**CIENCIAS NUCLEARES**

**Monte Carlo simulation of the efficiency response
of a well-type HPGe detector at 46.54 keV**

** **

**Simulación por Monte Carlo de la respuesta en eficiencia
de un detector HPGe tipo pozo a la energía de 46.54 keV**

**Yasser Morera Gómez ^{1-4}, Héctor A. Cartas Águila^{1},**

**Carlos M. Alonso Hernández**

^{1},**José L. Bernal Castillo**

^{2-3}, Aniel Guillén Arruebarrena^{1}^{1}Centro de Estudios Ambientales de Cienfuegos. Cienfuegos, Cuba

^{2}Instituto Superior de Tecnologías y Ciencias Aplicadas (InSTEC)

Ave. Salvador Allende y Luaces. La Habana, Cuba

^{3}Instituto de Física, Universidad de Sao Paulo, Sao Paulo, Brasil

^{4}Departamento de Química y Edafología. Universidad de Navarra, España

ymore24@gmail.com

yasser@ceac.cu

**ABSTRACT**

In this paper, we used the Monte Carlo simulations method in a well-type HPGe detector using directly
the manufacturer supplied data in order to simulate the effi ciency response at 46.54 keV. The
efficiency values were calculated as a function of the filling height of the sample into the measurement
geometry and results were found in good agreement with experimental data. The main deviations
were less than 2.5 % with a mean of 0.9 %, which is totally satisfactory for the purposes of environmental
samples measurements. We also present a brief discussion about the response of the detector

to different values of its geometric parameters.

**Key words: **high-purity Ge detectors; Monte Carlo method; calibration; accuracy; efficiency.

**RESUMEN**

En el trabajo se utilizaron los métodos de simulación por Monte Carlo en un detector HPGe tipo pozo, usando directamente los parámetros del fabricante para simular la respuesta en eficiencia a la energía de 46.54 keV. Los valores de efi ciencia se calcularon en función de la altura de la muestra en la geometría de medición y los resultados se correspondieron con los valores experimentales. Las mayores diferencias fueron menores que el 2.5 % con un promedio de 0.9 %, lo que es totalmente satisfactorio para la medición de muestras ambientales. Se presentó una breve discusión sobre la respuesta del detector para diferentes parámetros geométrico.

**Palabras claves:** detectores de Ge ultrapuro; método de Monte Carlo; calibración; precisión; eficiencia

**INTRODUCTION**

Well-type HPGe detectors are very useful for radionuclide activities quantification in small environmental samples, especially when low energy photons are to be measured, because the near 4 geometry results in a high counting efficiency and a lower limit of detection. For example, these detectors are widely used for detections of the naturally occurring (T1/2 = 22.3 years) via its 46.5 keV (4 %) gamma ray [1,2]. has numerous applications in atmospheric, oceanography and marine geology research [3–5]. However, in lots of these studies, the available sample mass is limited so it is essential to have an accurate efficiency calibration at the given energy, which often requires a large experimental work because it is necessary to take into account the coincidence summing and self-absorption effects [6–8].

In these cases, Monte Carlo (MC) simulations could be a potential tool to replace or complement the calibration processes. However, the MC calculations require a precise knowledge about the characteristics of the detector and sample [9]. Generally, the efficiency values obtained experimentally and by MC simulation based on nominal values of the parameters supplied by the manufacturer show signifi cant differences due to the inaccuracy in some critical parameter such as the thickness of the dead cap, the relative position of the Ge crystal and the active volume [10,11]. In many cases the optimization of these parameters can result in a substantial decrease of the deviations between the experimental and calculated values [12–14]. However, even when precise geometrical data are available, it is necessary to refine the model by feeding it back with experimental results when accuracy is desired. This is because some parameters involved in the response of the detector cannot easily be assessed. They include the distribution of the electrical fi eld in the crystal and its mounting [15] and the dimensions and properties of the dead layers [16].

In this work we focused on the MC efficiency calibration
of a well-type HPGe detector for the measurement
in small environmental samples. The main purpose
of this work is to show that the efficiency calibration at
46.54 keV by MC simulation provides accurate results
for small sample volumes even when an environmental
sample is studied. We aim to verify the accuracy of
the calculated values to extend the use of the detector
model and MC calculations to other environmental matrices.
In order to refine the model we made an analysis
of the detector’s response to different values of some of
its geometric parameters.

**MATERIALS AND METHODS **

We used the MC code MCNPX 2.6 to build a welltype HPGe detector model just using the data supplied by the manufacturer. In a second step, we calculated the efficiency values for different filling heights of the sample into the measurement geometry. This procedure was applied for the Certificated Reference Material DL- 1a and results were compared with experimental efficiency values obtained from activity reported for this material [17].

**Detector: **We used a Canberra HPGe well detector
model EGPC100 P-15, with an absolute efficiency
of 12.1% at 661 keV and a resolution (FWHM) of 1.15
keV at 122 keV and 1.86 keV at 1332 keV. This detector
is surrounded by a cylindrical low-background chamber
made with the following elements: 240 mm of steel,
37 mm of lead, 1 mm of copper and 1 mm of aluminum
from outside to the inner region. The data acquisition
system consists of a PSC822 preamplifier, Canberra
amplifier model 7245 and electronic card MCA 5000
which includes a 7602 ADC with 8192 channels and InterFast
multichannel analyzer connected to a PC. The
spectra were recorded and analyzed using Winner 6.0
software.

**Experimental efficiency determination:** In order to
calculate the efficiency values of the well-type HPGe
detector at 46.54 keV for different sample volumes, the
Certified Uranium-Thorium Reference Ore DL-1a was
measurement as a function of the filling height *h*(*cm*) of
the sample into the measurement geometry. The geometry
is a cylindrical polystyrene vial of 4.5 and internal
diameter of 1 cm, placed in the well of the detector
as shown in figure 1. The vial was virtually divided into
9 sections (0.5 cm each of them) for the measurement.
For each section, the experimental efficiency value e (h)
was calculated considering the activity concentration of
reported for DL-1a (1.40 ± 0.02 Bq/g) and
mass of the sample packed , according to the
following equation:

where* T* (*h*) is the experimental count rate (s-1) and is
the gamma decay probability at 46.54 keV for .

**Monte Carlo simulation: **At present work, the MC
code MCNPX 2.6 was applied to calculate the efficiency
values of the well detector at 46.54 keV just using the
nominal values of the parameters supplied by the manufacturer.
Table 1 shows the values of these parameters
and vial’s dimensions. For the thickness of the internal
dead cap we considered 50 nm. Metallic conductors
were not taken into account because its influence is negligible
at low energies in well configuration. We used
the pulse-height tally (F8) per photons emitted from the
source to compute the absolute efficiency and we generally
obtained relative errors lower than 0.1 %.

The chemical composition reported for DL-1a [17] was used for the matrix implementation during the MC simulation processes. The results obtained by MC calculation were compared with the experimental values in order to verify the accuracy of the calculated values using the detector model.

**RESULTS AND DISCUSSION**

Figure 2 shows the measured and calculated efficiency for DL-1a as a function of the filling height of the sample into the measurement geometry. As we can see, there is a good agreement between measured and calculated efficiency. The main deviations do not exceed 2.5 % with a mean of 0.9 %. For all heights considered, the measurement uncertainty is greater than the difference between the measured and calculated values, therefore, these values do not show significant differences [18]. For this result, we just used the manufacturer’s supplied data. Nevertheless we obtained a very good result for an environmental sample. This is not always the case at such a low energy. Significant discrepancies have been reported in many works when the manufacturer’s data is directly used [12,19]. In these cases, it is necessary to explore the sensitivity of the simulation to geometrical parameters of the detector or to optimize the simulation within the expected uncertainties associated with these ones.

At the energy of 46.54 keV in well configuration, the most significant parameters to take into account during MC calculation are those which can change the solid angle of the source-detector geometry. The thickness of the internal dead cap (ion implanted) for the detector considered here is around 50 nm and slight changes in this parameter can be neglected [20]. Figures 3 and 4 show the behavior of the calculated efficiency for different values in two parameters i.e., the diameter of the Ge well and the distance between Al end cap and the Ge crystal. As it can be noticed, the largest deviations are observed for heights greater than 3 cm. However, the deviations related to nominal values are less than 2 %. Therefore, the detector model is sufficient to describe the efficiency response at this energy in the well configuration by MC calculations.

In order to obtain an efficiency calibration for the entire range of heights, the calculated efficiency values can be fitted to a third-degree polynomial function. Following this approximation we can calculate the efficiency at a given height (h) according to the equation,

with = 0.998

The efficiency dependence on the filling height as a cubic function is driven by the self-absorption of the photons in the used Reference Ore and the solid angle of measurement. With the increase of the filling height the self-absorption effect is more significant due to the increase of sample mass, at the same time the solid angle decrease.

This calibration is very useful in the laboratory when the amount of the sample to be analyzed is insufficient to complete the measurement geometry and is necessary to be interpolated between two heights of the sample under study [7, 21, 22].

Following the procedure described above the detector model can be used in the MC efficiency calculation with other environmental matrices in the same configurations and energy used here.

**CONCLUSIONS**

In this work, we applied the MC simulations methods to a well-type HPGe detector using the nominal values of the parameters supplied by the manufacturer. These calculations reproduced the experimental efficiency values at 46.54 keV for different volumes of the Certificated Reference Material DL-1a with a mean deviation of 0.9 %. Furthermore, we found that it is not necessary to optimize the geometrical characteristics of the detector for the MC efficiency calibration at this energy in the well configuration. Now, the detector model and MC calculations obtained in this paper can be used in the laboratory to complement the efficiency calibrations processes when small environmental sample are to be measured. Moreover, the simple procedure described here can be applied to other well-type HPGe detectors in the well configuration.

**Acknowledgements**

This research work was under taken in the framework of the IAEA TC Project CUB/7/008 “Strengthening the National System for Analysis of the Risks and Vulnerability of Cuba’s Coastal Zone through the Application of Nuclear and Isotopic Techniques”. The authors hereby would like to acknowledge the EJDS program at ICTP.

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**Received: **October 15, 2014

**Accepted:** April 23, 2015