JOURNAL OF MEDICINE CARE AND HEALTH REVIEW

Introduction

Gamma-ray spectrometry using germanium detectors is a reliable technique widely employed to determine the activity concentration of natural and artificial radioactive elements in the environment. The most critical step in gamma spectrometry analysis is determining the number of photons emitted by the source and detected by the detector [1, 2]. The efficiency calibration of a high-purity germanium (HPGe) detector is typically performed using standard gamma sources that have the same geometry, density, and chemical composition as the samples under study [3, 4].

To analyze complex gamma spectra and express a spectrum in terms of activity or the quantity of radioactive elements, it is useful to have an analytical function that describes the detector's efficiency as a function of energy [5, 6]. Of paramount importance, however, is the Full Energy Peak Efficiency (FEEP), which, as indicated by the following equation, represents the ratio of the total gamma-ray counts in the full energy peak to the gamma-ray emission rate from the source, denoted by ԑ [7, 8].

                                                             (1)

Where P is the probability of gamma decay of the radioactive nucleus, t is the spectroscopy duration (live time), and A is the number of decayed nuclei over time. By placing single-energy or composite sources with known energy and activity in front of the detector, counting the emitted gamma rays, and knowing the counting duration and decay probability, efficiency can be determined. By plotting the obtained efficiency values on an efficiency curve as a function of energy and fitting them, an equation for the efficiency calibration curve can be derived [7]. Finally, by placing a source with unknown activity in front of the detector and using the calibration curve equation, the activity of the source can be determined.

The sources used in this experiment are charcoal canisters, consisting of three main parts: two mesh caps (20% to 50% perforated) and a cylindrical middle section with two paper filters placed on it.

Methodology

The detector used in this experiment is a dual-sided HPGe semiconductor detector (GPD-50-400) with a diameter of 50 mm, a thickness of 15 mm, and a relative efficiency of 10%. The canisters are placed on the detector using a holder. To minimize errors in spectrum recording, the pulse shaping time is set to 5 microseconds, the gain to 0.484 keV/Channel, and the applied voltage to the detector is set at 3600 keV. The sources used in this experiment—Eu-152, Ba-133, Cs-137, and Am-241—have known activities and are added to charcoal canisters with the same dimensions and geometry as the samples. These sources cover an energy range between 60 and 1500 keV. By calculating the initial activity at the time of source preparation and considering a time interval of 14 years and two months between the preparation of the standard source and its current measurement in the detector, the present activity of the source is calculated using equation (2). The results are displayed in Table 1.

                                                        (2)

Results

After recording and saving the spectra of the standard sources, and with the activity of the radioactive elements available from Table 1, along with the counting duration, net area under the peaks, and decay probability, we can calculate the efficiency at different energies using equation (1). Variations in efficiency values across different energies are observed, which are attributed to the energy loss of the elements on the filter. With the activity of the radioactive element, counting duration, net area under the peaks, and decay probability known, efficiency at different energies can be calculated using equation (1). The variations in efficiency values at different energies are due to the energy loss of the respective element on the filter. A summary of this information is presented in Table 2.

To calculate the efficiency error, we must first determine the error in the full-energy peak area values. This can be done using the following equation.

                                                                          (4)

Now, with the errors in the activity and the full-energy peak area determined, the efficiency errors at different energies can be calculated using equation 5.

                                                (5)

The goal of all these procedures is to derive an equation that can describe efficiency as a function of energy. The efficiency calibration curve is fitted with a polynomial function to ensure accurate and precise results.

                     (6)

In this equation, P₁​ to P₅​ are the parameters of the fitted function. Using software like MATLAB, it is possible to calculate the fixed coefficients and derive a polynomial equation for point gamma-emitting sources. However, in this case, we use a direct approach with the software Table Curve. By considering energy as the horizontal axis and efficiency as the vertical axis, we obtain the efficiency curve and its equation as a function of energy (Figure 3). Through this process, by fitting a curve to the efficiency data, we arrive at a logarithmic equation (Equation 7) that describes efficiency as a function of energy.

                      y=(a+clnx+e(lnx)²)/(1+blnx+d(lnx)²)                 (7)

In this equation, a, b, c, and so on are constants with the following values.

a=-0.316, b=-0.40754, c=0.093, d=0.04248, e=-0.00077