## 3 Results and Discussion  
### Short Period Data  
Distributions of pulses generated by the scintillators in unit time \(t\) should correspond to Poisson distributions with an expected value equal to \(\lambda t\). This value (for a chosen time interval) depends mainly on the area of the detector and its vertical or horizontal position. Figure 3 presents distributions of the numbers of counts registered in one second by the scintillation detectors TOP, BOTOM and FRONT. In order to obtain experimental data (the cyan, red and pink lines in Figure 3), Poisson distributions were fitted with expected count rates \(\lambda_{\text{TOP}}\) = 71.93 counts/s (black), \(\lambda_{\text{BOTOM}}\) = 18.88 counts/s (green) and \(\lambda_{\text{FRONT}}\) = 14.43 counts/s (blue) for TOP, BOTOM and FRONT detectors, respectively. The horizontal detectors registered more particles in unit time than the FRONT detector, which was placed vertically. Additionally, Figure 3 demonstrates a great amount of data registered by a digital gamma-ray spectrometry system and supports the demand for the optimization process. Such factsare in accordance with previous research results described in [1]. Further data analyses involved the verification of the presence of correlated structures in detector signals. The gamma-ray measurement investigation lasted approximately 119 h.  
Figure 4a presents values of the ACF in the examined series in cases of up to ten events lag and from 10-1000 events lags. The ACF values oscillate around zero, indicating that there were no correlations in this signal. This means that practically every registered muon can be considered as a single independent event. The same results were achieved for other scintillators, implying that singular scintillators detect non-correlated cosmic-ray muons. Additionally, conducted analyses proved that signals generated by scintillation detectors are stochastic Poisson processes [15]. Figure 4b shows the obtained results from FFT analysis of the sequence of counts registered in one second by the TOP detector. A flat frequency spectrum (and, consequently, flat power spectrum) proves that data generated by the individual scintillation detectors during single gamma-ray spectrometric measurement correspond to white noise, and it is impossible to detect, using single scintillators, correlated muons created in the same air-shower event. This is because the time resolution of an active shield scintillator is mainly determined by two signal shaping parameters: the rise time of the trapezoid generated by the digitizer's energy filter and the length of its flat part [1]. Since the main purpose of the constructed active shield, muon detection, requires correct evaluation of the pulse height, the total shaping time is around 12 us, much longer than the intervals between any possible registered cosmic-ray particles generated in the same air-showers. Figure 3: Expected count rate distributions for scintillation detectors: TOP (71.93 counts/s), BOTTOM (18.88 counts/s) and FRONT (14.43 counts/s). Bearing in mind the previous results, coincidence events of signals from different scintillators have been studied. Coincidence events from four scintillation detectors, namely TOP, BOTTOM, FRONT and REAR, were found using the VETO software. The detection system registered 471 events of four-fold coincidences during the investigated gamma-spectrometric measurement. Figure 5 presents the distribution of the coincidence events found as a function of the maximum time interval between pulses from the same event. Due to the non-linear geometric positioning of the considered scintillators, generated signals must come from at least two correlated muons from the same air-shower. Furthermore, the width of the distribution (\(\sigma=12\) ns) is comparable with the digitizer time resolution, and correlated muons time travel through the distance between scintillators. This feature is interesting from the novel CREDO project point of view [16], which focuses on studying cosmic rays and cosmic-ray ensembles.