Response function simulation of the anti-coincidence detector based on NaI crystal with a complex shape in registration systems for the experiments SAGE and BEST

Response function simulation using Geant 4 for the detector based on NaI crystal of complex shape in registration systems for the SAGE and BEST experiments is presented. Cylindric NaI crystal has a large well for placing up to eight proportional counters. The detector is using as anti-coincidence shield for counters and an instrument for analysis of different γ-rays sources. The result of detector response function simulation for different background sources and their registration efficiency are given.


Introduction
Scintillation detectors based on NaI(Tl) crystals are used as anti-coincidence shield in lowbackground counting systems for radiochemical solar neutrino experiments, such as SAGE [1,2,3] and calibration experiments with artificial neutrino sources [4,5] based on SAGE also. In these experiments rare events of 71 Ge decays are registered inside small proportional counters in lowbackground environment during very long time. Scintillation detector has a well of cylindrical shape, where up to eight proportional counters can be placed simultaneously. 71 Ge itself does not produces any γ-rays at its decay. So, any event with arbitrary energy, which is registered by scintillation detector in coincidence with event in proportional counter is a background. From this point of view the role of anti-coincidence system is trivial. Nevertheless, there are few e-capture isotopes, which produces γ-rays at their decay and which has an interest either as background with cosmogenics nature ( 69 Ge and 68 Ga (daughter of 68 Ge decay)) or decay itself ( 127 Xe as a product of solar neutrinos interaction with nuclei of iodine target). In all pointed above cases it's necessary to know the response function of the scintillation detector on γ-lines and efficiencies of full and partial absorptions for energies of all these sources. SAGE continues to run nowadays. New Baksan Experiment on Sterile Transitions (BEST) [6] is proposed for detail investigation of so called "gallium anomaly" [7]. An active stage of preparation to BEST is ongoing in present time based on SAGE. The scheme of BEST assume 1 To whom any correspondence should be addressed. doubling of sample numbers with 71 Ge content compare to SAGE. Half of them will be measured by the SAGE counting system [1]. New counting system for BEST will provide a counting of second half of 71 Ge samples. It is completely compatible with SAGE counting system in all main parts, but its shield for proportional counters and scintillation detector for anti-coincidence system are developed anew. Therefore, knowledge of the response function and registration efficiencies of new scintillation detector are very important for further combine using of both systems in BEST.

Main objects of the job
Main objects of the job consists in following.
1. Build the model of real NaI(Tl)-based detector using Geant 4 simulation software and determine influence of its different components to the response function. 2. Find the model response on γ-sources ( 60 Co, 137 Cs and 22 Na) placed in calibration position and associate them with real calibration spectra. 3. Find the model response on γ-sources ( 40 K, 208 Tl and 214 Bi) uniformly distributed in the detector volume and associate them with real background spectra. 4. Find the model response on gamma-sources ( 68 Ga, 69 Ge and 127 Xe) placed in the position of proportional counter inside the detector well. 5. Calculate efficiencies of full and partial absorptions for energies of all these sources in the detector. 6. Determine possible sources of increased background of the detector. 7. Explain some peculiarities of measured spectra.

The detector description
The detector is based on NaI(Tl) scintillation assembly, developed and produced by "Amkris" (Kharkov, Ukraine) according to technical task from INR RAS. It has cylindrical shape ∅200×200 mm with large well ∅100×150 mm. The detector is developed as low background device. So, the envelope and all main parts of the detector made of stainless steel. Teflon is used as light reflector. The detector volume is viewed through four quartz windows by 3-inch photomultipliers (PMTs) model ET9757QL. Volume of the detector is 5105.1 cm 3 , mass is 18.74 kg.

The model description
The detector model is developed using Geant 4 simulation software (patch 10.2.0) 2 . The model includes next objects (or "volumes"): NaI(Tl) crystal, reflector (Teflon), damper (Teflon), stainless steel case, quartz windows, copper elements of passive shield described above.
Software description of mentioned "volumes" is maintained in DetectorConstruction file. Sensitive volume of the detector is defined by SensitiveDetector function which is created by subroutine of the same name. SensitiveDetector function accepts a parameter in the form of defined "volume" and creates sensitive region for calculation of energy loss produced by ionization particle. Calculation of energy loss and type of secondary particles is provided by DetHit and DetEventAction subroutines. Registered portion of energy is stored in corresponding bin of histogram, which is recorded to ASCII data file at the end of simulation for further analysis.
The physics of processes and interactions is provided by DetPhysicsList subroutine, which includes the library G4EMLOW6.48 with data files of low energy electromagnetic processes. The "Livermore physics" is used as a model of interactions in our case. Based on [8] the library G4RadioactiveDecay4.3.2 with data files of radioactive decay and hadronic processes is included also for modeling radioactive decay of different nuclei.
Radioactive source in any form is created by subroutine DetPrimaryGeneratorAction. This subroutine was modified for using together with The General Particle Source (GPS) system. This system of commands allows to generate a source of different shape, size and activity. For applying of these commands enough to create a special macros and changes in this macros does not requires recompiling the whole project. Using GPS, the ions of all mentioned in section 2 isotopes were generated.
For graphical presentation of the detector model OpenGL libraries are used. At the same time the files of special format .heprep are created. These files contains information about coordinates of "volumes" used in the model, coordinates of particle tracks and information about their nature. This type of files is intended for visualization system HepRep (Generic Interface Definition for HEP Event Display Representables). HepRep system allows to work with the graphical model of the detector and tracks of particles off-line.

Result
Calibration spectra of the detector are shown on figure 2. Efficiencies of registration for calibration sources are given in table 1. Calibration procedure carried out using sources without collimation at 1 m distance from the bottom along the detector axis. The detector was located inside "intermediate" copper shield (see section 3) in position above opened passive shield of the counting system (massive construction of lead and steel). The detector model does not includes many of these instants. Also, the model does not maintains now the processes of light collection and absorption inside the detector volume with simplification purpose. So, there is some difference between real and model spectra outside the peaks of full absorption. But inside the peaks conformity is sufficient and information about energy scale and resolution was taken from here. The values of efficiencies in this case are small because of long distance to the sources. The last column in table 1 represents the efficiencies of partial absorption with any energy release in the detector volume.
The background spectrum, basic model background components and their superposition are shown on figure 3. The detector was enclosed inside passive shield. All model components are uniformly distributed over the detector volume except 40 K. It has two sources. First one is located on the surface of quartz windows (imitation of the PMTs background). Second one is distributed over NaI(Tl) volume. The aim is investigation of reasons of increased  detector background compare to the same in the counting system for SAGE. In a case of 214 Bi isotope only γ-lines with the probability of occurrence more than 1% were generated 3 . This was done to reduce total computing time. Again, there is some difference between real and model spectra outside the peaks, in primary at low energies. Comparison of the shapes of 40 K background components shows that its origin is disposed mainly in the PMTs, not in the the detector volume itself. Otherwise the peak for energy 609 keV from 214 Bi would be invisible. It is one of the reasons to replace the PMTs in near future. Modeling is shown that 208 Tl background γ-source ( 232 Th origin) have not peak of full absorption it the detector of such geometry, therefore its peak is invisible on real background spectrum. The model response on different γ-sources in a place of proportional counter is shown on figure 4. Geometry and positioning of the sources inside the detector well corresponds to the same for proportional counter. Calculated efficiencies of registration for these sources are given in table 2. Data in the last column has the same sense as in table 1. Modeling is shown that complex geometry of the detector does not prevents one to count these sources with high enough efficiency. Given result should be compared with real data from the counter filled with 69 Ge and 127 Xe contamination in the future.

Conclusion
The job is mainly done with the detector of the registration system for BEST, but model can be easy applied to the detector of the SAGE registration system with corresponding adjustment. This is only the beginning of a large job. It will be continue for the detector of the SAGE registration system, which has another geometry, shield and environment. These results are important for further using of both systems in BEST.