Statistical Study for the Energy Resolution of the Cesium Source Using the NaI(Tl) Detector

Abstract

To investigate the statistical nature of gamma-ray decay, the energy resolution of the ¹³⁷Cs source spectrum was investigated using the statistical programming language R, as well as the moderation and homogeneity test for the data, as well as the Pearson correlation coefficient test and the linear regression test. It was observed that the investigated random variables had no strong statistical link, and that the random mean of the samples differs slightly from the expected mean for same variables using same statistical distribution.                                         

 Materials and Methods:

In this study, a scintillation detector of iodide sodium activated with thallium NaI(Tl) measuring (200) samples of ¹³⁷Cs spectrum at (200 sec) time for each spectrum and a distance is(7cm) between the radioactive source and the detector . The R programming language was used in calculating the statistical applications represented by the mean, median, variance and standard deviation, also the normality tests and homogeneity of variances tests were calculated by the R programming language, it had been found that all the models studied were homogeneous and that most of the models were not follow to a normal distribution.

Conclusions:

In this study, statistical distributions and statistical software were used, and it was revealed to the following:

1-The Kolmogorov-Smirnov test revealed that the data in the sampling random analysis are distributed in a regular manner.

2-The R.E. of the spectrum data was found to follow a normal distribution in a Shapiro test, depending on the p. value.

3-In the Q.Q. Normal Test, the points in R.E are applied in a straight line, indicating that the data is homogeneous.

4-Using the linear regression test, it was determined that the analyzed random variables have no statistically significant correlation.

5-It was discovered that the analyzed samples (R.E) follow a normal distribution using the T-Test.

6-The third group in Pearson correlation was less than zero, while the rest of the groups were near zero, with the first and second groups having negative values, indicating that the investigated variables have a weak inverse link. The third group had a positive correlation value, indicating that the 137Cs source's R.E. had increased.