# Alpha backgrounds in NaI(Tl) crystals of COSINE-100

G. Adhikari  N. Carlin  D. F. F. S. Cavalcante  J. Y. Cho  J. J. Choi  S. Choi
A. C. Ezeribe  L. E. França  C. Ha  I. S. Hahn  S. J. Hollick  E. J. Jeon
<EMAIL_ADDRESS>H. W. Joo  W. G. Kang  M. Kauer<EMAIL_ADDRESS>B.
H. Kim  H. J. Kim  J. Kim  K. W. Kim  S. H. Kim  S. K. Kim  S. W. Kim  W. K.
Kim  Y. D. Kim  Y. H. Kim  Y. J. Ko  D. H. Lee  E. K. Lee  H. Lee
<EMAIL_ADDRESS>H. S. Lee  H. Y. Lee  I. S. Lee  J. Lee  J. Y. Lee  M.
H. Lee  S. H. Lee  S. M. Lee  Y. J. Lee  D. S. Leonard  N. T. Luan  B. B.
Manzato  R. H. Maruyama  R. J. Neal  J. A. Nikkel  S. L. Olsen  B. J. Park  H.
K. Park  H. S. Park  J. C. Park  K. S. Park  S. D. Park  R. L. C. Pitta  H.
Prihtiadi  S. J. Ra  C. Rott  A. Scarff  K. A. Shin  M. K. Son  N. J. C.
Spooner  L. T. Truc  L. Yang  G. H. Yu<EMAIL_ADDRESS>(COSINE-100
Collaboration)  Department of Physics and Wright Laboratory, Yale University,
New Haven, CT 06520, USA  Physics Institute, University of São Paulo,
05508-090, São Paulo, Brazil  Center for Underground Physics, Institute for
Basic Science (IBS), Daejeon 34126, Republic of Korea  Department of Physics
and Astronomy, Seoul National University, Seoul 08826, Republic of Korea
Department of Physics and Astronomy, University of Sheffield, Sheffield S3
7RH, United Kingdom  Department of Physics, Chung-Ang University, Seoul 06973,
Republic of Korea  Center for Exotic Nuclear Studies, Institute for Basic
Science (IBS), Daejeon 34126, Republic of Korea  Department of Science
Education, Ewha Womans University, Seoul 03760, Republic of Korea  IBS School,
University of Science and Technology (UST), Daejeon 34113, Republic of Korea
Department of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin-Madison, Madison, WI 53706, USA  Department of
Physics, Kyungpook National University, Daegu 41566, Republic of Korea
Department of Physics, Sejong University, Seoul 05006, Republic of Korea
Korea Research Institute of Standards and Science, Daejeon 34113, Republic of
Korea  Department of Accelerator Science, Korea University, Sejong 30019,
Republic of Korea  Department of Physics and IQS, Chungnam National
University, Daejeon 34134, Republic of Korea  Department of Physics,
Universitas Negeri Malang, Malang 65145, Indonesia  Department of Physics,
Sungkyunkwan University, Suwon 16419, Republic of Korea  Department of Physics
and Astronomy, University of Utah, Salt Lake City, UT 84112, USA  Department
of Physics, University of California San Diego, La Jolla, CA 92093, USA

###### Abstract

COSINE-100 is a dark matter direct detection experiment with 106 kg NaI(Tl)
target material. 210Pb and daughter isotopes are a dominant background in the
WIMP region of interest and detected via $\beta$ decay and $\alpha$ decay.
Analysis of the $\alpha$ channel complements the background model as observed
in the $\beta$/$\gamma$ channel. We present the measurement of the quenching
factors and Monte Carlo simulation results of the $\alpha$ decay components of
the COSINE-100 NaI(Tl) crystals. The data strongly indicate that the $\alpha$
decays probabilistically undergo one of two possible quenching factors, but
this phenomenon is not understood. The fitted results are consistent with
independent measurements and improve the overall understanding of the
COSINE-100 backgrounds.

###### keywords:

NaI(Tl) , 210Pb , 232Th , surface , alpha , quenching

††journal: Astroparticle Physics

##  1 Introduction

The COSINE-100 detector consists of an array of eight ultra-pure NaI(Tl)
crystals with a combined mass of 106 kg. The experiment operated at the
Yangyang Underground Laboratory (Y2L) from September 2016 until March 2023.
Its primary goal is the direct detection of dark matter via the annual
modulation of WIMPs scattering from I or Na nuclei. The crystal array is
immersed in 2200 liters of liquid scintillator for background tagging.

A good understanding and precise measurement of the background sources
contributing events in the 1–10 electron-equivalent keV (keVee) region of
interest (ROI) is critical to NaI(Tl) direct detection WIMP searches. Bulk and
surface 210Pb are the dominant background sources in this region and are
observed in the $\beta$/$\gamma$ channel, as well as in the $\alpha$ channel.
Certain characteristics (gain calibration, energy resolution, light yield,
etc.) of the NaI crystals have been measured in situ [1]. The quenching
factors for $\alpha$ particles are important inputs to the simulation, as well
as the analysis of the $\alpha$ background. Analysis of the $\alpha$ channel
can improve the accuracy of the background model in the ROI. Analysis of the
$\alpha$ backgrounds using 2.7 yr data is presented in this work.

##  2 COSINE-100 experimental setup

The experimental setup and data acquisition are described in detail in Ref.
[1, 2]. The detector geometry used for simulations is shown in Fig. 1. Eight
NaI(Tl) crystals, arranged in two layers, are located in the middle of a four-
layer shielding structure. From outside inward, the four shielding layers are
plastic scintillator panels, a lead-brick castle, a copper box, and a
scintillating liquid. The eight NaI(Tl) crystal assemblies and their support
table are immersed in the scintillating liquid that serves both as an active
veto and a passive shield [3, 4].

Figure 1: COSINE-100 detector geometry implemented in Geant4 (Sec. 4).

The eight NaI(Tl) crystals were grown out of batches of powder provided by
Alpha Spectra Inc. with successive improvements. The first crystals labeled
AS-B and AS-C were produced with a reduction of 40K by an order of magnitude.
Then crystals labeled WIMPScint-II (AS-WSII) reduced the contamination of
210Pb. Finally the crystals labeled WIMPScint-III (AS-WSIII) were produced
with an additional reduction of 40K by a factor of two. The results are
summarized in Table 1 and a detailed description is found in Ref. [1].

The final crystals are cylindrically shaped and hermetically encased in OFE
copper tubes with wall thickness of 1.5 mm and quartz windows (12.0 mm thick)
at each end. Each crystal’s lateral surface is wrapped in roughly 10 layers of
250 $\mu$m thick PTFE reflective sheets. The quartz windows are optically
coupled to each end of the crystal via 1.5 mm thick optical pads. These, in
turn, are optically coupled to 3-inch Hamamatsu R12669SEL photomultiplier
tubes (PMTs) with a thin layer of high-viscosity optical gel. The PMTs are
sealed from the liquid scintillator by a housing made of copper and PTFE.

NaI(Tl) | Mass | Size (inches) | Powder | Total $\alpha$ Rate |  40K
---|---|---|---|---|---
Crystal | (kg) | (diam. $\times$ length) | Type | (mBq/kg) | (ppb)
C1 | 8.3 | 5.0 x 7.0 | AS-B | 3.20 $\pm$ 0.08 | 34.7 $\pm$ 4.7
C2 | 9.2 | 4.2 x 11.0 | AS-C | 2.06 $\pm$ 0.06 | 60.6 $\pm$ 4.7
C3 | 9.2 | 4.2 x 11.0 | AS-WSII | 0.76 $\pm$ 0.02 | 34.3 $\pm$ 3.1
C4 | 18.0 | 5.0 x 15.3 | AS-WSII | 0.74 $\pm$ 0.02 | 33.3 $\pm$ 3.5
C5 | 18.3 | 5.0 x 15.5 | AS-C | 2.06 $\pm$ 0.05 | 82.3 $\pm$ 5.5
C6 | 12.5 | 4.8 x 11.8 | AS-WSIII | 1.52 $\pm$ 0.04 | 16.8 $\pm$ 2.5
C7 | 12.5 | 4.8 x 11.8 | AS-WSIII | 1.54 $\pm$ 0.04 | 18.7 $\pm$ 2.8
C8 | 18.3 | 5.0 x 15.5 | AS-C | 2.05 $\pm$ 0.05 | 54.3 $\pm$ 3.8
Table 1: COSINE-100 crystal properties. The total $\alpha$ rates were
independently measured as part of the crystal commissioning effort. Details of
the measurements are described in Ref. [1].

It should be noted that Crystal-5 and Crystal-8 are excluded from this work
due to significant degradation of the light collection.

The scintillation signals are digitized and then integrated to determine the
charge in arbitrary units. Special calibration runs and prominent peaks from
in situ data are used to define the calibration function [2] that converts the
digitized charge into units of electron-volts (eV). The calibration function
is determined from the $\beta$/$\gamma$ scintillation signals and therefore is
referred to as the electron-equivalent energy (eVee).

##  3 Alpha quenching measurements

###  3.1 Alpha event selection and energy spectra

The scintillation signal from $\alpha$ particles in NaI(Tl) differs from the
one generated by $\beta$/$\gamma$ particles. The decay time of the
scintillation pulse by $\alpha$ is faster than the one from $\beta$/$\gamma$
particles. The scintillation decay time of the incident particles can be
identified from the charge-weighted duration time, called the meantime. The
meantime $\langle t\rangle$ is defined as

$\displaystyle\langle t\rangle=\frac{\Sigma_{i}A_{i}t_{i}}{\Sigma_{i}A_{i}},$
(1)

where $A$ and $t$ are the charge and time of the i-th digitized bin of a
signal waveform, respectively. The meantime is estimated within 1.5 $\mu$s
from the pulse start time. As a result, the populations of $\beta$/$\gamma$
events and $\alpha$ events are clearly separated due to the faster decay times
of the $\alpha$-induced events as shown in Fig. 2.

Figure 2: Typical crystal scatter plot of the meantime versus the energy for
COSINE-100. The $\alpha$ events (red dots) and the $\beta$/$\gamma$ events
(black dots) are clearly identified by the meantime as defined by Eq. 1.

Using the meantime selection criteria, the $\alpha$ events are selected from
data. We obtain the $\alpha$ energy spectra in units of electron-equivalent
energy (keVee) as shown in Fig. 3. Only a fraction of the $\alpha$ decay
energy is converted to light and is referred to as the $\alpha$ quenching
factor (QF). The two prominent peaks are due to 210Po and suggest the presence
of two quenching factors for these crystals. Therefore, in this work, we
consider two different quenching factors for all $\alpha$ events. The high QF
and low QF are referred to as $Q_{1}$ and $Q_{2}$ respectively.

Figure 3: Characteristic electron-equivalent energy spectrum of $\alpha$
events. 210Po makes up the two prominent peaks suggesting two quenching
factors.

###  3.2 Alpha-alpha time-correlated events

The high energy region ($>$ 3.3 MeVee) of the $\alpha$ distribution, as shown
in Fig. 3, is from the 228Th-group $\alpha$ decays and more specifically from
220Rn and 216Po. The 228Th-group activity can be measured by selecting the
time-delayed $\alpha$-$\alpha$ events from 220Rn and 216Po decays. The
$\alpha$ decay of 216Po has a short half-life of 0.145 s following its
production via the $\alpha$ decay of 220Rn.

The 228Th-group activity can be calculated from a single exponential fit to
the $\alpha$-$\alpha$ time-delay ($\Delta T$) distribution. Events with
$\Delta T$ greater than 5 seconds are rejected. The relatively long $\Delta T$
provides more events for the 210Po background estimation. A typical $\Delta T$
distribution and fitted function is shown in Fig. 4 and the fitted half-lifes
of all crystals are summarized in Table 2. The 228Th activities measured in
the $\alpha$-$\alpha$ coincidence study are listed in Table 6.

Figure 4: A typical $\Delta T$ distribution of total $\alpha$ events and exponential fitted function. |  216Po half-life (s)
---|---
C1 | 0.149 $\pm$ 0.006
C2 | 0.140 $\pm$ 0.002
C3 | 0.139 $\pm$ 0.006
C4 | 0.154 $\pm$ 0.003
C6 | 0.134 $\pm$ 0.005
C7 | 0.147 $\pm$ 0.007
Table 2: Measured half-lives from exponential fit to $\alpha$-$\alpha$ time
distribution.

###  3.3 Quenching factor calculation

The 220Rn and 216Po events that have been selected are shown in Fig. 5. These
events were estimated using the time-delayed method outlined in Section 3.2.
They are used to determine the energy-dependent quenching functions. The
observed $\alpha$ energy and standard deviation of 220Rn and 216Po events are
initially estimated by Gaussian fits to the identified spectral features in
data. The fitted parameters are used to define the energy window applied to
the $\alpha$-$\alpha$ event selection. The energy window is set by the
$\alpha$ energy mean plus or minus three standard deviations. A time
constraint is also applied to mitigate random coincident events from 210Po.
From the half-life of 216Po, 0.145 s, we apply a 1 s $\Delta T$ constraint.

(a)

(b)

Figure 5: Characteristic $\alpha$-$\alpha$ electron-equivalent energy
distributions of the selected and 216Po and 220Rn events for $Q_{1}$ and
$Q_{2}$.

The energy-dependent $\alpha$ quenching is approximated by

$\displaystyle Q_{\alpha}(E_{\alpha})=a+b\cdot E_{\alpha}[\text{MeV}]\,,$ (2)

and each data point for fitting is obtained from the ratio between the Q-value
and the electron-equivalent energy of $\alpha$ from 210Po, 220Rn, and 216Po.
Characteristic data points and energy-dependent quenching factor functions for
$Q_{1}$ and $Q_{2}$ are seen in Fig. 6. The fitted $a$ and $b$ parameters for
each crystal are summarized in Tables 3 and 4.

Figure 6: Characteristic data points and energy-dependent quenching factor functions for $Q_{1}$ and $Q_{2}$. | $Q_{1}$
---|---
| $a$ | $b$
C1 | 0.437 $\pm$ 0.008 | 0.0218 $\pm$ 0.0014
C2 | 0.465 $\pm$ 0.008 | 0.0210 $\pm$ 0.0013
C3 | 0.419 $\pm$ 0.008 | 0.0242 $\pm$ 0.0014
C4 | 0.458 $\pm$ 0.008 | 0.0214 $\pm$ 0.0013
C6 | 0.468 $\pm$ 0.008 | 0.0161 $\pm$ 0.0013
C7 | 0.493 $\pm$ 0.007 | 0.0114 $\pm$ 0.0012
Table 3: Energy-dependent $Q_{1}$ parameters as defined by Eq. 2. | $Q_{2}$
---|---
| $a$ | $b$
C1 | 0.274 $\pm$ 0.011 | 0.0425 $\pm$ 0.0018
C2 | 0.415 $\pm$ 0.009 | 0.0216 $\pm$ 0.0014
C3 | 0.394 $\pm$ 0.009 | 0.0238 $\pm$ 0.0015
C4 | 0.425 $\pm$ 0.008 | 0.0223 $\pm$ 0.0014
C6 | 0.383 $\pm$ 0.009 | 0.0165 $\pm$ 0.0015
C7 | 0.399 $\pm$ 0.009 | 0.0135 $\pm$ 0.0015
Table 4: Energy-dependent $Q_{2}$ parameters as defined by Eq. 2.

##  4 Alpha decay Monte Carlo

Radioactive background components are simulated using Geant4 (v10.0.4) [5, 6,
7]. The physics list classes of G4EmLivermorePhysics for low-energy
electromagnetic processes and G4RadioactiveDecay for radioactive decay
processes are used. Details of the simulation are described in Refs. [8, 9].

The $\alpha$ events are challenging to reproduce with simulation. Two
quenching factors are required to describe the two dominant $\alpha$ peaks
from 210Po as well as the higher energy features from 220Rn and 216Po.
Furthermore, the 210Po spectral shapes are highly asymmetric, and an
asymmetric probability density function (PDF) is required for the simulation
energy smearing. Lacking a physics explanation for the asymmetric energy
distribution, a PDF was selected that closely approximated the spectral shape
observed in data. In this work, the spectral shapes were approximated by the
normal-inverse Gaussian [10] as demonstrated in Fig. 7. The two quenching
factors and asymmetric spectral shapes are also observed by the ANAIS
experiment [11], which uses NaI(Tl) crystals produced by Alpha Spectra Inc.,
the same vendor that produced the crystals for COSINE-100. These phenomena are
not yet understood, and the investigation is ongoing.

Figure 7: Internal 210Po data approximated by simulation of two quenching
factors with normal-inverse Gaussian energy distributions.

The energy dependent $\alpha$ quenching functions determined in Sec. 3.3 are
separately applied to the simulated $\alpha$ decay events to create $Q_{1}$
and $Q_{2}$ quenched energy distributions. The quenched energies are then
smeared asymmetrically. The resulting simulated $\alpha$ spectra are in units
of electron-equivalent energy and make up the templates that are fit to data.
The fractional activities of the $Q_{1}$ and $Q_{2}$ templates are left as
free parameters of the fit.

###  4.1 Spectral components

The $\alpha$ spectra are dominated by three distinct components. They include
internal 210Po (2.2–3.2 MeVee), internal 228Th-group (3.2–4.2 MeVee), and PTFE
surface 210Po (1.0–2.2 MeVee). PTFE bulk 210Po and NaI surface 210Po are
included in the background model but do not contribute significantly to the
$\alpha$ spectrum. The activities of these components are measured in the
$\beta$/$\gamma$ channel and a detailed analysis is presented in Ref. [9].

####  4.1.1 Internal Po210

The $\alpha$ spectra are dominated by internal 210Po at 2.2–3.2 MeVee. It is
not understood why the 210Po $\alpha$ energy distribution is highly
asymmetric. For the purpose of this $\alpha$ modeling, the 210Po spectral
shape is parameterized by normal-inverse Gaussian distributions as this
approach best approximates the shape of the 210Po spectrum observed in data.
Internal 210Po is the dominant $\alpha$ background and Table 5 compares the
fitted activities to measurements of the total $\alpha$ rates [1].

####  4.1.2 Internal Th228-group

The features visible at higher energies ($>$ 3.2 MeVee) are dominated by
internal 232Th and particularly the 228Th-group consisting of 228Th, 224Ra,
220Rn, and 216Po $\alpha$ decays. The two quenching factors (Sec. 3.3) are
simulated and independently fit to data to determine the activity of the
228Th-group. The fitted results are compared to the time-correlated
$\alpha$-$\alpha$ measurements in Table 6. The discrepancies are not well
understood. It’s possible an $\alpha$ decay isotope is not accounted for in
the background model and has an energy in the region of the 228Th-group
causing the fit to overestimate the 228Th-group activity.

####  4.1.3 PTFE Surface Po210

Different $\alpha$ source locations and their resulting spectral shapes were
studied with Geant4 simulations. From these studies, it was determined that
the low-energy tail ($<$ 2.2 MeVee) of the $\alpha$ distribution (Fig. 3) is
caused by 210Po on the surface of the PTFE reflector that surrounds NaI
crystals. Furthermore, the depth profile of the 210Po in the PTFE correlates
to the slope of the low energy tail of the $\alpha$ distribution. A shallower
depth profile causes a steeper low-energy tail. The contamination depth
profiles differ among crystals and range from 2–5 $\mu$m. The fitted results
are summarized in Table 7.

Using MC, we investigated the NaI surface 210Pb at various depth profiles. We
also investigated the effects of a scintillation dead layer [12] extending to
various depths in combination with NaI surface 210Pb. These scenarios did not
describe the low-energy tail observed in the data.

Measurements of internal 210Pb and PTFE surface 210Pb half-lives were made.
The measured half-life of internal 210Pb was consistent with the known value
of 22.3 yr while the measured half-life of PTFE surface 210Pb was a much
longer 28.5 yr. One possible explanation is that the surface is continuously
contaminated by something radioactive from outside (222Rn for example) which
artificially increases the observed half-life of PTFE surface 210Pb.

###  4.2 Data fitting

Data are fitted by analytically maximizing the binned likelihood of two or
more MC background templates as described in Ref. [13]. For each $\alpha$
component, MC templates are created for two quenching functions and allowed to
be independently scaled by the fitting algorithm. The resulting fits to the
COSINE-100 crystals are shown in Fig. 8.

The activities of less significant components of PTFE bulk 210Po and NaI
surface 210Po are determined from analysis of the $\beta$/$\gamma$ channel as
presented in Ref. [9]. These background sources are included in the $\alpha$
background model but their activities are fixed for this work.

Figure 8: Results of fitting internal 210Po, internal 228Th-group, and PTFE surface 210Po $\alpha$ components to data for each COSINE-100 crystal. | Fitted MC | Total
---|---|---
|  210Po |  $\alpha$ Rate
| ($mBq/kg$) | ($mBq/kg$)
C1 | 2.93 $\pm$ 0.17 | 3.20 $\pm$ 0.08
C2 | 1.86 $\pm$ 0.17 | 2.06 $\pm$ 0.06
C3 | 0.65 $\pm$ 0.10 | 0.76 $\pm$ 0.02
C4 | 0.68 $\pm$ 0.11 | 0.74 $\pm$ 0.02
C6 | 1.62 $\pm$ 0.14 | 1.52 $\pm$ 0.04
C7 | 1.63 $\pm$ 0.14 | 1.54 $\pm$ 0.04
Table 5: Comparison of MC fitted activity of internal 210Po to the total $\alpha$ rate measured in Ref. [1]. | Fitted MC |  $\alpha$-$\alpha$ coinc.
---|---|---
|  228Th-group |  228Th-group
| ($\mu Bq/kg$) | ($\mu Bq/kg$)
C1 | 7.47 $\pm$ 0.84 | 3.34 $\pm$ 0.94
C2 | 4.56 $\pm$ 0.49 | 3.29 $\pm$ 0.06
C3 | 1.91 $\pm$ 0.20 | 1.69 $\pm$ 0.04
C4 | 3.93 $\pm$ 0.21 | 2.25 $\pm$ 0.04
C6 | 2.10 $\pm$ 0.12 | 0.54 $\pm$ 0.02
C7 | 2.14 $\pm$ 0.12 | 0.58 $\pm$ 0.02
Table 6: Comparison of 228Th-group activity measured by fitting MC to data and by $\alpha$-$\alpha$ coincidence as described in Sec. 3.2. | PTFE Surf.
---|---
|  210Po
| ($\mu Bq/cm^{2}$)
C1 | 0.77 $\pm$ 0.11
C2 | 1.25 $\pm$ 0.13
C3 | 1.10 $\pm$ 0.16
C4 | 1.08 $\pm$ 0.12
C6 | 1.61 $\pm$ 0.20
C7 | 1.14 $\pm$ 0.13
Table 7: PTFE surface 210Po activity measured by fitting MC to data.

##  5 Conclusion

Two quenching factors are required to describe the features in COSINE-100
$\alpha$ data. Normal-inverse Gaussian PDFs are applied to the simulation to
approximate the spectral shapes observed in $\alpha$ data. These phenomena are
not yet understood, and the investigation is ongoing.

The COSINE-100 $\alpha$ spectra are well described by dominant components of
internal 210Po, internal 228Th-group, and PTFE surface 210Po. NaI surface
210Po and PTFE bulk 210Po activities are determined from the $\beta$/$\gamma$
channel as described in Ref. [9] because their spectral features are more
prominent in the $\beta$/$\gamma$ channel. The $\alpha$ isotope activities
were measured in this work by fitting Geant4 MC to data. The dominant 210Po
fitted $\alpha$ rates are consistent ($<$ 1.1 $\sigma$) with the total
$\alpha$ rates (Table 5), as measured during commissioning of the crystals.

## Acknowledgments

We thank the Korea Hydro and Nuclear Power (KHNP) Company for providing
underground laboratory space at Yangyang and the IBS Research Solution Center
(RSC) for providing high-performance computing resources. This work is
supported by: the Institute for Basic Science (IBS) under project code
IBS-R016-A1, NRF-2019R1C1C1005073, NRF-2021R1A2C3010989, NRF-2021R1A2C1013761,
NFEC-2019R1A6C1010027, and NRF-2021R1I1A3041453, Republic of Korea; NSF Grants
No. PHY-1913742, DGE-1122492, WIPAC, the Wisconsin Alumni Research Foundation,
United States; STFC Grant ST/N000277/1 and ST/K001337/1, United Kingdom; Grant
No. 2021/06743-1 and 2022/12002-7 FAPESP, CAPES Finance Code 001, CNPq
131152/2020-3 and 303122/2020-0, Brazil.

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