1]organization=Department of Physics, Indian Institute of Technology Ropar,
Rupnagar - 140 001, Punjab, India

[orcid=0000-0003-3813-4322] [1]Pushpendra P. Singh

# Spectroscopic performance evaluation and modeling of a low background HPGe
detector using GEANT4

Swati Thakur  Soni Devi  Sanjeet S. Kaintura  Katyayni Tiwari  Pushpendra P.
Singh<EMAIL_ADDRESS>
###### Abstract

Low background gamma spectrometry employing HPGe detectors is a sensitive
technique for measuring low-level radioactivity in environmental applications,
material screening, and for rare decay searches. This work presents
spectroscopic performance evaluation and modelling of a low background
measurement setup developed at IIT Ropar in Punjab, India, to measure trace
natural radioactive elements, with a particular interest in studying low-level
radioactivity in soil and/or rock samples to generate specific inputs for low
background experiments. The performance test and characterization of a low
background cryocooled HPGe detector with relative efficiency of $\sim$33% have
been carried out. An effective detector model has been developed using GEANT4
Monte Carlo simulation to determine the response of the detector over an
energy range of 80.9–1408 keV and compared with the experimental performance
of the detector. The response of the detector obtained using Monte Carlo
simulations agrees reasonably well within 93% level of confidence, indicating
only 7% deviation in the comparison. The present setup offers improved
detection limits of primordial radionuclides (U/Th and K) to measure
radioactive contamination in environmental matrices, which has been used
elsewhere [1].

###### keywords:

Carbon loaded HPGe detector, Detector scanning, and characterization, GEANT4,
Monte Carlo simulation, Gamma-ray spectroscopy, Low background measurements
Environmental radioactivity, Soil sample analysis

##  1 Introduction

Gamma spectroscopy setups employing low background HPGe spectrometers play an
increasingly important role in measurements of environmental radioactivity and
material selection for rare event experiments [2, 3, 4, 5, 6, 7, 8]. The
experimental sensitivity of these low background measurements depends
critically on the identification and minimization of confounding background.
In above-ground measurements, the background is mainly dominated by cosmic
rays and cosmic ray-induced interactions, cosmogenic radionuclides (T1/2
$\sim$ d–y), primordial radioactivity consisting of gamma-ray radiation from
natural decay chains of 238U, 232Th and 40K (T1/2 $\sim$ $10^{8}$–$10^{10}$ y)
in and around the detector setup material, airborne radioactivity of radon and
its progeny and the detector itself is the source of $\alpha$, $\beta$,
$\gamma$ and neutrons background [7]. The environmental radioactivity
originating from naturally occurring radionuclides, namely; 238U, 232Th, and
40K are long-lived ($T_{1/2}$ $\sim$$10^{8}$ \- $10^{10}$ y) and present in
trace amounts in the earth crust. The gamma-ray background from these
naturally occurring radionuclides is a significant source of radiation
exposure for above-ground laboratories. Measurement at the environmental level
deals with low radioactivity concentration and involves inherent complexity
due to the typical interference of natural radionuclides over a wide energy
range. Additionally, the gamma-ray flux is subject to variation, possibly due
to experiment location in the laboratory/site, seasonal fluctuations, the
radon concentration near the experimental setup, or unknown systematic
uncertainties. Background statistical fluctuations can influence the
assessment of peak identification, peak area calculations, energy resolution,
confined intervals, and detection limits. These background fluctuations can
cause differences in the precise determination of activity concentrations in
weak samples. For reliable estimation of the radioactive impurities, it is
necessary to identify and minimize the background to improve the minimum
detection limits of the spectrometer. Due to the typical interference of
natural radionuclides, it is essential to accurately estimate the background
level by measuring the concentration of the members of these decay chains and
their variation [9, 10].

In India, the proposals for a potential underground laboratory driven by the
interest in rare event studies have been initiated [11, 12, 13]. As mentioned
earlier, other than the ambient background from the surroundings, the material
of the counting detectors itself contributes to the background contamination
levels in rare event experiments. To improve the sensitivity of measurement
and accurately determine radio impurities, an essential prerequisite is low
radioactivity around the detector as much as possible. The low background
cryostats contribute miniature to the sample spectrum, improving its signal-
to-noise ratio and significantly reducing the Minimum detectable activity
(MDA). Therefore, the radiopure cryostat with selectively refined detector
construction materials and applying passive shielding allows for lower minimum
detectable activity and high sample throughput for a specific counting time,
which is highly desirable in low background counting applications.
Furthermore, cryocooler-based low background HPGe detectors are desirable for
probing low background experiments in above-ground or remote underground
locations for long-term counting measurements. To maximize the counting
efficiency for investigating trace radioactive elements, it is necessary to
understand the detector performance in compact geometry over a wide energy
range and different counting setup configurations.

With this motivation, we have taken up the initiative to build a low
background measurement setup at the Indian Institute of Technology (IIT) Ropar
using the HPGe detectors. This setup is intended for radio-purity assessment
and understanding of the radiation background at IIT Ropar to carry out low
background experiments. This paper describes the performance test and
characterization of a low background carbon fiber HPGe detector with a
relative efficiency (R.E.) of $\sim$33%. The first set of studies presents
detector characterization with radioactive sources over a wide energy range
from 80.9–1408 keV. The performance specifications are successfully tested
against the warranted values provided by the manufacturer. Measurements have
been performed with point-like sources to calculate the peak shape, Peak-to-
Compton ratio (P/C), Full energy peak efficiency (FEPE), and Figure of merit
(FOM). Mono-energetic sources are used to perform close scanning of Ge crystal
along its parallel and perpendicular axis to determine the inner crystal
structure. A Monte Carlo model has been developed using GEANT4 to calculate
the FEPE of the HPGe detector for gamma spectrometry measurements associated
with the development of a low background setup. It has been observed that
germanium crystal volume and dead layers in the surroundings are crucial
parameters in the detector geometry [14, 15]. Over the operational lifespan of
the detector, the continuous diffusion of lithium ions into the germanium
crystal leads to an increase in the dead layer thickness and a decrease in the
active volume of the detector. Previous literature has reported a significant
deviation of 10$\%$–30$\%$ between the experimental and simulated FEPE
efficiencies in the energy range of 60-2000 keV [15, 16, 17, 18]. In order to
validate a simulation code, the detector has been optimized, which typically
involves adjusting various detector parameters, such as the dimensions, dead
layer thickness, and other relevant factors. The second set of studies
characterizes the natural gamma-ray background during long counting
measurement and its further reduction by incorporating a Pb shield at the
above-ground laboratory of IIT Ropar. The organized statistical data on this
topic would be valuable for inter-laboratory comparisons and unique in
different geological and geographical conditions than the rest of the studied
areas, especially quantifying low-level natural radioactivity. The activity
concentration and Minimum detectable activity (MDA) for common radioisotopes
in environmental samples are evaluated. The presentation of this paper is
organized as follows, section 2 describes the experimental setup and procedure
details, section 3 discusses the experimental characterization, detector
modelling, comparison with simulated data, and spectroscopy measurements for
characterizing background distributions. The summary and conclusions are given
in section 4.

##  2 Experimental setup and Methodology

The experimental setup (ILM-0) comprises of p-type co-axial HPGe detector,
ORTEC make (GEM30P4-83-RB) with a measured relative efficiency of 33% having a
crystal diameter of 62 mm and thickness of 46 mm. The detector crystal is
mounted inside a cryostat of low background carbon fiber (carbon-composite)
body, and the top face is 5 mm beneath a 0.9 mm thick carbon fiber entrance
window. The rear end of the detector is attached to the $\sim$ 150 mm long
vertical cold finger connected to the transfer hose of an electro-mechanical
cooler (ORTEC X-Cooler III) to cool the detector crystal to liquid nitrogen
(LN2) temperature (77 K). The typical cooldown time required by the electro-
mechanical cooler is found to be 10-16 h. The detector assembly is supported
with additional online UPS to protect during utility power failure. The HPGe
detector is surrounded by moderate passive shielding with lead bricks of
dimensions $22.9~{}\textrm{cm}\times 7.6~{}\textrm{cm}\times
5.1~{}\textrm{cm}$ and mounted on a custom-made stainless steel (SS) table, as
shown in Figure 1. In this arrangement, the detector with a preamplifier is
entirely shielded with adequate space for mounting voluminous samples
generally used in environmental radioactivity measurements. In addition, it
has a provision for an inner layer of passive shielding and an active muon
veto. It should be mentioned that different shapes and configurations of the
lead shields were also considered before the final implementation of bricks
geometry.

Figure 1: Schematic cross-section of the experimental setup of ILM-0 (IIT
Ropar Low Background Measurement setup). The soil sample is mounted on the
face of the detector, and the setup is placed on a thick stainless steel (SS)
table 1 m above the ground.

The detector is coupled with the pulse processing electronics and data
acquisition system, including a NIM-based high voltage power supply,
spectroscopic amplifier, and multichannel analyzer procured from ORTEC. The
multichannel analyzer records the data using the emulator software Maestro. A
list of relevant technical details, along with the associated electronics, are
summarized in Table 1.

Table 1: Technical specifications of the HPGe detector supplied by the manufacturer. Model | GEM30P4-83-RB
---|---
Manufacturer | ORTEC
In service since | 2017
Capsule type | Pop top
HV Bias | +2800 V
Crystal polarity | p-type
DAQ | Analog
Shaping time | 6 $\mu$s
Geometry | Closed end
Cryostat type | Vertical dipstick
Cryostat diameter | 75 mm
Crytal diameter | 62 mm

The characterization measurements have been carried out using a set of
standard sealed disk-type gamma sources of the active diameter of $\sim$6 mm
and thickness of $\sim$1 mm with absolute strength of gamma sources $\leq$95
kBq within 5% uncertainty. These sources cover a gamma ray energy range from
80.9 keV to 1408 keV, as shown in Table 2.

Table 2: Radioactive gamma-ray sources used in the measurements. Sources | Gamma | Decay | Half- | Branching
---|---|---|---|---
| Energy | mode | life | Ratio
| (keV) |  |  | (%)
109Cd | 88.0 | EC | 461.4 d | 3.64
57Co | 122.1 | $\beta^{-}$ | 271.7 d | 85.60
| 136.5 | $\beta^{-}$ |  | 10.68
133Ba | 80.9 | EC | 10.5 y | 32.90
| 276.4 |  |  | 7.160
| 302.9 |  |  | 18.34
| 356.0 |  |  | 62.05
| 383.9 |  |  | 8.940
22Na | 511.0 | $\beta^{+}$ | 2.6 y | 180.7
| 1274.5 |  |  | 99.94
137Cs | 661.7 | $\beta^{-}$ | 30.1 y | 85.10
54Mn | 834.5 | EC | 312.2 d | 99.98
65Zn | 1115.5 | EC | 243.9 d | 50.04
60Co | 1173.2 | $\beta^{-}$ | 1925.3 d | 99.85
| 1332.5 |  |  | 99.98
152Eu | 121.7 | EC | 13.5 y | 28.53
| 244.7 | EC |  | 7.550
| 344.4 | $\beta^{-}$ |  | 26.60
| 411.1 | $\beta^{-}$ |  | 2.240
| 444.0 | EC |  | 0.298
| 779.0 | $\beta^{-}$ |  | 12.93
| 867.4 | EC |  | 4.230
| 964.0 | EC |  | 14.51
| 1085.8 | EC |  | 10.11
| 1089.7 | $\beta^{-}$ |  | 1.734
| 1112.1 | EC |  | 13.67
| 1213.0 | EC |  | 1.415
| 1299.1 | $\beta^{-}$ |  | 1.633
| 1408.0 | EC |  | 20.87
Figure 2: A cross-sectional view of the detector with scanning directions
indicated.

Radiography with X-rays and gamma-rays is used to determine the detector
structure and its dimensions. However, an active volume may differ depending
upon the electric field configuration inside the crystal [19, 20, 21]. In the
present work, radiography is not possible, and hence mono-energetic gamma
sources are used to scan the crystal in the energy range of 88-1332.5 keV. In
order to characterize the detector geometry, three types of scans, namely, i)
Distance scan, ii) Radial scan, and iii) Lateral scan, have been performed
around the detector. The scanning schemes of the detector are demonstrated in
Figure 2. The radial and lateral scans were carried out using 57Co, 60Co,
137Cs, 54Mn, 65Zn and 109Cd gamma sources, see Table 2 for the reference
energies. The radial scan was performed by moving the source parallel to the
top detector face at a distance of 10 mm from the top face of the detector
endcap (Carbon fiber window) in the position steps of 5 mm. It covered a range
of $\pm$ 6.5 cm w.r.t. the center of the detector. For the lateral scan, the
gamma source was moved parallel to its cylindrical axis at a distance of 10 mm
from the side face of the detector in 5 mm steps and covered a range of -2 cm
to 9 cm again w.r.t. the detector endcap. The distance scan was performed with
point-like sources at a regular interval from 5 cm to 30 cm along the axial
symmetry axis away from the top face of the detector. Typical uncertainty in
the positioning of the source in all scans is estimated to be $\leq$1 mm.
Since some of the parameters are unknown or maybe not even related to the
specific detector but are instead averaged over a set of detectors of the same
or similar type, generic parameters offered by the manufacturer are typically
insufficient. Therefore, parameters must be optimized. In order to determine
the actual value of the parameters, optimizations are made to the crystal
length (L), crystal radius (R), hole length ($L_{h}$), front gap, and dead
layers. Given relatively low source strengths, no pileup effects have been
observed in the spectra. Errors associated with the photopeak efficiency were
computed, including statistical and systematic errors. Typical errors obtained
in the present work were estimated to be $\sim$ 0.2% in radial/lateral scans
for $\textrm{E}_{\gamma}$ = 88 keV, $\sim$ 0.5% for $\textrm{E}_{\gamma}$ =
122.1 keV, $\sim$ 0.4% for $\textrm{E}_{\gamma}$ = 661.7 keV and $\sim$ 0.1%
for $\textrm{E}_{\gamma}$ = 1115.5 keV. It should be noted that the
statistical errors are mainly due to the difference in strengths of various
sources and energy-dependent variation in detection efficiency. Similarly,
scan errors in the experiment were $\sim$ 0.1% for the axial distances.
Measurements were also performed with multi-gamma sources such as 60Co, 152Eu
and 133Ba at z $\geq$ 10 cm to ensure that the coincidence summing is
negligible. Data have been acquired for at least 10,000 counts for
characterization measurements to reduce the statistical error to 1%. Detector
dead time has been monitored throughout the measurement and maintained to be
less than 1%. No significant worsening of energy resolution and shift in
energy was observed at different times of long counting measurements of soil
samples. The data of the background spectrum was recorded in a timestamp of 24
h. The raw data is then converted and analyzed using LAMPS [22] software. Each
photopeak is fitted to the sum of Gaussian and second-order polynomials for a
background to extract the net photopeak area.

Table 3: Typical clay loam composition of of soil samples [23]. Compound | Mass fraction | Compound | Mass fraction
---|---|---|---
SiO2 | 0.5890 | K2O | 0.0325
Al2O3 | 0.1625 | Na2O | 0.0235
Fe2O3 | 0.1340 | MgO | 0.0135
CaO | 0.0360 | TiO2 | 0.0090

##  3 Results and Analysis

###  3.1 Spectroscopic performance of the detector

The accuracy of the measurements depends profoundly on the performance and
stability of the detector and associated electronics. Different
characteristics of the HPGe detector, such as energy calibration and
resolution, peak shape and Peak-to-Compton ratio (P/C), Full energy peak
efficiency (FEPE), and Figure of Merit (FoM), are determined as a function of
gamma-ray energies against the warranted values provided by the manufacturer.
The radioactive gamma sources used in the scanning of the detector are given
in Table 2. For the present HPGe detector, R.E. was found to be 33 (0.3)% in
the laboratory test, which is 6% lower than the measured value provided by the
manufacturer. The HPGe detector has been calibrated using different standard
gamma sources and shown in Figure 3 (a). The line through the data points
represents a fitting function of type y = a + ${\textrm{b}}{{x}}$, where a =
0.4 $\pm$ 0.03 and b = 0.38185 $\pm$ 1.59279 $\times 10^{-5}$. As can be
noticed from this figure, a good linear relationship with the channel number
can be observed. The statistical correlation coefficient is found to be 1 for
each measured data point with the detector. The energy resolution measures the
width (FWHM) of a single energy peak at a specific energy, usually expressed
in keV for germanium detectors. It may be pointed out that the typical energy
resolution of NaI and HPGe detectors are found to be 50 keV and 1.5 keV at
1332.5 keV, respectively [24]. Hence, HPGe is preferred over NaI detectors for
high-resolution gamma-ray spectroscopy, even though the NaI is likely to have
greater counting efficiency. Generally, the energy resolution of a detector is
expressed as the ratio of FWHM to the gamma-ray energy. The distribution of
energy resolution with different gamma-rays is shown in Figure 3 (b) and
fitted to an empirical three-parameter function of type,

$\textrm{R}=\frac{{\textrm{A}}}{{\textrm{E}}^{{\textrm{B}}}}+\textrm{C}$ (1)

The best-fit values to the fitted parameters A, B, and C are 0.4 $\pm$ 0.03,
0.9 $\pm$ 0.01 and 6.42229 $\times 10^{-4}$ $\pm$ 3.43594 $\times 10^{-5}$,
where A and B are in keV. The typical energy resolution of this detector at
1332.5 keV is 1.72 keV and found to be similar to another LN2 based HPGe
detector of similar relative efficiency present in the laboratory. No
worsening of the energy resolution has been observed over the running period
of about five years. In addition to the FWHM taken at each peak, the full
width at one-fifth maximum (FW.2M), full width at one-tenth maximum (FW.1M),
and full width at one-fiftieth maximum (FW.02M) are also recorded to check for
the worsening of the tail.

---
Figure 3: Energy calibration and resolution of the HPGe detector are shown in
(a) and (b), respectively. The solid line through the data points is the best
fit.

The peak-to-Compton ratio has been measured from the same gamma line, 1332.5
keV, which has been used for the resolution measurement obtained from 60Co
source. The value of this ratio was measured at various axial distances, and
the mean value of the peak-to-Compton ratio was found to be 62:1, following
the manufacturer data.

The efficiency calibration of a spectrometer is of great importance in
analyzing radionuclides of interest. Different physical parameters, such as;
the crystal volume and shape, source dimensions, gamma-ray absorption cross-
section, attenuation layers in front of the detector, and the distance and
position from the source to the detector, determine the efficiency of the
detector [19, 20, 25]. Absolute efficiency, also known as full energy peak
efficiency (FEPE), is defined as the ratio of the number of photopeak counts
detected to the total number emitted by the source and can be determined
according to the following equation:

$\varepsilon=\frac{\textrm{N${}_{\gamma}$}}{\textrm{A${}_{\gamma}$}\ast\textrm{I${}_{\gamma}$}\ast\textrm{t}}$
(2)

Where Nγ is the net photopeak area (background subtracted), Aγ is the present
activity of source (Bq), Iγ is the gamma-ray emission probability. t is the
time elapsed (taking into account the analyzer counting losses). Figure 4
shows the efficiency measurements for all the considered gamma-ray energies at
a distance of 25 cm.

Figure 4: Efficiency calibration curve of the HPGe detector at source to
detector distance of 25 cm.

The quoted errors may be due to the number of counts in the photopeak
(statistical) and source activities (systematic). As shown in Figure 4, the
solid line through the data points represents the best fit to the data. The
efficiency curve is fitted using an inverse square fitting function of type,

$\textrm{$\varepsilon$}=\textrm{A}+\frac{\textrm{B}}{\textrm{E}}+\frac{\textrm{C}}{\textrm{E}^{{2}}}$
(3)

where $\varepsilon$ is the photopeak efficiency, and E is the gamma-ray
energy. The best-fit values to the fitted parameters A, B, and C are found to
be 1.23209 $\times 10^{-5}$ $\pm$ 0.91263 $\times 10^{-5}$, 0.5 $\pm$ 0.01 and
-30 $\pm$ 1\. The fitting function yields good approximations over different
energy ranges and for different crystal sizes. As can be noticed from the
figure, some fluctuations in the data points are primarily due to variations
in peak shape and low count rates. The HPGe detector has a closed-end coaxial
configuration of p-type material and a thick attenuation layer at the detector
entrance contact. Correspondingly, the detector’s efficiency was found to be
less for low energy gamma-rays below 80.9 keV as clearly visible in Figure 4.
The efficiency curve shows a rapid increase from 80.9 keV of 133Ba source,
peaks at 121.8 keV of 152Eu, and sharply decreases as a result of an increase
in gamma-ray energy. This implies that the efficiency is maximum at low energy
and decreases exponentially at higher emitted gamma-rays consistent with
similar detectors by ORTEC [17]. The efficiency curve demonstrates the
excellent performance of the measurements and analysis applied in this work.
Measurement of photopeak efficiencies using the above radioactive sources can
help better estimate the detector’s active volume and surrounding materials.

###  3.2 Detector modelling

The Monte Carlo simulation program was developed using the GEANT4 framework
(version 4.10.00.p02). The photopeak efficiencies have been estimated directly
by determining the energy deposition in the simulated volume of the detector.
The source-detector geometry, as shown in Figure 2, has been implemented using
the information provided by the manufacturer. The primary particles were
generated from the input files using G4ParticleGenerator class. The 106
photons were generated uniformly from the radioactive source to keep the
statistical error below 1%. The photons cutoff energy was set at 1 keV using
the electromagnetic processes PhysicsList. The energy calibration obtained
from the experiments has been utilized to set up the energy bins in the
simulated spectra. In order to avoid summing effects, the photopeak
efficiencies were calculated using the mono-energetic sources at close
distances. The photons that entirely lose their energy in the active volume of
the detector are taken into account for evaluating photopeak efficiencies. The
efficiency at the given energy was calculated by generating the histogram for
a number of events against the energy deposited inside the active volume of
the crystal. The simulation results have been analyzed using the ROOT data
analysis framework. The simulated photopeak efficiency
($\varepsilon$${}^{\textrm{Sim}}$) has been determined from the stored energy
histograms using the following equation,

$\textrm{$\varepsilon$${}^{\textrm{Sim}}$}=\frac{\textrm{N${}_{c}$}}{\textrm{N${}_{g}$}}$
(4)

Where Nc is the number of photons that deposited energy in the crystal after
the background elimination and Ng is the number of photons generated. The
relative deviations ($\sigma$R) between simulated and experimental photopeak
efficiencies were calculated using equation 5, where n is the total number of
data points in each set corresponding to a specific energy and
$\textrm{r}_{i}$ represents the individual data points in the data set.

$\textrm{$\sigma$${}_{\textrm{R}}$}=\frac{1}{\textrm{n}}{\Sigma_{i=1}^{\textrm{n}}{\frac{{\textrm{$\varepsilon$${}^{\textrm{Exp}}$}(\textrm{$\textrm{r}_{i}$}})-{\textrm{$\varepsilon$${}^{\textrm{Sim}}$}(\textrm{r}_{i})}}{\textrm{$\varepsilon$${}^{\textrm{Sim}}$}(\textrm{r}_{i})}}}$
(5)

Equation 6 defines the total relative deviation ($\sigma$${}_{\textrm{TR}}$),
where m is the number of data sets that correspond to the various energy scans
and $\textrm{$\sigma$${}_{R}$}(\textrm{E}_{i})$ is the relative deviation
corresponding to the different energies.

$\textrm{$\sigma$${}_{\textrm{TR}}$}=\frac{1}{\textrm{m}}{\Sigma_{i=1}^{\textrm{m}}\textrm{$\sigma$${}_{\textrm{R}}$}(\textrm{E}_{i})}$
(6)

---
Figure 5: Relative deviation ($\sigma$R) as a function of (a) front gap (g)
and (b) crystal radius (R) for a radial scan with 1115.5 keV for the initial
estimate of g and R.

A polynomial function is used to fit the given data points and determine the
minimum value of $\sigma$${}_{\textrm{R}}$ that yields the optimal fit. As
low-order polynomials exhibit greater smoothness in comparison to high-order
polynomials, the parabolic $\sigma$${}_{\textrm{R}}$ = ${\textrm{a}}{{x}^{2}}$
\+ ${\textrm{b}}{{x}}$ \+ c function was used to fit the given data. As an
illustration, the best-fit values of front gap (g) and crystal radius (R) are
shown in Figure 5 (a) and Figure 5 (b), initial estimation was done using 65Zn
source.

####  3.2.1 Parametric study

Initially, the detector model was constructed according to the specifications
provided by the manufacturer. Step-by-step adjustments were carried out to
optimize the parameters, namely, crystal radius (R), hole depth (Lh), dead
layers (td, tb, and ts) and front gap (g) to obtain an effective detector
model (see Table 4).

Table 4: List of detector parameters, range, and step size used in the simulations. Parameters marked in $\oplus$ are unaltered in the present work. Parameter | Manufacturer | Varied from | Step size | Optimized
---|---|---|---|---
| (mm) | (mm) | (mm) | (mm)
Crystal Radius (R) | 31 | 25-31 | 0.5 | 29.53 $\pm$ 1.2
Hole radius⊕ (hr) | 5.55 | – | – | 5.55
Disc length (L1) | 6.12 | 5.3-6.1 | 0.1 | 5.83 $\pm$ 0.1
Hole length (Lh) | 33.7 | 30.4-34.4 | 0.4 | 32.4
Crystal length (L) | 46 | 42-46 | 1 | 44 $\pm$ 0.3
Top dead layer (td) | – | 0-2.6 | 0.3 | 1.8 $\pm$ 0.2
Side dead layer (ts)∗ | 0.7 | – | – | 1.7
Bottom dead layer (tb) | – | – | – | 2
Front gap (g) | 4 | 4-13 | 1 | 9 $\pm$ 1.0
Front carbon fiber⊕ | 0.9 | – | – | 0.9
Side carbon fiber⊕ | 1.6 | – | – | 1.6
Cu cup thickness⊕ | 0.8 | – | – | 0.8
Ge crystal volume (V) | 135 $\textrm{cm}^{3}$ | – | – | 120 $\pm$ 4.8 $\textrm{cm}^{3}$
∗ similar to CRADLE [26] |  |  |  |

To replicate the experimental data, the detector’s size must be optimized. The
two main dimensions that have a significant impact on volume are R, and L.
Crystal length (L) was constructed as solid and hollow cylinders and optimized
in two parts, namely, Disc length (L1) and hole depth (Lh) and optimized
independently. Low-energy gamma-rays are considered optimal for estimating the
thickness of the top dead layer (td) on a crystal, as this layer attenuates
gamma-rays. This has negligible effects on photopeak efficiencies at higher
energies. Therefore, 88 and 122.1 keV energies are used for top dead layer
determination. Depending on how long the detector has been in operation, it
can decrease its active volume. The manufacturer did not supply the td value.
Because both detectors are identical, the same side dead layer (ts) as CRADLE
[26] was implemented. A passive Ge dead layer with a thickness of b=L-Lopt is
introduced into the model when employing the manufacturer’s specified physical
length, L. In the simulation, uniform dead layers were employed. The effect of
air gap has significant effects on small source-detector distances. However,
influence can be considered negligible at large distances. It can also be
estimated better with low-energy gamma-rays. The results of the lateral scan,
as shown in Figure 7, indicate a significant deviation at the end side of the
crystal. However, this issue was successfully addressed after the integration
of the bottom dead layer into the model.

---
Figure 6: Simulated and experimental absolute photopeak efficiency as a
function of distance scan for 122.1 keV, 661.6 keV, 834.5 keV and 1115.5 keV
(a), (b), (c) and (d) respectively.
---
Figure 7: Simulated and experimental absolute photopeak efficiency as a
function of lateral scan for 122.1 keV, 661.6 keV, 834.5 keV and 1115.5 keV
(a),(b), (c) and (d) respectively.
---
Figure 8: Simulated and experimental absolute photopeak efficiency as a
function of radial scan for 122.1 keV, 661.6 keV, 834.5 keV and 1115.5 keV
(a), (b), (c) and (d) respectively.
---
Figure 9: (a) Comparison of simulated absolute photopeak efficiency using
optimized and nominal parameters with the experimental photopeak efficiency.
(b) Simulated and experimental absolute photopeak efficiency for 152Eu at
distances 10, 15, 25 cm.

Figure 6 to Figure 7 compares distance, radial, and lateral scan data for
gamma-rays of various energies with corresponding simulated data using the
optimized detector model. Figure 9 illustrates a comparison of the
experimental data with simulated efficiencies within the energy range of
88-1408 keV. It is observed that the measured value of 33% relative efficiency
of the detector corresponds to an active volume of about 120
${\textrm{cm}}^{3}$, which is 11% smaller than the manufacturer’s stated value
of 135 ${\textrm{cm}}^{3}$. As it is clear from the Figure 10 that
$\varepsilon$${}^{\textrm{Exp}}$ and $\varepsilon$${}^{\textrm{Sim}}$ using
the nominal parameters for E= 122.1-1115.5 keV at d = 5-25 cm produced a
significant $\sigma$${}_{\textrm{TR}}$ of 26.2%, which was reduced up to 7%
after optimisation.

Figure 10: Comparison of total relative deviation ($\sigma$TR) between nominal
and optimized parameters over an energy range of 88-1408 keV for d=5-25 cm.

###  3.3 Radioactivity measurements

The ambient background in the laboratory has been measured using an HPGe
detector without any shielding at different times since its installation to
check for possible changes in the background due to incoming and outgoing
materials (for impurity control), daily variations of radon concentration, and
aperiodic variations of cosmic rays intensity. From a typical gamma-ray
background spectrum recorded for 24 h, about 120 gamma lines were identified,
emitted from the uranium and thorium decay chains in the room environment
around the detector. The prominent radionuclides present in the spectra are
due to the airborne radioactivity of radon and its short-lived decay products,
i.e., the intermediate members of radioactive decay series of 238U and 232Th.
Day-wise investigations of full gamma-ray spectra have shown a considerable
variability of the areas of the 226Ra progeny lines (214Pb, 214Bi) in a range
of about 14-18%. In contrast, the gamma lines of 1460.8 keV and 2614.5 keV
from 40K and 208Tl, respectively, were comparatively constant within the
experimental uncertainty. The integral background from energy range of 40 keV
to 2700 keV is 5.9 $\times$ 105 /kg/h with a total count rate of 116
counts/day. Long background measurements were also performed to observe the
day-wise variation in the overall background and estimate the statistical
fluctuation in the prominent gamma peaks. Most of the variations were
attributed to radon dynamics in the laboratory, while the background count
rate over the energy region of 40–2700 keV is found to be similar. The
spectrometer exhibits good gain stability and negligible calibration drifts
($<$1 keV) over a long duration of measurements. A one-day ambient background
spectrum of HPGe detector without and with Pb shielding is shown as a
representative case in Figure 11. As a result of lead shielding, the overall
background has been significantly reduced from 116 to 2 counts/day in the
energy range of 40-2700 keV. The background rate for 1460.8 keV (40K) and
2614.5 keV (208Tl) lines is 634 and 443 counts/day, respectively. It can be
seen that the Pb shield effectively stops most of the gamma-ray from entering
the active volume of the detector crystal. At the same time, the reduction
ratio of the integration of the count rate depends on the gamma-ray energy.
The background reduction achieved has been compared with unshielded data for
major peaks and various energy ranges. The ratio is reduced to 1.2% at 40–600
keV. In the energy range from 40 to 2700 keV, the ratio is 1.7%. The photopeak
intensity reduction of major gamma lines visible in the unshielded setup has
been compared with a shielded setup as given in Table 5. For 228U, the
activity levels are reduced to 0.52% for 214Bi and 214Pb. In case of 232Th,
the ratios fluctuate between 0.25% and 2.46% for 208Tl and 0.57 % for 228Ac.
Photopeaks of 137Cs and 60Co are completely disappeared in the shielded setup.
The ratio of 40K is 1.14%, and the annihilation peak drops to 20.3% of its
original value without shielding.

---
Figure 11: Ambient gamma-ray background in ILM-0 with (red line) and without (black line) Pb shield (t = 1 d). Some of the intense gamma-ray lines corresponding to different radionuclides are marked. Table 5: Observed activity with and without Pb shield along with the reduction factor. Element | Energy | Without Shield (X) | With Shield (Y) | Reduction factor
---|---|---|---|---
| (keV) | (counts/day) | (counts/day) | Y/X(%)
212Pb | 238.6 | 37812(147) | 127(47) | 0.34(3)
214Pb | 295.3 | 16937(266) | 86(54) | 0.51(20)
214Pb | 351.9 | 31365(329) | 219(25) | 0.70(8)
208Tl/Ann. | 511.0 | 14956(903) | 3039(110) | 20.32(12)
208Tl | 583.2 | 21159(286) | 54(23) | 0.25(8)
214Bi | 609.3 | 32746(349) | 170(23) | 0.52(7)
137Cs | 661.7 | 858(98) | – | –
214Bi | 806.4 | 1084(139) | – | –
228Ac | 835.6 | 1356(133) | – | –
228Ac | 911.2 | 16609(232) | 94(28) | 0.57(12)
214Bi | 1120.3 | 9411(208) | 106(21) | 1.13(10)
60Co | 1173.2 | 654(130) | – | –
60Co | 1332.5 | 464(87) | – | –
40K | 1460.8 | 61137(834) | 700(37) | 1.14(4)
214Bi | 1764.5 | 8916(154) | 199(33) | 2.23(21)
208Tl | 2614.5 | 19101(400) | 469(31) | 2.64(8)

Ambient background in the shielded setup has been counted for a duration of 49
d over a span of 3 months. It should be mentioned that the stability of the
energy scale was monitored with background gamma-rays such as 1460.8 and
2614.5 keV, where calibration with standard sources was only sometimes
convenient due to heavy passive shielding. In summed gamma-ray background
spectra of 49 d besides gamma-rays emitted by natural radionuclides, another
source of background is generated by neutron interactions. The anthropogenic
radionuclides 137Cs and 60Co were found below detection limits and no
contribution from long-lived cosmogenically produced radionuclides, e.g.,
22Na, 60Co and 65Zn were observed. In above-ground low-level gamma
spectrometry systems, some peaks associated with the activation of germanium
and fast neutron scattering in the shielding material occur in the background
spectrum. For example, 139.7 keV gamma line produced via neutron-induced
process 74Ge(n,$\gamma$)75Ge. Peaks at 569.7 keV and 1063.3 keV from
scattering reaction (n,n’) on lead were also observed. Another gamma ray at
803.3 keV is detectable and corresponds to the de-excitation of 206Pb∗ which
can result from the decay of 210Po or from fast neutron scattering on lead. An
important characteristic in low activity measurements is the Minimum
detectable activity ($\textrm{A}_{\textrm{D}}$) that defines the least amount
of activity in the sample to quantify the radiation level slightly above the
unavoidable background. Shorter measurement times and higher background
radiation levels would increase the $\textrm{A}_{\textrm{D}}$ and reduce the
sensitivity of all detectors. The detector efficiency significantly affects
the detection levels. In addition to the detection efficiency, amount of
sample, measurement time, and photon emission probability, the
$\textrm{A}_{\textrm{D}}$ in gamma spectrometry depends on the background
level at a specific energy. These background events mainly come from three
primary sources: the sample, the Compton continuum, and natural radioactivity.
The $\textrm{A}_{\textrm{D}}$ in Bq/kg at a given gamma-ray energy is
calculated using Currie’s method [27] and given by:

$\textrm{A}_{\textrm{D}}=\frac{\textrm{N}_{\textrm{D}}}{\textrm{I${}_{\gamma}$}\ast\textrm{m}\ast\varepsilon_{\gamma}\ast\textrm{t}}$
(7)

Where ${\textrm{N}}_{\textrm{D}}$ = 2.7 + 4.65 $\sigma_{\textrm{B}}$ is
minimum detectable counts and $\sigma_{\textrm{B}}$ is the standard deviation
in the background counts, ${\textrm{I}}_{\gamma}$ is the branching ratio of
the gamma-ray, $\varepsilon_{\gamma}$ is the photopeak detection efficiency
computed using GEANT4 simulation, m is the mass of the sample and t is the
counting time. It should be noted that simulated efficiencies
($\varepsilon^{\textrm{Sim}}$) were obtained with the optimized detector model
for 106 events uniformly distributed within the studied sample modeled in
GEANT4 similar to the counting geometry kept during the measurement.

###  3.4 Measurement of Soil and Rock Samples

The sensitivity of the ILM-0 setup was estimated using sub-surface soil (30 cm
depth) and rock samples. The soil samples were collected from the Katli
village (30.99582 N, 76.534 80 E) in the Ropar region of Punjab (India), and
the rock samples were collected from the Aut region of Himachal Pradesh
(India). It may be noted that the rock samples were remeasured in the present
work to assess the performance of the ILM-0 setup as compared to TiLES
measurements reported elsewhere [13]. The soil samples were oven dried
(110∘C), fine powered, and then sieved through a 150 $\mu$m mesh. Each sample
was packed and sealed in a cylindrical polypropylene container of $\sim$3.5 cm
dia. and $\sim$2.2 cm height and stored for stabilization. The smaller sample
geometries are desirable over voluminous sample geometries because the
attenuation of gamma-rays within the sample matrix is negligible. A total of
10 soil samples, average mass ⟨m⟩$\sim$20 g were counted in compact geometry
for 24 h. The mean soil density ⟨$\rho$⟩, as packed in the container, is
estimated to be $\sim$1.3 g/cm3 with an overall variation of $\sim$10%. It has
been reported [28] that the Punjab soil is mainly of clay loam type and thus
expected to have a similar composition as listed in table 3.

Figure 12: A typical gamma-ray spectra of soil sample (red line), Aut rock
sample (blue line) and ambient background (black line) without the sample (t=1
d). The soil sample and ambient background are scaled arbitrarily for better
visibility. The gamma-rays of interest are indicated (*) in the spectra.

To enhance the counting efficiency, the soil samples were counted on the front
of the detector face and confined within 60% of the radial extensions to avoid
edge effects. The effect of the elemental composition and sample density were
taken into account. The average sample mass of ⟨m⟩$\sim$20 g was counted in
compact geometry for 24 h. The same geometry was adopted for counting of rock
samples. Figure 12 compares typical one-day spectra of ambient background
(x0.1), Ropar soil (x3), and Aut rock samples. The lines and notations are
self-explanatory. In order to determine the detection limit of ILM-0 for low
activity measurements, ${\textrm{A}}_{\textrm{D}}$ for soil matrices were
computed from the minimum detectable counts (${\textrm{N}}_{\textrm{D}}$)
using the Eq. 7. In close counting geometry, coincident summing affects the
observed photopeak yield [13]. In the present analysis, nuclides in natural
radioactive decay chains were considered to be in secular equilibrium, and the
gamma-rays with negligible coincidence summing were chosen to estimate
activities. ${\textrm{A}}_{\textrm{D}}$ is calculated for several
radionuclides often encountered in the environmental samples from which the
most dominating ones are shown in Table 6. MDA values for 137Cs nuclide have
the lowest value and hence determine the nuclide detection limit.

Table 6: Estimated sensitivity of the setup. Radionuclide | Energy | $\textrm{N}_{\textrm{D}}$ | $\textrm{A}_{\textrm{D}}$
---|---|---|---
(/Parent) | (keV) | (counts/day) | (Bq/kg)
212Pb (/232Th) | 238.6 | 65 | 1
214Bi (/238U) | 1764.5 | 76 | 25
214Pb (/238U) | 295.3 | 85 | 5
228Ac (/232Th) | 911.2 | 39 | 4
137Cs | 661.6 | 3 | 0.1
60Co | 1332.5 | 38 | 2
40K | 1460.8 | 120 | 49

The specific activities were estimated from the measured photopeak yield after
background correction, defined as activity per unit mass $\textrm{A}_{\gamma}$
corresponding to a given transition of the radionuclide was determined using,

${\textrm{A}}_{\gamma}=\frac{{\textrm{N}}_{\gamma}}{\textrm{I${}_{\gamma}$}\ast\textrm{m}\ast\varepsilon_{\gamma}\ast\textrm{t}},$
(8)

where $\textrm{N}_{\gamma}$ is the net observed counts in the photopeak after
correcting for the ambient background. The uncertainty in the specific
activity includes the error in efficiency and peak fitting. Most of the gamma-
rays were visible from the uranium and thorium decay chains. However, only
those gamma-rays that could be unambiguously assigned to a particular nuclide
were considered for further analysis. Therefore, correction factors due to
sample self-absorption and coincidence summing can be reasonably neglected.
For 238U single gamma line of 214Pb at 295.3 keV, for 232Th gamma line of
212Pb at 238.6 keV and 40K 1460.8 keV were selected for the analysis. The
observed specific activity of primordial radionuclides in the soil samples was
found to range between 32–67, 66–107, and 590–860 with a mean specific
activity of 50, 85, and 670 Bq/kg for 238U, 232Th, and 40K, respectively. The
measured activity of 238U and 232Th showed a consistent distribution of
primordial radionuclides among all the soil samples, while a somewhat large
scatter is observed in 40K data. In the case of rock sample measurements, the
measured specific activity of 238U in Aut rock is 7 (1) Bq/kg, which is
similar in comparison to the value reported in Ref [13], while for 232Th and
40K no measurable activity could be observed above the ambient background at
the present experimental sensitivity. To estimate the activity concentration
in rock samples, reducing the overall background by an order of magnitude is
necessary, as seen in Figure 12. The existing setup needs augmentation with
thicker low activity lead/copper shields to improve the detection limits. As
discussed earlier, above-ground laboratories are mostly dominated by muon-
induced interactions; therefore, deploying additional cosmic muon veto systems
are desirable to improve the sensitivity with an overall background reduction
of about 50% in the present setup.

##  4 Summary and Conclusions

In summary, a moderately shielded low background counting facility has been
set up at IIT Ropar to investigate environmental radioactivity and rare
decays. The GEANT4 simulations employing Monte Carlo procedures have been
performed to determine the photopeak efficiency of the HPGe detector, and an
effective detector model has been obtained. Various parameters, such as;
crystal radius (R), crystal length (L), front gap (g), dead layers (td, tb,
and ts) have been compared and optimized through the lateral, radial and
distance scanning measurements. The relative deviations between simulated and
experimental efficiencies were found to be $\sim$7% within the photon energy
range of 80.9–1408 keV, indicating as high as $\sim$93% confidence level in
the comparison between experimental characterization and simulation. In order
to assess the performance of the setup, the trace concentration of radioactive
elements has been measured in soil samples from the agricultural test site in
Ropar with ILM-0. The studied site has mean specific activity of 50, 85, and
670 Bq/kg for 238U, 232Th, and 40K, respectively. While 238U and 232Th
activities among the samples are consistent within overall uncertainty, 40K
shows a somewhat more significant variation. The Aut rock measurements have
shown specific activity of 238U to be 7 (1) Bq/kg, while for 232Th, and 40K
furthur measures to improve signal-to-noise ratio are essential. Efforts are
underway to augment the setup with low activity lead shields and plastic veto
detectors to improve the sensitivity for studies relevant to rare decay
searches. Measurements of the studied site with rich datasets employing two
detector configurations are proposed.

##  5 Acknowledgments

The authors thank Prof. R. G. Pillay and Prof. Vandana Nanal for their
suggestions during the development of the setup. The Indian Institute of
Technology Ropar acknowledged for an ISIRD grant for setting up ILM-0 for rare
decay physics. One of the authors, Swati Thakur thanks the Ministry of
Education (MoE), Government of India, for the doctoral fellowship, and iHub -
AWaDH, a Technology Innovation Hub established by the Department of Science
$\&$ Technology, Government of India, in the framework of the National Mission
on Interdisciplinary Cyber-Physical Systems (NM - ICPS), for financial support
to execute this work. Soni Devi and Katyayni Tiwari thank the doctoral
fellowships received from the University Grant Commission and DST - INSPIRE,
respectively.

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