Simulation of 4 π HPGe Compton-Suppression spectrometer

Compton-suppression spectrometer is well suited to the analysis of low levels of radioactive nuclides. Monte Carlo simulations can be a powerful tool in calibrating these types of detector systems, provided enough physical information on the system is known. A simplified Compton-suppression spectrometer model using the Geant–4 simulation toolkit was discussed. The spectrometer model was tested to evaluate photo peak efficiency of detecting point and disk sources. The efficiency calibration was calculated for incident gamma energy from 200 to 3000 keV in both the suppressed and unsuppressed mode of operation. The applicability of the efficiency transfer method in various measurement geometries was tested successfully. It can save time and avoid tedious experimental calibration for different samples geometries.


INTRODUCTION
Gamma ray spectrometry based on high pure germanium (HPGe) detectors is an important tool in the field of radioactivity measurements.The reason is due to the excellent energy resolution of HPGe detectors that permits the analyses of various radionuclides in composite samples selectively as well as the high efficiency of recently produced HPGe detectors (L'Annunziata, 2012).
Improved detection system for experiments need low background environment and is strongly needed especially in the field of high energy physics; dark matter, low-energy solar neutrino experiments.Comptonsuppression spectrometer is considered a powerful technique to reduce the contribution from Compton scattered photons in a measured sample.Generally, it consists of primary detector surrounded by secondary detectors, and the pulse produced by the primary detector is accepted by analyzer only when the secondary detectors do not produce a pulse within a time period.The most wide Compton-suppression spectrometer consists of high pure germanium (HPGe) detector surrounded by scintillator crystals such as CsI (Tl), NaI(Tl) or BGO in 4π geometry coupled by photomultipliers (PMTs) as in Exogam, Miniball, Gamma-Sphere, Euroball, GASP.By operating spectrometer in a fast anticoincidence regime (tens of nanoseconds time resolution) can be obtained as a significant reduction of the Compton background with high resolved spectra (Fan et al., 2013;Breier and Povinec, 2009 and detectors websites).
Samples suitable to be measured are generally disk sources (various geometries and matrices) which would require certain measurements.The spectrometer accuracy is essential for the absolute measurements of radioactive materials.Experimental measurements can be applied to limited different geometries, compositions *Corresponding author.E-mail: medhatme@ymail.comand densities of sources and cannot be applied directly to all configurations.This can be a time consuming process and in some cases impossible to replicate.As an alternative approach, Monte Carlo simulations are recommended to do this task and then to continue with experimental measurements.Monte Carlo simulation is a powerful and flexible tool for simulating various physical phenomena.These types of simulations can be powerful complement to experimental installations.Modeling the geometry in computer environment gives flexibility and ease of use instead of performing experiment in different geometries (Britton, 2012;McNamara et al., 2012;Rehman et al., 2011).
One of the main problems faced in any detection system is evaluation of detection efficiency.So, instead of performing efficiency calibration for each sample, which of course is impractical, the model can be used to calculate the efficiency of the spectrometer for that particular geometry.This work aims to present a preliminary evaluation of detection efficiency of Comptonsuppression spectrometer in both of the suppressed and unsuppressed mode using Geant-4Monte Carlo simulation based on object-oriented methodology and C++ language (Agostinelli et al., 2003).

Geant-4Toolkit
Geant-4 is a simulation tool kit that can simulate accurately the detectors and interactions of photon and particles through matters.
The code was written in C++ and developed by CERN (CERN, 2007).It simulates accurately the passage of particles through matter.It offers the possibility to include a complete description of an experiment and extract information that might be useful in many different fields, such as nuclear and high energy physics, medical physics and astrophysics.
Geant-4 toolkit contains a complete range of functionalities including tracking, geometry; physics models and hits.It is controlled through the instantiation of the appropriate Geant4 classes to define the geometry, applicable physics, and particle source and to control the execution.The key class for all Geant4 applications is the G4RunManager which controls the initializations of geometry, physics list and primary particle generation.The user has full freedom to develop an own simulation program.The user must implement several mandatory classes to describe the detector geometry, the primary particle generator and a class to describe the relevant particles and physics processes.Other non-mandatory classes must be created to resolve proper objectives.

Simulation of spectrometer geometry
Modeling the spectrometer geometry in computer environment gives flexibility and ease of use, instead of performing an experimental determination of detection efficiency for different geometries.For this reason, the model of spectrometer system would be useful for further experiments when the geometry is changed.Then, instead of performing efficiency calibration for each sample, which may sometimes be impractical, the model can be used to calculate the efficiency of the system for that particular geometry (Chirosca et al., 2013;Baccouche et al., 2012).
The supposed Compton-suppression spectrometer geometry HPGe detectors surrounded by a CsI(Tl) cylindrical scintillator crystal with photomultipliers attached.The simulated detector is p coaxial type detector.A sketch of the HPGe detector, adapted from the manufacturer manual, is shown in Figure 1 and the provided dimensions of the HPGe detector are further summarized in Table 1.
The HPGe cylinder is oriented inside a scintillator cylinder with diameter 150 mm and length 250 mm.Sample with diameter 5 mm and length 15 mm is placed at distance 10 mm from the top of the HPGe crystal.The detection system of germanium crystal works in anticoincidence with photomultipliers, trying to eliminate a part of Compton electrons generated by gamma rays which are not absorbed by photoelectric effect in HPGe crystal.The proposed Geant-4code was written using ten user classes: three user mandatory classes and some user action classes.The geometry of the Compton-suppression spectrometer was coded in the mandatory class (Detector Construction).For this study, physics process was defined in the other mandatory class (Physics List).For gamma rays, Compton scattering, photo electric absorption, pair production and Rayleigh (coherent) scattering processes are defined with valid energy range down to 250 eV.The definition is also disk to include electrons and positron multiple scattering, ionization and bremmsstrahlung processes.Atomic effects after photoelectric effect, as X-rays emission and Auger effect are included.Two Sensitive Detector classes, one for HPGe detector and one for CsI(Tl) scintillator were built.Registration of interesting processes is made in Stepping Action class.Algorithm for generating computing efficiency was implemented in (Run Action) class.

RESULTS AND DISCUSSION
The full model of efficiency calculation and efficiency transfer has been written in ten user classes: three user mandatory classes and some user action classes are   written.Registration of interesting processes is made in Stepping Action class.In Run Action class the simplified algorithm for computing efficiency was implemented.The detector system was modelled in both the suppressed and unsuppressed modes.In the unsuppressed mode, the coincidence registering (sensitive detector) of the surrounding CsI is turned off.While for the suppressed mode, a photon hit in the HPGe detector is triggered if a hit in the NaI detector does not occur within the same event.Both the HPGe and CsI detectors were set as sensitive detectors in the model and photon hits in each were collected using the G4HCofThisEvent class.
The principle of calculating full-energy peak efficiency is started by initialization of the decay process; then the deposited energy of each photon in the detector is summed after completing the photon tracking.The tracking of a single photon is stopped when it leaves the volume of interest or when the energy of photon becomes lower than a specified threshold value called cut-off energy.Consequently, a realistic spectrum of energy deposited in the detectors is obtained through simulation and the experimental efficiency can be compared to the simulated one so-called apparent efficiency obtained by calculating the peak area, after correcting for the continuum to match the measured one.
The efficiency of the investigated Compton suppression -spectrometer was generated using Geant-4 model for both isotropical point source and volume source, placed at five different positions ( A, B, C, D, E) of the spectrometer as shown in Figure 2. The visualization model of the investigated Compton suppression spectrometer generated by Geant-4 is shown in Figure 3.Total of 10 6 events for each energy for each different source positions, from 200 to 3000 keV, were utilized to determine system efficiency.The summation effects are also considered a source of errors in the simulated efficiency values.This effect appears at 60 Co (1173.2, 13323.5 keV).Geant 4 code has been applied to correct these summation and to improve their values of peak efficiencies.
The first round of simulations was performed using a point source.Variation of photo-peak efficiency in cases of including CsI (Tl) scintillator as a suppressed mode to the detection system at different positions is shown in Figure 4.The trend is same for various gamma ray energies (356.5;661.6; 1173.2;1332.5)but is more pronounced for lower gamma ray energies than higher energies as presented in Table 2.
The second round of simulations was performed using a disk source.The variation of simulated efficiency in the two spectrometer cases is shown in Figure 5 and presented in Table 3.It is clear from Tables 2 and 3 that the efficiency in the suppressed mode is lower.This is largely due to the coincidence detection of two different photopeak photons from the same source, in a time frame shorter than the timing resolution of the detector system.
The applicability of the efficiency transfer in various measurement geometries on the basis of the simulated efficiency for reference point source geometry can be applied successfully.The detector efficiency was calculated for the same locations of the point sources and also for the disk sources.Figure 6 shows relation between point and disk source.It is clear that there is an increase at 1000 to 14500 keV in comparison with the fitting.It returns to the coincidence summing effects of 60 Co (1173.2, 13323.5 keV) for the transformation between point and bulk samples.The transfer efficiency is computed for discreet values of the fitted efficiency data of point source to derive new efficiencies values for a disk source which can be applied successfully to transfer efficiency data between the two geometries as presented in Table 4.

Conclusion
Monte Carlo simulation is a powerful tool in designing and calibrating different types of detection system and spectrometers.The applicability of this method is greatly dependent on the accuracy of detector geometry model.Additionally, the geometry, composition and density distribution of the sample matrix may be particularly important in models used for low level background.The Geant-4simulation toolkit was used to model a simplified Compton-suppression spectrometer operating in both the suppressed and unsuppressed mode to determine the photo peak efficiencies incident gamma energy in a range 200 to 3000 keV.The simulations show that the efficiency in the suppressed detector mode is lower than anti-suppression mode.This is largely due to the coincidence detection of two different photons from the same source which is not within the analyzer time period.The simulated efficiency values for point as well as for disk sources at different position can be mathematically

Figure 2 .
Figure 2. Detected source at different positions.

Figure 3 .
Figure 3. Visualization model of the detection system.

Figure 6 .
Figure 6.Mathematical efficiency transfer relation between point and disk sources.

Table 1 .
Summary of the components and dimensions of the HPGe detector provided by the manufacturer.

Table 2 .
Simulated photopeak efficiency for a point source at various positions.

Table 3 .
Simulated photopeak efficiency for disk source at various positions.

Table 4 .
Photopeak efficiency transfer between point and disk sources.