutron capture.