Introduction

Two different materials detector type are being modeled, semiconductor (HPGe Coaxial P-type detector), and a scintillator one (LaCl3(Ce), and LaBr3(Ce)) in this work, these detectors and their setups are an important component of metrology system which will be used to standardize radionuclides and various new nuclear installations. There are new ways to look for performing primary standardizations of activity at the high energy gamma system at ELI-NP facility. This instrument will complement the existing measurement capability of the gamma system by providing a computational capability to aid in detection techniques and experimental situation. The scope of this work is the characterization of the gamma-ray detectors instrumentation by means of computational methods i.e. Monte Carlo (MC) and deterministic methods. This methodology is justified since it is widely recognized that the application of MC techniques to radiation detector modelling is important in understanding the complex physical interactions that take place, particularly those which cannot be measured directly [5, 6,7,8,, 9,10,11,, 12,13,, 14, 25].

A secondary scope is the validation and verification of methods, software employed, gives valid data that can be applied to the radiation measurements techniques both at theoretical and practical level. The MC simulation provides an invaluable resource for the characterization and analysis of a radiation detector and supports the understanding of operating limitations. A MC simulation needs to be validated against experimental measurements in order to quantify the accuracy of the results qualitatively coming from it, in the present work is presented the validation for the MCNP simulation for HPGe detectors against experimental, for second type of detectors we assumed that the initial geometry for germanium detector without additional experimental data just the MC simulation [25]. Further on the coincidence-summing effects that alter the integral of the full energy peak (FEP), impacting the efficiency value and the derived activity is being corrected and compensated. Coincidence-summing arises when two or more γ-rays are emitted from a single decay and are detected at the same time. Moreover, other radiation such as -β particles and their bremsstrahlung, X-rays (from electron capture or internal conversion), and annihilation radiation from β + decay also can be in coincidence with the γ-rays. It has been demonstrated that MC simulations can provide a satisfactory correction for these effects [7,8,9,, 10, 11]. In present work the aim is to model a fully functional detector in terms of, full energy peak efficiency with coincidence-summing correction. The candidate materials chosen are Ge (HPGe) semiconductor type present at Metrology Department, LaBr3(Ce)/LaCl3(Ce) scintillation type present at ELI-NP facility, model of the HPGe detector-type is validated against experimental results, performed at the Department Radioisotopes Measurement and Ionizing Radiation Metrology of National Institute for R&D in Physics and Nuclear Engineering (IFIN-HH). The simulation study provided a way to determine if or any required corrections and supply important information about the experimental conditions to be met in order to achieve optimal measurement efficiency and contribute to the data set credibility. Further to enhance the results we employ software used regularly for quantitative analysis in gamma-ray spectrometry analysis of spectra such as Fitzpeaks to provide the photopeak activity and later for correction of coincidence summing using EFFTRAN & GESPECOR 4.2 [2, 3,4,5,6,7,, 8, 15, 16, 26,27,28,29,30,, 31,32,33,34,35,, 36].

Experimental

A 152Eu source with an activity of 12.992 Bq has been measured experimentally at 5 cm from a HPGe coaxial detector preset in National Institute for R&D in Physics and Nuclear Engineering (IFIN-HH). The details of the detectors used in both the experimental as well as the simulations are presented in the Methods section [13,14,15,16,, 17, 18].

Methods

For the HPGe simulation (Fig. 1 gives the dimensions supplied by the manufacturer) we simulated a coaxial HPGe manufactured by ORTEC-AMETEK with a serial number S/N 47-TP22323A and model number GEM25P4 with a 25% relative efficiency available at (IFIN-HH). The crystal detector dead layers have been supplied by the manufacturer ORTEC. Based on these characteristics and the crystals dimensions we build the virtual detector in MCNP, GESPECOR and EFFTRAN. Figure 1 shows the manufacturer dimensions of our crystal detector [17, 18, 41, 42].

Fig. 1
figure 1

Detectors characteristics supplied by manufacturer

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For the scintillation simulation we employed a general cylindrical shaped type detectors similar to those found in metrology laboratories.

Scintillation detectors type LaBr3(Ce) and LaCl3(Ce) are being less complex in construction as the material designed for radiation interaction is homogenous and of a single type either LaBr3(Ce) or LaCl3(Ce). The users should be warned that MCNP defines the material characteristics for these two types of detectors as LaBr3 or LaCl3 in material cards and no Cerium is present. Material doping is still a work in progress for the MCNP developing team. Figure 2 presents the scintillation detector in a similar manner previously for HPGe detector, for saving space and not to be too repetitive only one of the scintillation detector figure is used, a similar approach but with LaCl3(Ce) material is used for the third detector [19,20,21,, 22].

Fig. 2
figure 2

HPGe, LaBr3(Ce) detector

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Short details about the employed softwares, starting with SUPERSynth interface for MCNP 6.2, Fitzpeaks for efficiency calculations and spectral analysis, and coincidence correction software employed on the analyzed 152Eu photopeaks [24]. The best way to model the response of any detector is by using a standardized source like 152Eu which was selected and alongside a real-life detector [13]. Figure 3 shows side views of HPGe detector using MCNP plotter window (left hand side), and the geometry construction of the detector in MCNP (right hand side) [1, 23].

Fig. 3
figure 3

Shows the detectors setup used with the Lead shield around

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SUPERSynth is an easy-to-use interface to build up the MCNP input card, thus reducing the time spend of user to generate the input file for running. The menu is easy to use and self-explanatory and most users with advanced experience or little experience in running MCNP simulations will find it very useful in gamma-ray spectrometry works. Used in generating our data was MCNP 6.2, mode P for photons with Doppler Broadening and Gaussian Energy Broadening (GEB) terms active. Computer time was ~ 2262.47 min (135,748.2 s).

After the MCNP finished successfully the output was converted to ORTEC spe file format which was read with Fitzpeaks. Fitzpeaks is a gamma- ray analysis software used in both experimental and simulated data. We employed Fitzpeaks to get the photopeaks areas and the efficiencies per photopeaks of the spectrum.

Germanium Spectrum Correction (GESPECOR) is software that employs Monte Carlo method for getting the correction factor for coincidence gamma- ray spectrometry. GESPECOR can be applied to coaxial and well-type HPGe or to Ge (Li) detectors and to various types of sources, including point, cylindrical, and spherical sources or Marinelli beakers.

EFFTRAN is a Monte Carlo efficiency transfer code, recently was updated with a deterministic code for coincidence correction factor calculation. The approach is aimed at the analysis of extended samples measured on p-type HPGe detectors in environmental gamma-ray spectrometry and was verified against the results of a state-of-the-art full Monte Carlo code [4, 28, 33, 39, 40].

The applied MC method from GESPCOR 4.2 and EFFTRAN deterministic method for benchmarking between the two-software coincidence correction is being used for HPGe detector. Experimentally the full energy peak efficiency ε is given by the equation:

$${\varvec{\varepsilon}}=\frac{{{\varvec{N}}}_{\mathbf{m}\mathbf{e}\mathbf{a}\mathbf{s}}}{{\varvec{A}}\bullet {{\varvec{I}}}_{{\varvec{\gamma}}}\bullet {{\varvec{L}}{\varvec{T}}}_{\mathbf{m}\mathbf{e}\mathbf{a}\mathbf{s}}}$$
(1)

Nmeas is the measured counts, A is the known activity of the source in becquerels, Iγ is the γ-emission intensity and LTmeas is the live-time of measurement in seconds.

Table 1 Presents the decay peaks of the 152Eu, intensity, transitions, and decay mode.

Table 1 Characteristics of 152Eu source (transitions, decay mode, etc.) [35]
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We selected a widely used and relevant geometry and distance source- detector, a 5 cm distance from the source emitter and the detectors have been employed, this is a typical distance in most calibrations, simulations, and experiments performed in the literature.

Figure 3 gives detail picture of the setup of the present work using HPGe detector but similar position has been employed for scintillation detectors, we can see the lead shield detector and the source at 5 cm place on top of detectors.

No absorber has been used, electronics, the counting parameters (gain, channels number, live time), the gain was set 1, channel number was selected to a typical experimental acquisition of 4096 channels, and a live time of 200.000 s. the shielding used around the setup was a 5 cm thickness shield made of lead with 0.1 mm thickness copper layers covering the ceiling, walls, floor of the shield.

Results and discussion

In the present work, results of 152Eu source at 5 cm from the detection setup is being presented. Experimentally it has been employed a source with an activity of 12.992 Bq at 5 cm from the detector, while the MCNP simulation used 4 sets of data (5 cm, 10 cm, 20 cm, 30 cm). The input development has been done with the help of SUPERSynth interface for MCNP all the details of geometry, source definition, detectors characteristics, electronics, environment, furthermore all the results have been simulated with MCNP 6.2 version. The results were processed, by calculating the efficiency separately and with the aid of Fitzpeaks 3.90 and we obtained a comparison of detectors efficiencies, further we employed two different software for gamma coincidence predictions for benchmarking and comparison reasons on experimental and on the HPGe, LaBr3(Ce) and LaCl3(Ce) detector simulation, GESPECOR 4.2 (licensed to IFIN-HH), EFFTRAN from European Commission (Dr. Tim Vidmar) [3, 15, 16, 31, 36]. GESPECOR correction is being used for the laboratory spectra with 12.992 as well as the simulated ones taken, as a comparison for our work. 152Eu, the lines overlap on both software’s which provide good agreement of the value of data in this work.

We have obtained data on efficiency of the detectors of HPGe, LaBr3(Ce), LaCl3(Ce). Further ahead tables with correction factors used. A single experimental data set was taken with HPGe detector from the Spectrometric laboratory from (IFIN-HH) with the source placed at 5 cm. Four different sets at four different distances from the detectors have been simulated plus a laboratory measurement have been chosen for this work so to establish the efficacy of the softwares and methods employed in the current work. LaBr3(Ce) and LaCl3(Ce) where observed in a similar process and both have close if not identical data sets. The efficiency curve has been fitted with a decay function which fits the data sets in good agreement and some points overlap perfectly.

Table 2 Contains data for the experimental source with selected 13 photopeaks, data contained are energy, initial photopeaks area, correction factors from EFFTRAN/GESPECOR, and the error in percentages. Table 3 @5 cm, Table 4 @10 cm, Table 5 @20 cm, Table 6 @30 cm, data for all 3 type detectors [27,28,, 29, 30,31,, 32,33,, 34,35,36,, 37, 38].

Table 2 Data for experimental source of 152Eu @ 5 cm
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Table 3 Simulated Data for 152Eu @ 5 cm
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Table 4 Simulated Data for 152Eu @ 10cm
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Table 5 Simulated Data for 152Eu @ 20cm
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Table 6 Simulated Data for 152Eu @ 30cm
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Figures 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, present the efficiency curves obtained. Figure 4 presents the curves for experimental and MC simulations so the readers will have a better view of differences obtained from experiments compared with simulations.

Fig. 4
figure 4

Efficiencies (%) of experimental source and simulated 152Eu @ 5 cm

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Fig. 5
figure 5

Shows efficiencies calculated based on data from spectra at various distances

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Fig. 6
figure 6

Shows efficiencies fitted based on data from spectra at various distances

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Fig. 7
figure 7

Shows efficiencies measured based on data from spectra at various distances

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Fig. 8
figure 8

Shows efficiencies calculated based on data from spectra at various distances

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Fig. 9
figure 9

Shows efficiencies fitted based on data from spectra at various distances

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Fig. 10
figure 10

Shows efficiencies measured based on data from spectra at various distances

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Fig. 11
figure 11

Shows efficiencies calculated based on data from spectra at various distances

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Fig. 12
figure 12

Shows efficiencies fitted based on data from spectra at various distances

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Fig. 13
figure 13

Shows efficiencies measured based on data from spectra at various distances

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The efficiency was calculated and computed with the aid of Fitzpeaks Gamma Analysis and Calibration software, it was performed directly on the spectrum generated from MCNP. The analysis is performed automatically by peak searching, activity of the source, and then a calibration curve in efficiency is obtained from the data set. The results and correction data are in line with the published benchmarked data on correction factors codes. Data in the graphs is being fitted with a decay function. There have been no large discrepancies between measured from the spectras obtained from MCNP. The efficiency of the Scintillation is higher than the HPGe as expected [24].

Conclusions

The results show that the simulated data performs well and can in some cases substitute the laboratory manual work, and could be used for further training of people in gamma spectrometry metrology, or development of new methods and techniques in gamma-ray metrology.

Both the experimental measurements and simulated data sets are in good agreement and have been performed in accordance with the known and established gamma-ray spectrometry way, which gave a good proposition to benchmark software and methods for coincidence problem and efficiency.

Fitzpeaks software previously used for peak fittings here we employed very well in getting the efficiency of the detector from spectra either measured using a live laboratory source (in our case the 12.992 Bq 152Eu source) or the ones that have been generated/simulated with the aid of Monte Carlo method (MCNP). Fitzpeaks software which deals with both theoretically generated MCNP data and also experimental obtained spectra can be an extremely useful tool in aiding the laboratory in performing new measurements on a different radionuclide saving time in measuring the efficiency of the detector and getting the photopeak areas.

The downside is the need for computational power, the higher the activity and the more complex the decay of the radionuclides employed will further add to the computation time.

MCNP with the aid of SUPERSynth interface is of a real help to a gamma- ray spectrometrist, it saves precious time and removes the errors in making the input files, the downside for SUPERSynth interface is lack of multiple detectors at the same time, at the moment a single detector can be added to the simulation, so for adding a second detector would be a complex task. The experiment performed here in 152Eu is in good agreement with the available data published. The result obtained here are with the ENDF VII.1 version [4, 43].