aainstitutetext: LIBPhys, Physics Department, University of Coimbra, Rua
Larga, Coimbra, 3004-516, Portugal

# Unraveling xenon primary scintillation yield for cutting-edge rare event
experiments

C.A.O. Henriques a J.M.R. Teixeira a P.A.O.C. Silva a R.D.P. Mano a J.M.F. dos
Santos a,1 C.M.B. Monteiro 111Corresponding authors<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Xenon scintillation has been widely used in rare event detection experiments,
such as in neutrinoless double beta decay, double electron captures and dark
matter searches. Nonetheless, experimental values for primary scintillation
yield in gaseous xenon (GXe) remain scarce and dispersed. The mean energy
required to produce a scintillation photon, $w_{sc}$, in GXe in the absence of
recombination has been measured to be in the range of 34–111 eV. Lower
$w_{sc}$-values were reported for $\alpha$-particles when compared to
electrons produced by $\gamma$\- or x-rays. Since $w_{sc}$ is expected to be
similar for x-, $\gamma$-rays or electrons and almost equal to that obtained
for $\alpha$-particles, the above difference can not be understood. In
addition, at present one may also pose the question of a dependence of
$w_{sc}$ on photon energy. We carried out a systematic study on the absolute
primary scintillation yield in GXe under reduced electric fields in the 70–300
V cm-1 bar-1 range and near atmospheric pressure, 1.2 bar, supported by a
robust geometrical efficiency simulation model.

We were able to clear-out the above standing problems: $w_{sc}$ was determined
for x/$\gamma$-rays in the 5.9–60 keV energy range as well as for
$\alpha$-particles in the 1.5–2.5 MeV range, and no significant dependency
neither on radiation type nor on energy has been observed. Our experimental
$w_{sc}$-values agree well with both state-of-art simulations and literature
data obtained for $\alpha$-particles. The discrepancy between our results and
the experimental values found in the literature for x/$\gamma$-rays is
discussed in this work and attributed to unaddressed large systematic errors
in those previous studies. These findings can be extrapolated to other gases,
and have impact on experiments such as double beta decay, double electron
capture and directional dark matter searches while also on potential future
detection systems such as DUNE-Gas.

Neglecting the 3rd continuum emission, as is the case of most of the
literature values, a mean $w_{sc}$-value of 38.7 $\pm$ 0.6 (sta.)$\
{}_{-7.2}^{+7.7}$ (sys.) eV was obtained. If the Xe 3rd continuum emission is
to be considered, the average energy to produce a 2nd and a 3rd continuum
photon was calculated as $w_{2^{nd}}=$ 43.5 $\pm$ 0.7 (sta.)$\
{}_{-8.1}^{+8.7}$ (sys.) eV and $w_{3^{rd}}=$ 483 $\pm$ 7 (sta.)$\
{}_{-105}^{+110}$ (sys.) eV, respectively, while the energy to produce either
a 3rd or a 2nd continuum photon is $w_{2^{nd}{+3}^{rd}}=$ 39.9 $\pm$ 0.6
(sta.)$\ {}_{-7.4}^{+8.0}$ (sys.) eV.

##  1 Introduction

Gaseous xenon (GXe) is playing an increasingly significant role in important
areas of neutrino physics such as double beta decay and double electron
capture experiments NEXT:2019gtz ; Obara:2019tnh ; Gomez-Cadenas:2019ges ;
Galan:2019ake ; Gavriljuk:2018pez ; NEXT:2020sux , and it may be used as
detection medium in directional dark matter experiments as well as in MeV-
region $\gamma$-ray imaging nygren2013columnar ; mimura2009xenon ;
10.1117/1.OE.53.2.021108 . The capability for simultaneous readout of both
ionization and scintillation signals and for topology reconstruction of the
ionizing particle tracks are important advantages of GXe. In addition, GXe
allows for improved energy resolution when compared to liquid xenon (LXe)
BOLOTNIKOV1997360  due to the observed fluctuations in energy deposition
between the ionization and the scintillation channels in LXe EXO-200:2003bso ,
an effect that can be corrected to some extent by combining both channels
EXO-200:2012pdt . Better energy resolution may lead to improved
electron/nuclear recoil discrimination, being also a major asset for the
neutrinoless double beta decay sensitivity, and the topology of the ionization
track will be an additional tool, providing information about the direction of
the WIMP scatter or discrimination between single and double electron
ionization tracks.

The precise knowledge of the xenon response to radiation interactions in both
scintillation and ionization channels is of utmost importance for the exact
understanding and modelling of the detector. The primary scintillation yield
of GXe is far less understood than the ionization yield due to the limited
number of studies existing in the literature. Mimura _et al._
10.1143/JJAP.48.076501  discusses the results obtained until then, while Serra
_et al._ 10.1088/1748-0221/10/03/P03025  provides an update with further
results published meanwhile.

The dominant scintillation mechanism in xenon at the atmospheric pressure is
the so-called 2nd continuum, a Gaussian-like emission spectrum, 10 nm in
width. Its centroid has been reported in the 172–178 range
10.1016/0167-5087(83)90028-5 ; 10.1016/0029-554X(79)90453-1 ; 10.1063/1.436349
; 10.1063/1.440803 ; 10.1016/j.nima.2015.05.065 ; 10.1103/RevModPhys.82.2053 .
In this work we consider the most recent value, 175 nm
10.1016/j.nima.2015.05.065 . Nonetheless, other non-conventional scintillation
mechanisms have been observed, such as the broadband Neutral Bremsstrahlung
(NBrS) NBrS_prx  emission and the 3rd continuum emission in the 250–400 nm
range 10.1063/1.436349 . All the $w_{sc}$-values present in the literature,
except for the most recent study carried out for $\alpha$-particles
10.1140/epjc/s10052-022-10385-y , consider the 3rd continuum and neutral
bremsstrahlung emissions to be negligible.

At reduced electric fields, i.e. the electric field normalized by the gas
pressure, $E/p$, above 60 V cm-1 bar-1, the recombination of primary
electrons/ions produced during the radiation interaction is negligible
10.1088/1748-0221/10/03/P03025 ; 10.1088/1748-0221/8/05/P05025 ;
10.1143/JJAP.48.076501 ; 10.1109/tns.2004.836030 . In those conditions, the
average energy required to excite a xenon atom, $w_{ex}$, is similar to the
average energy expended per scintillation photon $w_{sc}=E_{dep}/N_{ph}$,
where $N_{ph}$ is the number of scintillation photons and $E_{dep}$ the
deposited energy 10.1088/1748-0221/10/03/P03025 ;
10.1088/1748-0221/8/05/P05025 . $w_{ex}$ does not depend on gas density, below
0.2 g/cm3, $\sim$20 bar at room temperature 10.1143/JJAP.48.076501 .

Several measurements of the $w_{sc}$ for x- and $\gamma$-ray interactions have
become available, although with highly dispersed values from 61 to 111 eV
10.1088/1748-0221/5/09/P09006 ; 10.1088/1748-0221/3/07/P07004 ;
10.1016/j.nima.2023.168038 ; 10.1109/23.106674 ; 10.1016/j.nima.2015.04.057 .
The $w_{sc}$-values obtained for 5.5-MeV $\alpha$-particle interactions are
less dispersed, in the 34–60 eV range, and $\sim 40$% lower on average than
its x/$\gamma$-ray counterpart despite being obtained for similar working
conditions 10.1088/1748-0221/10/03/P03025 ; 10.1143/JJAP.48.076501 ;
10.1109/TNS.2003.820615 ; 10.1109/tns.2004.836030 ;
10.1140/epjc/s10052-022-10385-y . An overview of the $w_{sc}$-values present
in the literature can be found in Table 1.

The average energy expended per excited atom in GXe is expected to be similar
for x-, $\gamma$-rays or electrons and almost equal to that obtained for
$\alpha$-particles 10.1143/JJAP.48.076501 . However, results presented in the
literature are inconsistent with that expectation. The difference between the
above results is presently not fully understood, as can be only partially
ascribed to the different gas density and/or drift field conditions. In
addition, at present one may also pose the question of a dependence of
$w_{sc}$ on photon energy.

These inconsistencies motivated us to pursue further experimental studies in a
dedicated setup where the primary scintillation could be isolated and studied
in detail. In this work, we report new results on the xenon $w_{sc}$-value in
absence of recombination, for $\alpha$-particles in the 1.5- to 2.5-MeV range
and for x/$\gamma$-rays in the 6–60-keV range. These findings can be
extrapolated to other noble gases, like Ar and Kr, and might have also impact
on potential future detectors such as DUNE-Gas 10.48550/arXiv.2203.06281 .

$w_{sc}$ (eV) | radiation | energy (keV) | observations
---|---|---|---
74 $\pm$ 10 | x-rays | 5.9 | 1 bar, 10.1088/1748-0221/5/09/P09006
111 $\pm$ 16 | x-rays | 5.9 | 1 bar, 10.1088/1748-0221/3/07/P07004
80 $\pm$ 12 | x-rays | 5.9 | 1 bar, 10.1016/j.nima.2023.168038
76 $\pm$ 12 |  $\gamma$-rays | 59.5 | 15 bar, 10.1109/23.106674
61 $\pm$ 18 |  $\gamma$-rays | 662 | 14 bar, 10.1016/j.nima.2015.04.057
39.2 $\pm$ 3.2 |  $\alpha$-particles | 5486 | 10 bar 10.1088/1748-0221/10/03/P03025
34.1 $\pm$ 2.4 |  $\alpha$-particles | 5486 | 5 bar 10.1143/JJAP.48.076501
34.5 $\pm$ 1.7 |  $\alpha$-particles | 5486 | 1-10 bar 10.1109/TNS.2003.820615
59.4 $\pm$ 1.5 |  $\alpha$-particles | 5486 | 1-2 bar 10.1109/tns.2004.836030
50.5 $\pm$ 5.9 |  $\alpha$-particles | 5486 | 1 bar, VUV 10.1140/epjc/s10052-022-10385-y
Table 1: A summary of $w_{sc}$-values presented in the literature. All values
are considered to be obtained with negligible electron-ion recombination,
since authors used reduced electric fields of at least 70 V cm-1 bar-1. Some
relevant working conditions such as the gas pressure, radiation type and
energy are also listed.

##  2 Experimental setup

For detailed studies of the primary scintillation, we built a gas proportional
scintillation chamber (GPSC) with photomultiplier tube (PMT) readout, Fig. 1.
This apparatus allows us to study both primary and secondary scintillation
signals, S1 and S2, respectively. The primary scintillation occurs mostly in
the absorption region, where a weak electric field prevents electron-ion
recombination and guides the ionization electrons toward a stronger electric
field region, where the secondary scintillation produced by electron impact,
also known as electroluminescence (EL), takes place.

Figure 1:  Schematic of the gas scintillation chamber used in this work.

The absorption region is delimited by a Kapton window, 12-$\mu$m thick,
aluminized on the inner side, and the gate wire mesh, 0.9-mm pitch stainless-
steel wires with 80 $\mu$m in diameter. The anode is made from a similar wire
mesh, placed above the photosensor. The chamber, filled with $\sim$1.2 bar of
xenon, consists of a stainless-steel cylinder, 10 cm in diameter, the bottom
part of the body being a Macor disc epoxied to the PMT and to the detector
wall for electrical insulation. The GPSC is operated at room temperature, with
the xenon gas circulating by convection through St707 SAES getters saes ,
heated to temperatures up to 250 ∘C. A field cage of four equally-spaced
copper rings interconnected through resistors was assembled in the absorption
region to ensure electric field uniformity. A polytetrafluoroethylene (PTFE)
structure supports the copper rings. Electric field maps of the GPSC were
obtained using a finite element method solver elmer . The electric field was
found to vary by 8% along the 3.6-cm thick absorption region and by 0.7% along
the 1-cm electroluminescence region. These values are conservative, as they
represent the maximum field variation in a 7-mm radius cylindrical volume,
where 95% of the transversely diffused electrons are contained within.

The PMT is an eight dynode model EMI D676QB with a diameter of 52 mm, an
effective cathode diameter of 45 mm, and a spectral sensitivity in the range
of 155–625 nm. The PMT quantum efficiency (QE) curve as provided by the
manufacturer is depicted in Fig. 2. Accordingly, a QE of $(20.9\pm 1.5)\%$, is
expected for the Xe 2nd continuum, the error stemming from the differences
between emission spectra in the literature.

Figure 2:  Quantum efficiency (QE) curve of the PMT used in this work. The Xe
VUV scintillation wavelength is also represented, assumed to be 175 nm
10.1016/j.nima.2015.05.065 .

The PMT signals are directly recorded with a WaveRunner 610Zi oscilloscope
from LeCroy, featuring a sampling rate of 10 GS/s. The PMT output is connected
to a load resistor of 200-Ω to convert the signal current into voltage. A 50-Ω
resistor would be preferable to match the cable impedance and to reduce wave
reflections. However, due to the low gain of our PMT, $\sim 10^{5}$, a higher
resistor value was required to increase the signal-to-noise ratio up to
acceptable levels. Nonetheless, wave reflections in the cable terminations are
properly handled, as will be explained in the following sections.

Four radioactive sources, 109Cd, 244Cm, 241Am, and 55Fe having the 6.4 keV
x-rays removed by means of a chromium filter, collimated up to 2 mm and
positioned 1 mm above the detector window, were used in the present study to
produce x/$\gamma$-rays in the range of 5.9–60 keV and 5.5-MeV alpha particles
(being $\sim$2 MeV deposited in the Xe gas). In addition, a Tb target was
irradiated with 59.5 $\gamma$-rays to provide fluorescence x-rays in the 14-50
keV range. Overall, the counting rate was kept around 10 Hz to avoid pulse
pileup, maintaining the cleanliness of the waveform baseline.

##  3 Monte Carlo simulations

Despite the large solid angle subtended by the PMT with respect to the
secondary scintillation region, most of the primary scintillation photons are
produced near the detector window, far away from the photosensor (see Fig. 1).
Consequently, photon reflections on the detector materials play an important
role in the optical geometrical efficiency. Since this parameter is crucial to
estimate the number of emitted primary and secondary scintillation photons, we
developed a detailed optical simulation of the detector geometrical efficiency
(GE) using the GEANT4 toolkit 10.1016/j.nima.2016.06.125 .

Detector components were designed and meshed with the software FreeCAD.
Components made from the same materials were grouped and their CAD geometries
were directly imported into GEANT4 using the open-source CADMesh header
10.1007/s13246-012-0159-8 . Optical processes such as photon reflection and
refraction are handled by the G4OpticalPhysics class. The GEANT4 simulation
was developed to account for the full wavelength range from 150 nm to 650 nm,
allowing to study other light emission mechanisms beyond the Xe 2nd second
continuum, such as the 3rd continuum and the neutral bremsstrahlung
10.1140/epjc/s10052-022-10385-y ; NBrS_prx . The refractive indexes of the
fused silica PMT window and Xe gas were implemented as a function of photon
wavelength, allowing for full simulation of Fresnel reflections and
refractions 10.1364/JOSA.55.001205 ; 10.1109/tdei.2006.1657967 . The glisur
model was used for boundary processes, and the respective optical surface
properties, e.g. reflectivity, absorption, and finishing, were defined. Some
of the most relevant parameters comprise the reflectivity of both aluminium
and stainless steel; the former covers the detector window inner surface, and
the latter is used in most of the inner surfaces, including the gate and anode
meshes. Experimental reflectivity values measured in
10.1016/j.nuclphysbps.2007.08.059  were considered for the 2nd continuum of
xenon scintillation, while the remaining wavelength region was covered with
values reported in 10.1364/JOSA.51.000719 ; 10.1016/0165-1633(89)90039-7 .
Less relevant materials like the PMT Macor holder, the field cage’s copper
rings and the PTFE structure were also included in the GEANT4 simulation,
their reflectivity values being taken from 10.1063/1.3318681 ;
silva2010reflection ; macor .

Figure 3 shows a 3-dimensional view of the GEANT4 simulation model and the
ray-tracing of 10 scintillation photons generated 36 mm away from the PMT. The
detector GE along the central axis perpendicular to the PMT can be found in
Figure 5. The GE refers to the ratio of photons reaching the PMT photocathode,
i.e. a sensitive area placed below the PMT window, when photons are generated
with random directions at different distances from the PMT. The impact of
radial effects, such as the incident beam divergence, the size of the
ionization electron cluster and the electron transverse diffusion of the
ionization electron cloud have been taken into account.

Figure 3: A 3-dimentional representation of the GEANT4 optical simulation,
showing the raytracing of 10 photons.

###  3.1 Primary scintillation emission

The beam divergence of $\alpha$-particles and x/$\gamma$-rays was obtained
from a non-optical GEANT4 simulation, considering the aperture of the
collimators used in the experimental campaign. Alpha-particles and
x/$\gamma$-rays are generated isotropically at random positions above the
collimator and tracked. For $\alpha$-particles the energy deposition along the
track is computed with a small step size and used to estimate the distribution
of primary photons and ionization electrons produced in the xenon gas. Figure
4 left shows an example of $\alpha$-particle tracks inside the gas volume.
However, for x/$\gamma$-rays we rely on the more accurate Degrad model, a
Fortran toolkit developed by S. Biagi degrad , to simulate the primary cluster
of xenon excited states and ionization electrons, including the shell
absorption by photoelectric effect and subsequent Auger, shake-off and
fluorescence emission. For this reason, the GEANT4 tracking of x/$\gamma$-rays
is stopped as soon as they interact inside the xenon volume, the interaction
positions being recorded. This is only possible for x/$\gamma$-rays because
$\alpha$-particles are not supported by Degrad.

The working conditions used in our experimental campaign were assumed in
Degrad, including the electric field values, pure xenon pressure of 1.2 bar,
and estimated temperature of 296 K. Incident x-rays with energies in the
5.9-59.5 keV range were simulated and the total number of primary electrons
and xenon excitations per event were obtained, along with their (x,y,z)
coordinates. The overall distributions of the primary scintillation photons
and electrons are computed, combining the distributions of xenon excited
states and electrons obtained from Degrad with the x/$\gamma$-ray interaction
positions obtained from GEANT4. Figure 4 right shows an example of the
positions where primary scintillation photons are generated for 22.1-keV
x-rays.

Figure 4: (Left) Tracking of 100 $\alpha$-particles in xenon gas at 1.2 bar,
as obtained from GEANT4; (right) the position distribution of S1 and S2
photons produced by 22.1-keV x-ray events in xenon at 1.2 bar and $E/p$ values
of 0.15 and 2.3 kV cm-1 bar-1 in the absorption and EL region, respectively,
as obtained from the combination of GEANT4, Degrad and Garfield++. The S1
distribution comprises 100 x-ray interactions, while the S2 data stem from 100
electrons randomly selected from a much larger sample. For clarity, only 10%
and 20% of S1 and S2 photons, respectively, are represented.

Finally, the GEANT4 optical simulation is supplied with a randomized sample of
photons emitted isotropically following the aforementioned distributions,
allowing to compute the GE curve in the absorption region.

###  3.2 Secondary scintillation emission

The cluster of ionization electrons obtained for $\alpha$-particles from
GEANT4 and for x/$\gamma$-rays from the GEANT4-Degrad combination are imported
into Garfield++, a toolkit for the detailed simulation of detectors that use
gases or semi-conductors as the sensitive media garfieldpp . Garfield++
provides an interface to Magboltz, a simulation tool that computes the
electron transport parameters in the gas Magboltz . In Garfield++ the geometry
is defined using the class GeometrySimple and the uniform electric field is
set using the ComponentConstant. This is done independently for the absorption
and the EL region, allowing to set different drift models for computational
time requirements, enabling to achieve a better balance between computational
efficiency and accuracy of the simulation results. Gas parameters are also set
for both regions using the class MediumMagboltz. The drift path is computed
using Monte Carlo integration with the class AvalancheMC. After the electrons
drift throughout the absorption region, their final positions are imported to
the electroluminescence region where the electric field value is higher than
the gas scintillation threshold. The movement of the electrons in this region
is modelled using the class AvalancheMicroscopic, where the electron is
tracked from collision to collision. This model enables the detailed
calculation of ionisation and excitation processes. With this method both the
coordinates and the number of excited xenon atoms are retrieved and
subsequently imported into GEANT4 where the optical simulation takes place.
Accordingly, the radial distribution of the excited states of xenon in the EL
region obtained from Garfield++ accounts for the x/$\gamma$-ray beam
divergence, the initial electron cloud size and the transverse electron
diffusion in both regions. Figure 4 also shows an example of a distribution
for xenon excited states in the EL region simulated for 22.1-keV x-rays.

###  3.3 Geometrical efficiency simulation results

Figure 5 depicts the GEANT4 GE simulation results for photon emission as a
function of distance to the PMT window. For obtaining the GE curves two
different cases were considered, namely assuming the on-axis approximation
and, for $\alpha$-particles and for three different x/$\gamma$-ray energies,
considering radial effects, taking into account the respective collimator
sizes and experimental working conditions. The simplistic GE curve calculated
considering only the solid angle and the transparency of gate and anode meshes
is also depicted for comparison.

Figure 5: GE simulation results for photon emission as a function of distance
to the PMT window, considering the on-axis photon emission and the
3-dimensional photon emission when taking into account radial effects, such as
beam divergence, electron cluster size and transverse electron diffusion. The
GE curve calculated considering only the solid angle and the transparency of
gate and anode meshes is also depicted for comparison. The anode and gate
meshes were placed at 0 and 10 mm, respectively.

As expected, calculations based solely on solid angle considerations are
highly inaccurate. The GE near the detector window can be underestimated by
almost 50% due to the relatively higher contribution of photon reflections.
Moreover, the simplistic assumption of the mesh transparency fails when
neglecting photons hitting the mesh planes at wide angles. Figure 5 also shows
the 68%-confidence level error of the GEANT4 on-axis simulation, which is
dominated by the uncertainty in reflectivity and unknown polishing degree of
some materials.

The degradation of the GE arising from radial effects is about 5% in the EL
region and negligible in the absorption region. Remarkably, the GE curves
obtained for different x/$\gamma$-ray energies and $\alpha$-particles are
comparable even in the EL region. For simplicity, the four GE curves
considering radial effects depicted in Fig. 5 are averaged, the result being
used in further GE corrections.

##  4 Analysis methodology

###  4.1 Waveforms sampling and pre-processing

The PMT signal is split into two oscilloscope channels: a “full-channel” that
is used to record the S2 pulse without saturation, and a “zoomed-channel” that
is optimized for S1 measurements. The signal of the oscilloscope is triggered
on the “full-channel” using the rising edge of the S2 pulse. This setup allows
us to measure simultaneously the S2 and S1 pulses with high amplitude
resolution. Moreover, the “zoomed-channel” delivers lower baseline
fluctuations dominated by the oscilloscope electronic noise.

PMT waveforms have been sampled at 5–10 GS/s. Nevertheless, we were forced to
compress the data due to memory limitations in larger x/$\gamma$-ray
acquisitions. This was accomplished by averaging successive waveform data
points at periodic intervals. On the one hand, such a procedure degrades the
time resolution of waveforms, from 0.1–0.2 ns to 10–70 ns, which is still
adequate for our studies. On the other hand, it increases the amplitude
resolution beyond the 8-bit limit of the oscilloscope. For convenience, the
PMT waveforms are inverted, i.e., waveforms presented from now on have
positive amplitude, despite the PMT signal being negative.

Figure 6 depicts a typical, already compressed PMT waveform obtained for
5.9-keV x-rays. The large pulse around 63 $\mu$s is the S2 pulse of an x-ray
event, and the small spike around 34 $\mu$s is likely an S1 single
photoelectron. The x-ray and gamma-ray energy range, from 6 to 60 keV, studied
in this work produce on average only 1 to 15 photoelectrons per interaction,
which combined with the low gain of our PMT makes the primary scintillation
yield difficult to quantify in a per-event basis. Therefore, despite the S1
footprint being clearly seen in the example of Fig. 6, it might be
indistinguishable from the electronic noise for other events. For this reason,
we rely on waveform averaging to cancel out the electronic noise hence
revealing the primary scintillation signal. Low-frequency fluctuations of the
oscilloscope baseline are the major source of statistical error in the S1
measurements. Yet, this can be mitigated with a sufficiently large
accumulation of waveforms. Each of the data runs comprises between 105 and
2$\times$106 waveforms, and can span 1 to 3 days of continuous data
acquisition. The stability of the system has been continuously monitored
during such long acquisition periods, by surveilling the centroid of the
highest peak in the energy spectrum of the radioactive source being in use,
obtained from the S2 pulse integration.

Figure 6:  Typical PMT waveform obtained for 5.9-keV x-rays, showing both the
primary and the secondary signals, S1 and S2.

A pre-processing algorithm was developed to discriminate background events
(e.g., cosmic radiation), as well as waveforms with features that are
unsuitable for further analysis. This is particularly important for the
accuracy of primary scintillation measurements. Since S2 pulses are 4 orders
of magnitude larger than S1 pulses, a single background event can jeopardize
the entire sample of events over which S1 is averaged. An example is a
waveform with two S2 pulses for which one of them falls into the S1 region.
Therefore, the discrimination algorithm rejects waveforms based on the
baseline cleanliness, as well as on the duration, time offset and shape of the
S2 pulse. In addition, the oscilloscope baseline offset is measured at the
beginning of every recorded waveform and corrected accordingly.

###  4.2 PMT calibration

An accurate calibration of the photosensor gain is crucial to quantify both
primary and secondary scintillation yields. A blue LED biased with direct
current was used to obtain the single photoelectron charge distribution of the
PMT. Since the detector radiation window can transmit visible light into the
PMT, there was no need to place the LED inside the gas chamber. PMT waveforms
were digitized with a sampling rate of 10 GS/s, allowing to resolve the short
pulses of single-photoelectrons. The oscilloscope trigger threshold was set as
low as possible without being overly saturated by background spikes. The LED
light intensity was adjusted for the probability of having more than one
photoelectron event in the same waveform to be negligible. Several
measurements with different trigger levels and LED intensities were carried
out to access the experimental uncertainty. The PMT gain calibration was
performed several times along the full experimental campaign to monitor its
performance. The gain variation was found to be within experimental errors.

Since a 200-Ω load resistor is used to collect the anode signal, wave
reflections at both ends of the signal cable are significant and needed to be
account for. However, due to the relatively large baseline fluctuations,
waveform integration of the single photoelectron pulse for time durations
above 200 ns, necessary to take into account those reflections, results in a
large noise peak in the PMT charge distribution, engulfing the single
photoelectron peak. Therefore, instead of integrating the full single
photoelectron signal, only a short region of the waveform containing the first
pulse was integrated, between -2 and 7 ns with respect to the oscilloscope
trigger time. This small integration time alleviates the impact of the
baseline fluctuations, with the disadvantage of excluding the reflected
pulses. Figure 7 left shows the charge distribution resulting from that
integration. A sum of three Gaussians was fitted to this charge distribution:
the first Gaussian accounts for the electronic noise with area, centroid, and
sigma being left as free parameters, while the other two Gaussians account for
single- and double-photoelectron emission. Their centroids follow the scaling
$1pe$ and $2pe$, respectively, where $pe$ is the centroid of the single-
photoelectron Gaussian, with standard deviations $\sigma$ following
$\sigma\sqrt{1}$ and $\sigma\sqrt{2}$, respectively, and the areas being
related through Poisson statistics. The centroid and the standard deviation of
the single-photoelectron Gaussian were left as free parameters, as well as the
rate parameter, $\lambda$, of the Poisson distribution.

This charge distribution was, then, used to select a sample of single-
photoelectron events, with charge values between $pe-0.5\sigma$ and
$pe+0.5\sigma$, falling outside the electronic noise and the double-
photoelectron Gaussians, Fig. 7 left. The waveforms of these selected events
are then averaged and the baseline offset, measured before the photoelectron
pulse, subtracted. Figure 7 right shows a typical average waveform obtained
from those selected events, highlighting the full pulse and the baseline
offset regions. The chain of reflected pulses is, now, clear, due to the
cancellation of the electronic noise. As expected, the spacing between pulses,
$\sim$16 ns, corresponds to twice the cable delay, which is 8 ns. The full
photoelectron signal was integrated between -10 and 200 ns. A mean charge
value per single photoelectron of 10.9 $\pm$ 0.3 mV ns was obtained for a PMT
biasing of 1450 V.

As a crosscheck for the above value, a second method was used: subtracting
previously the baseline to each individual waveform, by considering its
baseline as a straight line defined by the two offset values in the regions
just before the starting of the pulse and just after the 200-ns pulse
duration, and integrating the full waveform. Averaging over all waveform
integrals, one obtains a charge value 4% lower than what was obtained by the
former method, being this difference most likely due to the baseline
correction constraints.

We note that the probability of double-photoelectron emission from the PMT
photocathode is negligible in the visible region, but may reach 20% for VUV
photons Faham:2015kqa . Accordingly, one could expect that our experimental
results would also be affected by the double-photoelectron effect. However,
this contribution is cancelled out in calculations, since we use the PMT QE
curve provided by the manufacturer, which also includes this effect.

Figure 7:  (Left) Charge distribution of the first pulse of single-
photoelectron waveforms integrated between -2 and 7 ns. The corresponding fit
function is also depicted, along with the selected region of single-
photoelectron events. Only the electronic noise and single-photoelectron
Gaussian functions are represented, as the double-photoelectron contribution
is not visually perceptible; (right) average waveform for the events selected
in the left panel. The integration regions of the baseline offset and the
photoelectron signal are also shown.

As the PMT used in this work is old, we also took into account in its
calibration the effect of the afterpulsing, generated by the ionization of
residual gases inside the PMT and the subsequent drift of the positive ions
towards the photocathode where they induce the emission of further electrons.
The PMT afterpulsing contribution can be quantified using primary
scintillation events, because they are sufficiently separated in time from the
afterpulsing, given the short scintillation pulse of pure Xe, $\sim$100 ns
decay time for the dimer triplet state. Figure 8 depicts a typical waveform
averaged over 1.5 $\times$ 103 primary scintillation waveforms, obtained from
$\alpha$-particle interactions. The reduced electric field in the absorption
region was set to 140 V cm-1 bar-1 to prevent ion recombination
10.1088/1748-0221/10/03/P03025 ; 10.1088/1748-0221/8/05/P05025 ;
10.1143/JJAP.48.076501 ; 10.1109/tns.2004.836030 , while keeping the neutral
bremsstrahlung emission at residual levels NBrS_prx . The primary
scintillation waveforms were aligned using the rising edge at 50% of the
pulse’s height. The PMT afterpulsing is noticeable well separated from the
primary scintillation tail. An exponential function was fitted between 130 ns
and 250 ns to avoid the contributions from both the fast xenon scintillation
component of the singlet state and the afterpulsing. In this way, the
afterpulsing signal could be obtained subtracting the reconstructed S1 pulse
from the average waveform, as illustrated in Fig. 8. An afterpulsing
contribution of (24.9 $\pm\ $1.3) % was measured. This value was crosschecked
using waveforms obtained from a fast pulsed LED, attaining a 6% lower value,
relative to the former result.

We note that the results of Fig. 8 allow us to infer upper limits for the
impurity content in our chamber 10.1016/j.nima.2017.08.049 ;
10.1016/j.physletb.2017.09.017 ; 10.1007/JHEP01(2019)027 . From the above fit,
a value of $\tau_{3}=$ 108 $\pm$ 5 ns was obtained for the decay time of the
Xe dimer triplet state, to be compared with an average reference value of
$\tau_{3}=$ 100.9 $\pm$ 0.7 ns 10.1063/1.454313 . Using Eq. (1) from
10.1016/j.nima.2017.08.049  together with the two-body quenching rates for
excited xenon atoms reported in the literature, N2, CO2, O2, and CH4 from
10.1063/1.436447  and H2O from 10.1021/j100211a041 , an upper limit of 21 ppm
can be inferred for H2O, O2, CO2, and CH4 concentrations at 95% confidence
level, and 409 ppm for N2. Lower values can be derived for heavier molecules
based on the same references. Therefore, our absolute measurements of primary
or secondary scintillation yields are unlikely to be biased by impurity
quenching, since higher concentrations are typically required to have a
sizable impact on Xe scintillation 10.1016/j.nima.2017.08.049 ;
10.1016/j.physletb.2017.09.017 ; 10.1007/JHEP01(2019)027 .

Figure 8:  Average wavefrom obtained from $\alpha$-particle S1 pulses. The
pure S1 contribution is reconstructed using an exponential curve fitted to the
initial part of the tail. The afterpulsing contribution is obtained by
subtracting the S1 contribution to the average waveform.

###  4.3 X-ray and $\gamma$-ray runs

####  4.3.1 Energy and pulse duration cuts

Secondary scintillation pulses were integrated, allowing to build the energy
spectrum of the radioactive sources, being the highest peak used as reference
for energy calibration. The reconstructed energy spectra have shown good
linearity, with a deviation lower than 3% from the different theoretical
values. In this way, waveforms originated for different energies can be
selected for subsequent S1 measurements. The peaks of interest were fitted to
Gaussian functions, and events within 1.4 sigma, $\sigma$, with respect to
their centroids, $c$, were selected. A double Gaussian fit was applied when
the energy peak is highly asymmetrical due to the presence of two different
energies, e.g. $L_{\beta 1}$ and $L_{\beta 2}$ lines, with both the ratio
between the centroids, $c$, and the $\sigma$ dependence on $\sqrt{c}$ being
fixed. Accordingly, in those latter cases, the selected energy ranged from
$c_{1}\ –1.4\,\sigma_{1}$, of the first Gaussian, to $c_{2}+1.4\,\sigma_{2}$,
of the second Gaussian. The ratio between the areas of the two fitted Gaussian
functions was used to estimate the weighted theoretical energy of the selected
double peak, required for further calculations. Figure 9 shows two examples of
energy cuts performed for the x-ray energy spectrum of a 244Cm radioactive
source, including the Gaussian fits used for calibration and energy cuts.

Figure 9:  X-ray energy spectrum from a 244Cm radioactive source as obtained
from the S2 charge distribution. The selected events of the 14.3- and 18.0-kev
peaks (Pu $L_{\alpha}$ and Pu $L_{\beta_{1,2}}$) are depicted together with
the respective Gaussian fits. A double Gaussian function was used for the
18-keV peak. The 14.3-keV Gaussian fit was used for energy calibration.

Since S2 pulse duration is directly proportional to the path length drifted by
the primary electron cloud along the EL region, this parameter was used to
further discriminate the waveforms. Figure 10 shows the distribution of S2
pulse duration, measured between the 50%-thresholds of the S2 rising- and
falling-edges, obtained from 14.3-keV interactions that passed in the energy
cut, Fig. 9. The shape of the distribution is attributed to the longitudinal
electron diffusion: the longer the path length drifted by the electrons in the
absorption region, the larger the electron cloud, therefore producing longer
S2 pulses. The pulse width selection region was defined to be between the 15%
and 1.5% thresholds of the rising and falling edges, respectively, as
illustrated in Fig. 10. The lower cut discriminates events corresponding to
x-ray interactions occurring inside the EL region, e.g. from x-ray
interactions with higher energies, while the higher cut rejects some
background and anomalous waveforms.

Figure 10:  Distribution of the S2 pulse width of selected 14.3-keV events.
The S2 duration cuts are also illustrated.

Finally, waveforms passing both the energy and the pulse duration cuts are
averaged to cancel out the electronic noise. The 50%-threshold of the S2
rising edge was chosen for the alignment of waveforms avoiding the jitter
introduced by S2 pulse-width fluctuations. Figure 11 shows an average waveform
obtained for 14.3-keV x-rays, being computed from the events sampled in Fig. 9
and Fig. 10. Owing the large x/$\gamma$ -ray penetration along the absorption
region, a S1 continuum is unveiled, due to interactions occurring at different
depths, despite being 4 order of magnitude weaker when compared to S2. This
continuum can’t be separated from the S2 rising tail.

Figure 11:  Average waveform obtained for 14.3-keV x-rays after energy and
time cuts have been applied. The amplitude of the S1 continuum is zoomed-in by
a factor of 104.

####  4.3.2 Spatial cuts

To avoid contaminating S1 measurements with the S2 contribution, the primary
scintillation yield obtained from the average waveforms was determined
selecting only x/$\gamma$-ray interactions occurring in the first few
centimetres of the absorption region. These spatial cuts were defined using
the electron drift velocity, which was measured for all the studied energy
peaks and all the reduced electric fields applied to the drift region.
Electron drift velocities were computed from the time elapsed between S1 and
S2 rising edges of the average waveform, corresponding to the transit time of
electrons across the full absorption region. Figure 12 shows the electron
drift velocity obtained for all studied peak energies as a function of reduced
electric field. Our experimental data agree within two sigma with the
theoretical curve obtained from a Magboltz simulation, which is also depicted.

The electron drift velocity can be used to plot the waveform as a function of
distance travelled by the primary electron cloud in the drift region. The
integration of the S1 continuum of the average waveform was performed for the
first 2.5 cm of the absorption region. This region was chosen to maximize the
S1 statistics while keeping possible S2 contribution negligible.

Figure 12:  Electron drift velocity values obtained experimentally compared
with the Magboltz simulation curve.

####  4.3.3 S1 yield determination

The waveform of Fig. 11 can be, now, corrected for the detector geometrical
efficiency, section 3, to estimate the isotropic primary scintillation
emission. Figure 13 shows a typical average waveform obtained for 14.3-keV
x-rays, corrected for the GE curve, in terms of the depth where the
scintillation occurs: -3.6 cm and 0 cm correspond to the detector window and
gate mesh positions, respectively. The baseline offset is measured immediately
before the S1 integration region and subtracted to the waveform.

Figure 13:  Average waveform obtained for 14.3-keV x-rays and corrected for
the GE curve, plotted as a function of depth where the primary scintillation
occurs, with -3.6 cm and 0 cm corresponding to the detector window and gate
mesh, respectively. The regions of interest used to compute the baseline
offset, already subtracted, and the S1 yield are depicted together with the
theoretical absorption curve of 14.3-keV x-rays in the 1.2-bar xenon gas.

As shown, the GE-corrected waveform follows the theoretical exponential
x/$\gamma$-ray absorption law, which is also plotted in Fig. 13. This
observation supports the reliability of the developed GE simulation model.

The average waveform was composed by all events under a specific energy peak
that occurred inside the whole absorption region. Therefore, the ratio of
events in the S1 integration region to the total number of S1 events occurring
in the absorption region had to be accounted for in the determination of the
primary scintillation yield. This parameter, $R_{e}$, was estimated from the
exponential absorption law of x/$\gamma$-rays in xenon expected for the
respective experimental working conditions, i.e. the theoretical energy of the
impinging x/$\gamma$-ray, the gas pressure and the temperature.

From the integration of the waveform amplitude, the total charge induced in
the PMT anode by the x/$\gamma$-ray interactions was determined. This charge
was converted into number of photoelectrons produced in the PMT photocathode
from the single-photoelectron mean charge, $pe$, corrected for the
afterpulsing contribution, as obtained in section 4.2. Therefore, the number
of primary scintillation photons per event $N_{ph}$ was calculated from the
amplitude of the corrected average waveform, $U_{m}$, according to the
following equation:

$N_{ph}=\frac{1}{R_{e}\ pe\ QE}\int_{-3.6cm}^{-1.1cm}\frac{U_{m}}{v_{d}\ GE}\
dz,$ (1)

where $QE$ is the PMT quantum efficiency at 175 nm, $v_{d}$ is the
experimental electron drift velocity, $U_{m}/v_{d}$ the waveform amplitude and
$GE$ the geometrical efficiency, both as a function of distance to the
detector window $z$, integrated over the -3.6 to -1.1 cm interval.

The energy required to produce one scintillation photon $w_{sc}$ was obtained
assuming the theoretical deposited energy $E_{dep}$ of the peak being studied
or, in the case of double peaks, the theoretical weighted energy:

$w_{sc}=\frac{E_{dep}}{N_{ph}}\ .$ (2)

####  4.3.4 S2 yield determination

In addition to the primary scintillation determination, our setup allows
measuring the electroluminescence yield. This parameter was calculated using
the average charge of the S2 signal, $c_{S2}$, obtained from the centroid of a
Gaussian fitted to the selected energy peak of the S2 charge distribution, as
can be seen in Fig. 9. In this way, the number of EL photons produced per
drift path length, per ionization electron and per unit of pressure, $Y_{el}$,
was computed according to the equation:

$Y_{el}=\frac{c_{S2}}{\ pe\ QE\ \overline{GE_{el}}\ \Delta z\ P\
\overline{N_{e}}}\ ,$ (3)

where $\overline{GE_{el}}$ is the average geometrical efficiency in the EL
region, 31%, see Fig. 5; $\Delta z$ is the EL gap length; $P$ is the gas
pressure, $\sim$1.2 bar; and $\overline{N_{e}}$ is the mean number of
ionization electrons produced in a x/$\gamma$-ray interaction.
$\overline{N_{e}}\ =E_{dep}/w_{i}$ where $w_{i}$ is the mean energy required
to create one electron-ion pair in xenon. A $w_{i}$-value of 21.6 $\pm$ 0.2 eV
was considered, as measured experimentally for xenon at a pressure around 1
bar in 10.1109/TNS.2008.2003075 .

As a cross-check, the $c_{S2}$ parameter can also be obtained from the
integration of the S2 pulse average waveform, as was done for the primary
scintillation analysis method. The $Y_{EL}$ obtained for both the S2 charge
distribution method and the average waveform integration method were found to
agree within a 3%-error, supporting the reliability of the average waveform
analysis used in primary scintillation studies. The former method for $Y_{el}$
calculations has been henceforth applied, the difference between the two
methods being included in the experimental uncertainty.

###  4.4 Alpha-particle runs

The energy of 241Am $\alpha$-particles is 2 orders of magnitude higher than
the studied x/$\gamma$-ray energy range. To avoid PMT saturation for S2
pulses, it was biased at a lower voltage, 800 V instead of 1450 V. The PMT
gain scaling factor was measured using the centroid of the 5.9-keV x-ray peak
from the 55Fe energy spectrum, acquired for both PMT voltages and using the
same reduced electric field values. The theoretical energy deposited by
$\alpha$-particles in GXe cannot be accurately simulated, due to the unknown
thickness of both the aluminium-deposited film on the detector window and the
gold protective layer of the radioactive source. Therefore, the detector was
calibrated with the 5.9-keV peak from the 55Fe radioactive source, using the
same reduced electric field values and gas pressure as in $\alpha$-particle
runs. Figure 14 shows a typical energy spectrum obtained for the S2 charge
distribution of $\alpha$-particles after calibration. The different layers of
materials degraded energy and trajectory of $\alpha$-particles before they
reached the xenon gas, resulting in a left-tailed peak. Low energy events were
discriminated as they might have occurred too close to the detector window
where the electric field is weaker, and some of the produced ionization
electrons could have been lost to the window electrode. Thus, only events with
energies higher than 40% of the height of the energy peak were accounted for
in primary scintillation calculations, as illustrated in Fig. 14. Pulse
duration cuts were not required for $\alpha$-particles because they did not
reach the EL region.

Figure 14:  Energy spectrum for 241Am $\alpha$-particles obtained from the S2
charge distribution. The energy cut is also shown. Despite the fact that no
Mylar foils have been used in this case to further reduce $\alpha$-particle
energies, a significant part of their energy was lost to the detector window.
The 241Am x/$\gamma$-ray peaks are not visible due to the chosen oscilloscope
trigger threshold, which was set above the amplitude of these pulses.

As in the x/$\gamma$-ray analysis method, the average waveform was computed
from selected events and corrected for the baseline offset that is measured
before S1. Figure 15 depicts a typical waveform averaged over 6 $\times$ 103
events. Since the $\alpha$-particle penetration is short and the electron
cloud drift time is similar for all the events, the S1 pulse is sharp and
localized. Therefore, the primary scintillation yield can be obtained directly
from the integration over the full S1 pulse, hence avoiding the need for
spatial cuts. Figure 15 illustrates as well the waveform regions used for
baseline offset correction and for S1 integration.

Figure 15:  Average waveform of selected 2.5-MeV $\alpha$-particle events. The
regions of interest used for baseline offset, already subtracted, and the
calculated S1 yield values are also shown.

The GE correction was calculated from the simulated GE curve, Fig. 5, weighted
over the energy deposition along the $\alpha$-particle interaction depth, Fig.
4 left, as obtained from GEANT4 $\alpha$-particle tracking, described in
section 3.1. Mylar films with different thicknesses were used to degrade the
$\alpha$-particle energies in order to irradiate the detector with
$\alpha$-particles of different energies. Accordingly, for every data
acquisition, the energy of simulated $\alpha$-particles was adjusted for the
deposited energy distribution to match the mean energy measured experimentally
after the energy cuts were applied. The mean geometrical efficiency value,
$\overline{GE}$, was found to be in the 6% to 7% range, depending on the
$\alpha$-particle energy being studied. In this way, the number of primary
scintillation photons generated per event, $N_{ph}$, was computed as:

$N_{ph}=\frac{1}{\ pe\ QE\ \overline{GE}\ }\int_{-2\ \mu s}^{5\ \mu s}U_{m}dt\
,$ (4)

where $U_{m}$ is the amplitude of the average waveform integrated between -2
$\mu s$ and 5 $\mu s$ with respect to 50% of the S1 pulse rising edge. $QE$
and $pe$ are the same values as in the x/$\gamma$-ray analysis method.
Finally, the $w_{sc}$-value was obtained from:

$w_{sc}=\frac{E_{dep}}{N_{ph}}\ .$ (5)

Where $E_{dep}$ is the measured deposited energy, averaged over the selected
events, Fig. 14.

In contrast to x/$\gamma$-ray runs, the S1 pulse was large enough to be
detected in the individual $\alpha$-particle waveforms, allowing to perform
per-event statistics. For this analysis method the S1 pulse-time was
automatically detected as the maximum amplitude in the S1 region of the
waveform, which was previously processed with a software-implemented
differentiator and a moving average to remove both low- and high-frequency
fluctuations. Finally, the baseline offset and the S1 pulse were integrated in
the intervals -4.2 $\mu s\ $to -0.2 $\mu s$ and -0.2 $\mu s$ to 3.8 $\mu s$,
respectively, with respect to the S1 peaking time. Figure 16 left shows an
example of a single $\alpha$-particle waveform with highlighted integration
regions. Figure 16 right shows the distribution of integration values for both
baseline offset and S1 pulse. Despite the energy of the selected
$\alpha$-particle events not obeying a Gaussian distribution, the S1 integral
distribution is roughly Gaussian due to the large number of statistical
fluctuations. Therefore, both S1 mean charge value and mean baseline offset
could be estimated from the centroid of a Gaussian function fitted to each
distribution, as shown in Fig. 16 right.

Figure 16:  (Left) Waveform of a typical S1 pulse produced by an
$\alpha$-particle interaction. The integration regions considered for baseline
offset and S1 yield calculations are also depicted; (right) charge
distribution from the baseline and S1 regions of interest obtained for 2.5-MeV
$\alpha$-particles, along with the corresponding Gaussian fits.

The difference between $w_{sc}$-values obtained from both methods, average
waveform and per-event statistics, was under 2%. This agreement supports our
assumption that the waveform average method does not introduce a meaningful
systematic error in the results. $w_{sc}$ results for $\alpha$-particles
reported henceforth correspond to the mean value obtained with both methods.

##  5 Results and discussion

The reduced electroluminescence yield, $Y_{el}/p$, as a function of reduced
electric field, $E/p$, in the EL region is shown in Fig. 17, together with the
theoretical curve obtained with Garfield++ simulation, as described in section
3.2. 5.9-keV x-rays from a 55Fe radioactive source were used, although with
much lower acquisition times when compared with primary scintillation runs.
Only the systematic error is depicted since the statistical uncertainty was
lower than 3%, thus negligible. EL yield values that were obtained from the
primary scintillation acquisition runs are depicted as well. The typical
approximately linear dependency of EL yield with electric field is observed. A
line fitted to the experimental data is also depicted, having the following
fit parameters: $Y_{el}/p=(157\pm 4)\ E/p\ –\ (127\pm 5)$, where $Y_{el}/p$
and $E/p$ have units of $ph/(e^{-}\ cm\ bar)$ and $kV/(cm\ bar)$,
respectively. The interception of the fitted line with the $E/p$ axis, defined
as the EL threshold is $0.81\pm 0.04$ $kV/(cm\ bar)$. The experimental EL
yield is about 7% higher than theoretical predictions and 14% higher when
compared to the experimental values obtained in a driftless GPSC
10.1088/1748-0221/2/05/P05001 . Nevertheless, these differences are within
experimental uncertainties.

Figure 17:  Experimental electroluminescence yield as a function of reduced
electric field together with the corresponding linear fit. Yield values
obtained from S1 data runs are also shown, along with the Garfield++
simulation data.

###  5.1 $w_{sc}$ absolute measurements

The $w_{sc}$-value was measured for different electric field values in the
absorption and in the EL region to evaluate possible systematic errors and the
role of electron-ion recombination. In the absorption region, the electric
field was varied in the 70–300 V cm-1 bar-1 range. At moderately high electric
field values, the recently unveiled neutral bremsstrahlung emission in xenon
becomes significant when compared with the weak primary scintillation
emission. We resorted to the NBrS photoelectron yield measured in NBrS_prx  to
estimate its contribution in our data. The NBrS contribution in the S1
integration region was estimated considering the geometrical efficiency model
and the distribution of event position along the absorption region. For the
highest electric field value, 300 V cm-1 bar-1, the NBrS accounted for 11% of
the total S1 charge, being negligible below 150 V cm-1 bar-1. These
corrections were included in the $w_{sc}$ calculations. For $\alpha$-particle
runs the NBrS impact was negligible because only a short region of the
waveforms was integrated. We did not find any significant dependency of the
$w_{sc}$-value, duly corrected for NBrS contribution, on the electric fields
either in the absorption region or in the EL region, within the studied
ranges. Therefore, any major systematic error associated to electric field is
unlikely to occur.

Figure 18 shows the $w_{sc}$-values measured in the absence of recombination
for x/$\gamma$-ray and $\alpha$-particle interactions in the energy range
between 5.9 keV and 2.5 MeV, assuming a negligible 3rd continuum emission.
Data points corresponding to the same energy were statistically combined for
clarity. Systematic and statistical errors at the 68% confidence level are
displayed with separated error bars. The systematic uncertainty arises mainly
from the detector geometrical efficiency simulation, Fig. 5, though with
sizeable contributions from the PMT single-photoelectron calibration and
quantum efficiency, 9% and 7%, respectively. Whereas the latter two
contributions are energy-independent, the GE uncertainty is generally lower
for high energy x/$\gamma$-rays, since the relevance of photon reflection
becomes smaller for interactions occurring closer to the PMT. This partially
explains the large systematic error in $\alpha$-particle runs, which also
includes an additional error source stemming from the detector energy
calibration, 14%. The statistical uncertainty was dominated by the
oscilloscope’s baseline fluctuations. Therefore, this error was lower in
$\alpha$-particle data due to the much higher S1 amplitude when compared to
the baseline fluctuations.

Figure 18:  Absolute $w_{sc}$-value obtained experimentally for x-rays,
$\gamma$-rays and $\alpha$-particles as a function of deposited energy;
simulation and literature experimental data are included for comparison. The
statistical and systematic uncertainties in our experimental data are
presented in black and blue error bars, respectively, both referring to the
68% confidence level. The statistically combined $w_{sc}$-value obtained from
our experimental data is also shown, the overall uncertainty being depicted as
a red band. For all the data in the literature, the 3rd continuum emission is
assumed to be negligible, except for Leardini’s value.

The mean $w_{sc}$-value of our experimental data, 38.7 $\pm$ 0.6 (sta.)$\
{}_{-7.2}^{+7.7}$ (sys.) eV, is also depicted in Fig. 18, being computed from
the entire dataset weighted over the respective statistical errors. When the
dataset was split into x/$\gamma$-ray and $\alpha$-particle runs, the mean
$w_{sc}$-values obtained were 41.8 $\pm$ 1.0 (sta.)$\ {}_{-6.2}^{+6.8}$ (sys.)
eV and 36.6 $\pm$ 0.8 (sta.)$\ {}_{-7.7}^{+8.2}$ (sys.) eV, respectively.
These differences are within the experimental uncertainty, preventing us from
precisely observe any fundamental distinction between the primary
scintillation yield for electrons and alpha particles.

All the values depicted in Fig. 18 assume the 3rd continuum emission to be
negligible, except the value reported by Leardini _et al._ , which refers to
the 2nd continuum only, as they used optical filters to suppress the most part
of the 3rd continuum emission 10.1140/epjc/s10052-022-10385-y . However, the
measured values for the primary scintillation yield includes the contribution
of both the 2nd and the 3rd continuum, as the PMT is sensitive to wavelengths
in the 150-650 nm region. Our PMT QE, Fig. 2, was a factor of 1.32 higher for
the xenon 3rd continuum with respect to the 2nd continuum, while the GE of the
detector was a factor of 1.05 higher, as obtained from the GE simulation
model. At 1.2 bar, the ratio between the contributions from the 3rd and the
2nd continuum to the primary scintillation emission in the absence of
recombination was measured to be 0.09 $\pm$ 0.01
10.1140/epjc/s10052-022-10385-y . Therefore, the mean energy required to
produce a 2nd continuum scintillation photon $w_{2^{nd}}$ was estimated to be
$w_{2^{nd}}=(1\ +\ 1.32\times 1.05\times 0.09)\ w_{sc}$ = 43.5 $\pm$ 0.7
(sta.)$\ {}_{-8.1}^{+8.7}$ (sys.) eV, where $w_{sc}$ is the measured value
when neglecting the 3rd continuum emission. The mean energy required to
produce a 3rd continuum photon was computed as $w_{3^{rd}}=(1/0.09)\
w_{2^{nd}}=$ 483 $\pm$ 7 (sta.)$\ {}_{-105}^{+110}$ (sys.) eV and the mean
energy required to produce a primary scintillation photon was obtained as
$w_{2^{nd}{+3}^{rd}}=\ w_{2^{nd}}/(1+0.09)=$ 39.9 $\pm$ 0.6 (sta.)$\
{}_{-7.4}^{+8.0}$ (sys.) eV.

As a crosscheck, instead of relying on the PMT single photoelectron response
and the absolute simulated GE for optical calibration of the detector, one
could use the S2 charge distribution and the corresponding yield value given
by simulation. Since the experimental EL yield depicted in Fig. 17 is 7%
higher than the simulation value, one may argue that data obtained by the
former method are overestimated, e.g. due to a systematic uncertainty related
to the PMT calibration. Accordingly, the $w_{sc}$-values obtained with that
method could be underestimated. Assuming this second method, the results
obtained with the former method could be normalized considering the ratio
between theoretical and experimental EL yields, as the latter was measured for
every run by integrating the S2 pulses of the waveforms. Such a correction
would make $w_{sc}$-values 7% higher on average, which nevertheless is still
within the 68% confidence level of the present data of Fig. 18. If, on one
hand, this second analysis method has the advantage of eliminating the
systematic uncertainty introduced by both PMT calibration and QE, as well as a
sizeable part of the GE uncertainty. On the other hand, it introduces new
error sources, such as the width of the EL region and the gas temperature,
both contributing $\sim$5%. For this reasons, we consider the absolute
$w_{sc}$-values depicted in Fig. 18 to be more accurate than EL-corrected
values.

As another crosscheck to our $w_{sc}$-values we applied the same analysis
method used in this work to other two gas scintillation chambers filled with
Xe, namely a driftless GPSC used in NBrS_prx ; 10.1016/j.physletb.2017.09.017
; 10.1007/JHEP01(2019)027  and a similar chamber built for Kr-gas studies
daniel . The $w_{sc}$-values obtained for 5.9-keV x-rays and 2-MeV
$\alpha$-particles agree within experimental uncertainties with the values
presented here.

###  5.2 $w_{sc}$ comparison with literature values

Figure 18 illustrates well how dispersed is the data from the literature.
Despite the theoretical values, around 40 eV, are compatible with most of the
$\alpha$-particle results, there is a clear disagreement with x/$\gamma$-ray
data. $w_{sc}$ is expected to be similar for x-, $\gamma$-rays or electrons
and almost equal to that obtained for $\alpha$-particles
10.1143/JJAP.48.076501 . However, the results presented so far in the
literature are inconsistent with that expectation, being this difference not
understood. The $w_{sc}$ results presented in this work agree with both
theoretical predictions and most of $\alpha$-particle experimental values. In
addition, the present results do not show a dependency of $w_{sc}$ with the
nature or the energy of the impinging radiation, being incompatible with
literature’s values obtained for x/$\gamma$-rays, even considering the
experimental uncertainties. The different experimental conditions reported in
the literature seem insufficient to explain the discrepancies. The impact of
gas pressure is expected to be minor up to 20 bar 10.1016/j.nima.2017.08.049 ;
10.1143/JJAP.48.076501 ; 10.1140/epjc/s10052-022-10385-y  and for electric
field values above 60 V cm-1 bar-1, recombination is negligible
10.1088/1748-0221/10/03/P03025 ; 10.1088/1748-0221/8/05/P05025 ;
10.1143/JJAP.48.076501 ; 10.1109/tns.2004.836030 .

In order to clarify this puzzle, we attempted to replicate the experimental
methodology of Fernandes’ and Carmo’s works 10.1088/1748-0221/3/07/P07004 ;
10.1088/1748-0221/5/09/P09006 , since their experimental apparatus were
similar to the one we have used. A major difference was the fact that the data
acquisition system in those works consisted of conventional x-ray spectroscopy
electronics, i.e. instead of feeding the PMT signal directly into the
oscilloscope, the PMT signal was first integrated and shaped by a pre-
amplifier and a linear amplifier chain. Like in our analysis method, the weak
primary scintillation signal was unveiled by averaging several PMT waveforms,
though with far less statistics, 128 against 106 events. Due to hardware
signal integration, the S1 and S2 heights were proportional to the PMT charge
produced by the primary and secondary scintillation emissions. Hence, the S1
and S2 pulse heights from 5.9 keV x-rays were measured from two averaged
waveforms acquired in different runs: one with a low amplification level set
in the linear amplifier to avoid S2 pulse saturation, and the other with high
amplification to reveal the S1 pulses. The ratio between the two pulse heights
was corrected for the difference between the solid angles subtended by the PMT
with respect to the primary and secondary scintillation emissions, being the
absolute EL yield established in the literature used to estimate the total
number of primary scintillation photons, in spite of the 4 orders of magnitude
difference between them.

We were able to reproduce Fernandes’ and Carmo’s findings by replicating the
above methodology. We identified several issues in the analysis method leading
to large systematic errors, which in our opinion were not properly accounted
for in those works. The lack of an adequate light propagation model to
quantify the geometrical efficiency in the absorption and in the EL region was
the most obvious one. Figure 5 illustrates how important photon reflection is.
From our simulation data, a $\sim$50% underestimation of the $w_{sc}$-value
would be expected, yet this is the opposite that is shown in Fig. 18.
Therefore, a much larger and opposite experimental error would be required to
explain those results.

A major source of systematic errors is the oscilloscope trigger threshold,
which serves in this analysis as the only method of event selection and
discrimination. Since S1 and S2 pulses were averaged over every waveform,
their heights include all background events occurring above the trigger
threshold, such as cosmic rays. Indeed, we observed a $\sim$100% increase of
the $w_{sc}$ parameter just by tightly collimating the 55Fe radioactive
source, thus increasing the ratio between background and 5.9-keV x-ray events.
This finding is disruptive, since it demonstrates how the $w_{sc}$ measurement
can be easily biased by the radioactive source activity and by the background
levels of a given experiment. When measuring the S1 height of the average
waveform, the signal needs to be amplified by about 3 orders of magnitude by
the linear amplifier. Consequently, the maximum setting of the oscilloscope’s
trigger threshold is much lower than S2 amplitudes. In such conditions, all S2
pulses with energies above $\sim$0.0059 keV are triggered, and even some S1
pulses can be triggered as if they were S2 pulses. Many of these backgrounds
or badly sampled waveforms do not actually have any photon emission in the S1
region, thus leading to an underestimation of the average S1 height. Indeed,
we found out that by simply decreasing the trigger threshold, the
$w_{sc}$-value could increase from 60 eV to 150 eV.

##  6 Conclusions

We have carried out an experimental campaign to measure the gaseous xenon
primary scintillation yield, $w_{sc}$ – the average energy to produce a
primary scintillation photon, for interactions of alpha particles in the 1.5 –
2.5 MeV range and for x/$\gamma$-rays in the 6 to 60 keV range. We used a gas
scintillation chamber instrumented with a PMT to readout both the primary
scintillation, S1, produced upon radiation interaction and the secondary
proportional scintillation, S2, produced by the primary ionization electrons.
For the purpose we digitized the PMT waveforms using the large S2 pulses to
trigger the digitizer, and averaged a very large number of pulses, $\sim$106,
to cancel out the electronic noise and unveil the signal from the primary
scintillation.

Two methods have been used: optical calibration through single photoelectron
response and optical calibration using the area of the S2 waveform being the
corresponding yield value given by simulation. Both methods agree within the
experimental uncertainties.

Measuring the $w_{sc}$-value is far more challenging for low energy x-rays
than for $\alpha$-particles. Whereas per-event statistics can be used in
$\alpha$-particle runs, waveforms averaging is required for x/$\gamma$-rays.
We validated the latter method by comparing it with per-event statistics for
$\alpha$-particles, achieving similar results well within the experimental
uncertainties.

We obtained a $w_{sc}$-value that is simultaneously compatible with well-
established literature data reported for $\alpha$-particles and in good
agreement with state-of-the-art simulations performed for x/$\gamma$-ray
interactions. In addition, the present results do not show a significant
dependency of $w_{sc}$ with the nature or the energy of the impinging
radiation. These arguments sustain our hypothesis that some literature
$w_{sc}$-values obtained for x/$\gamma$-ray are unreliable due to undressed
systematic errors.

The results obtained in this work are summarized in Table 2 for the absolute
$w_{sc}$-value. We chose to present the mean $w_{sc}$-value of all our
experimental data, being computed from the entire dataset weighted for the
respective statistical errors. In addition, we present the $w_{sc}$-value for
second and third continua separately, assuming a 3rd-to-2nd continuum yield
ratio of 0.09, as recently disclosed in the literature, and the $w_{sc}$-value
for the emission of either 3rd or 2nd continuum photon.

$w_{sc}$ (eV) | observations
---|---
38.7 $\pm$ 0.6 (sta.)$\ {}_{-7.2}^{+7.7}$ (sys.) | 3rd continuum neglected
43.5 $\pm$ 0.7 (sta.)$\ {}_{-8.1}^{+8.7}$ (sys.) | 2nd continuum
483 $\pm$ 7 (sta.)$\ {}_{-105}^{+110}$ (sys.) | 3rd continuum
39.9 $\pm$ 0.6 (sta.)$\ {}_{-7.4}^{+8.0}$ (sys.) | 2nd+3rd continua
Table 2: A summary of the mean $w_{sc}$-values measured in the present work
for x-rays, $\gamma$-rays and $\alpha$-particles in the 6–2500 keV energy
range, either considering or neglecting the Xe 3rd continuum.

###### Acknowledgements.

This work was fully funded by national funds, through FCT – Fundação para a
Ciência e a Tecnologia, I.P., under Projects No. UIDP/04559/2020,
UIDB/04559/2020, CERN/FIS-TEC/0038/2021 and PTDC/FIS-NUC/3933/2021, and under
Grant No. UI/BD/151005/2021. We thank C.D.R Azevedo for introducing to
simulation inter-using Magboltz, Garfield++ and Degrad. We thank D. Gonzalez-
Dias for fruitful discussions.

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