arXiv:1110.3056v1 [physics.ins-det] 13 Oct 2011
Prepared for submission to JHEP
Single electron emission in two-phase xenon
with application to the detection of coherent
E. Santos,1,2B. Edwards,3V. Chepel,1H.M. Ara´ ujo,2D.Yu. Akimov,4E.J. Barnes,5
V.A. Belov,4A.A. Burenkov,4A. Currie,2L. DeViveiros,1C. Ghag,5
A. Hollingsworth,5M. Horn,2G.E. Kalmus,3A.S. Kobyakin,4A.G. Kovalenko,4
V.N. Lebedenko,2A. Lindote,1,3M.I. Lopes,1R. L¨ uscher,3P. Majewski,3
A.StJ. Murphy,5F. Neves,1,2S.M. Paling,3J. Pinto da Cunha,1R. Preece,3
J.J. Quenby,2L. Reichhart,5P.R. Scovell,5C. Silva,1V.N. Solovov,1N.J.T. Smith,3
P.F. Smith,3V.N. Stekhanov,4T.J. Sumner,2C. Thorne2& R.J. Walker2
1LIP–Coimbra & Department of Physics of the University of Coimbra, Portugal
2High Energy Physics group, Blackett Laboratory, Imperial College London, UK
3Particle Physics Department, STFC Rutherford Appleton Laboratory, Chilton, UK
4Institute for Theoretical and Experimental Physics, Moscow, Russia
5School of Physics & Astronomy, University of Edinburgh, UK
Abstract: We present an experimental study of single electron emission in ZEPLIN–III,
a two-phase xenon experiment built to search for dark matter WIMPs, and discuss appli-
cations enabled by the excellent signal-to-noise ratio achieved in detecting this signature.
Firstly, we demonstrate a practical method for precise measurement of the free electron
lifetime in liquid xenon during normal operation of these detectors. Then, using a realistic
detector response model and backgrounds, we assess the feasibility of deploying such an
instrument for measuring coherent neutrino-nucleus elastic scattering using the ionisation
channel in the few-electron regime. We conclude that it should be possible to measure
this elusive neutrino signature above an ionisation threshold of ∼3 electrons both at a
stopped pion source and at a nuclear reactor. Detectable signal rates are larger in the
reactor case, but the triggered measurement and harder recoil energy spectrum afforded
by the accelerator source enable lower overall background and fiducialisation of the active
Keywords: xenon detectors, single electron emission, electroluminescence, ZEPLIN–III,
coherent neutrino scattering, reactor antineutrinos, stopped pion source
ZEPLIN–III is a two-phase xenon detector designed for the direct detection of WIMP dark
matter [1, 2]. The two-phase technique [3–5] produces two different signals for each particle
interacting within the active volume, one from primary scintillation in the liquid (S1) and
the other from electroluminescence in the gas phase (S2). This second signal is a measure of
the amount of ionisation drifted from the interaction site by application of an electric field
and subsequently emitted from the liquid surface. The scintillation and ionisation yields
differ for electron and nuclear recoils, providing a physical basis for the discrimination
between interaction types. Since discrimination requires both signals, in typical WIMP
dark matter searches the energy threshold is determined by the less sensitive S1 response
The ionisation signal is measured through cross-phase emission of electrons extracted
from tracks in the liquid into the xenon vapour above it. Here, they are accelerated by a
strong electric field and induce secondary scintillation (electroluminescence) in the xenon
vapour. The photon yield is a linear function of the field E and can be parametrised by
Nph= (aE + bn)x, where x is the thickness of the gas layer, n is the number density of
xenon atoms and the coefficients a and b were determined experimentally for saturated
xenon vapour in Ref. . For typical ZEPLIN–III operational parameters (E=7–8 kV/cm
in the gas at 1.6 bar, x ∼ 4 mm), some 300 photons are produced by a single electron
emitted from the liquid.
The possibility of exploiting the sensitivity of the ionisation channel down to the single
electron level (sub-threshold in S1) has been pointed out in the context of coherent neutrino-
nucleus scattering in 2004 . This motivated a programme based on two-phase argon
for nuclear reactor monitoring . Interest in this experimental technique has now also
extended to searches for light WIMPs . With this type of application in mind, we first
characterised the single electron signature using ZEPLIN–II data  and in work with a
smaller prototype chamber operating in a surface laboratory .
This article is organised as follows. In Section II we discuss the single electron signa-
ture and likely production mechanisms based on analyses of independent datasets acquired
under different conditions. This leads to the demonstration of a very practical application:
the determination of the free electron lifetime in the liquid phase by using WIMP-search
data only. This could be especially relevant for next-generation WIMP experiments based
on the noble liquids. In Section III we assess the feasibility of using the ionisation chan-
nel down to single electron level to measure the coherent elastic scattering of neutrinos
off nuclei, a Standard Model process not yet observed. We include realistic signal char-
acteristics and a background of single electron pulses which might be produced by the
mechanisms identified in the preceding section. Previous studies have typically assumed
idealised response models.
– 2 –
150 152 154 156 158 160 162 164
156.2 156.4 156.6 156.8 157 157.2 157.4
156.2 156.4 156.6 156.8 157 157.2 157.4
156.2 156.4 156.6 156.8 157 157.2 157.4
Figure 1. A single electron signal in ZEPLIN–III (sum waveform shown top left; channel waveforms
containing detected photoelectrons are zoomed in).
2 Single electrons in ZEPLIN–III
Single electron signals were studied using four independent datasets: two WIMP-search
exposures (of several months’ duration) and two dedicated runs. The main difference
between the two types of dataset is the origin of the trigger for data acquisition (DAQ).
During dark matter data-taking, the trigger function was derived from S1 or S2 pulses in the
detector, recording ±18 µs waveforms centred around the trigger point. In the dedicated
runs, on the other hand, the DAQ was triggered externally with a pulse generator at a fixed
(high) repetition rate, independently of any signals in the detector. In this instance the
acquired waveforms were 256 µs long, which exceeds significantly the maximum ionisation
drift time in the chamber (∼14.5 µs).We begin by describing the set-up and results
from the first dedicated single-electron run (hereafter ‘DSER’), which underwent the most
extensive analysis. Key parameters for this and other datasets are summarised in Table I.
2.1 Dedicated single electron run
A total live time of 161.4 s was recorded during the DSER acquisition over a 2-day period
after the completion of the first science run (FSR) in 2008. During that time, the xenon
pressure in the detector remained stable at 1.6 bar and E=7.6 kV/cm in the gas. The
signals from each of the 31 PMTs were digitised with 2 ns sampling and 8-bit resolution
over the 256 µs timelines. The DAQ system was forced to trigger at the maximum rate for
this configuration (18 s−1) by an external pulse generator. The raw waveform data were
reduced with the ZE3RA pulse analysis algorithms , using similar parameters to those
– 3 –
Table 1. Single electron rates in ZEPLIN–III
live time event rate‡
†Electric field in the liquid xenon away from cathode.
‡Higher energy background above normal trigger threshold (S2>4 electrons).
∗20 µs inhibit period
adopted for the FSR data, except that a Fourier transform digital filter was applied to the
waveforms to remove coherent noise induced by the pulse generator. The reduced data
were then searched for photoelectron clusters, characteristic of single electron emission, at
a minimum of 3-fold coincidence in the PMTs, with a pulse amplitude threshold of 4 times
the rms noise in each waveform. An example of such cluster is shown in Figure 1. In
this particular analysis, the number of single photoelectron pulses in a cluster is counted
by the number of threshold crossings individually in each channel using a constant 50-
ns integration time. A channel-by-channel correction is then applied to account for the
dead-time effect thus introduced (a constant-rate Poisson process is assumed).
The following selection cuts are applied in this analysis: i) no pulses present in the
preceding 20 µs in any waveform; this is greater than the ionisation drift time for the full
liquid depth and ensures that selected events are not induced directly by a previous energy
deposition in the liquid xenon; ii) the reconstructed x,y position of the event must be
within the central 60 mm radius of xenon (1.3 kg active mass); this allows the use of a
simple centroid position reconstruction algorithm and ensures uniform light collection.
Figure 2 (left) shows the size distribution of photoelectron counts in single electron
clusters for this dataset. The histogram was fitted by exponential and Gaussian compo-
nents, resulting in a mean number of 28.3±0.3(stat) photoelectrons per pulse. The very
large peak-to-valley ratio of the distribution confirms the excellent sensitivity to these
pulses. The observed single electron event rate was 5.7 s−1. The x,y spatial distribution of
these events, shown in Figure 3, is relatively uniform within the selected volume, although
a bias is observed at larger radii. This is attributed to a small and well-understood tilt of
the detector of a few mrad, which affects the thickness of the gas layer (and, to a lesser
degree, the electric field strength), causing a systematic variation in the detection efficiency
at large radii.
2.2The WIMP science runs
The first science run of ZEPLIN–III acquired WIMP-search data for 83 days. Details of the
data acquisition and primary dark matter analyses are described elsewhere [2, 13–15]. Two
populations of small S2-like pulses were observed in the waveforms. One follows large S1
– 4 –
27.65 / 16
photoelectrons per pulse
0 10 20304050 6070 80 90
94.15 / 41
pulse area, photoelectrons
0 1020 30 40 50 60708090
Figure 2. Single electron pulse size distributions in the first science run configuration of ZEPLIN–
III. Left: Number of photoelectrons per cluster obtained with the dedicated DSER dataset by
photoelectron counting (dead-time corrected), as described in §2.1. Right: Size distribution of
post-S1 pulses in the FSR science data, obtained by pulse area integration and converted subse-
quently into photoelectron numbers (§2.2.1).
-100 -500 50 100
Figure 3. Centroid-reconstructed position of ‘spontaneous’ single electron pulses in the DSER
dataset. This analysis extends to 60 mm radius. The bias observed at large radii is due to a small
detector tilt which increases the gas layer thickness where an excess of events is observed.
or S2 signals and is clearly induced by the VUV luminescence ; this population allows
for an accurate characterisation of single electron clusters. Another can be observed in the
quiet pre-trigger region of the waveforms, before S1 pulses, and may be unrelated (at least
directly) to energy depositions from interactions in the active volume; a ‘spontaneous’ rate
– 5 –
can be measured for this population.1We associate these clusters with those studied in
the DSER dataset. We now treat both types of signal in turn.
2.2.1Photon-induced signals and their application
In the FSR, a significant fraction of recorded events contained only an S1 pulse due to
interactions below the cathode grid from β and γ backgrounds from the PMT array. A
reverse electric field there does not allow electrons to drift to the sensitive volume and
produce S2 signals. These otherwise clean waveforms provide the ideal dataset to search
for the small single electron signals and to subsequently test the photoionisation production
mechanism suggested previously . The FSR waveforms were processed by the same data
reduction algorithms as those implemented for the dark matter search data, but with some
reduction parameters optimised for the clustering of even smaller S2-like signals.
Instead of the photoelectron counting method employed with the DSER, in this analysis
the areas of clustered pulses were integrated in each channel; these were then converted
into photoelectron numbers by using the single photoelectron response for each phototube
determined by the method described in Ref. . The pulse area distribution shown in
Figure 2 (right) yields a mean 31.4±0.07(stat) photoelectrons per electron, which is only
≈10% higher than the value determined by the counting method employed with the DSER
dataset. The standard deviation is also slightly larger in this instance (which is expected
for a dataset acquired over a much longer period and which includes uncertainties in the
single photoelectron response determined for each channel), but neither is far from the
Poisson limit of ≈5.5 photoelectrons. As had been observed in ZEPLIN–II, the frequency
of these events is proportional to the number of VUV photons in the preceding S1 pulse,
which points to a photoionisation origin .
The distribution of time elapsed between S1 and the single electron cluster is shown in
Figure 4 for a typical day’s data. The spike in event rate near 14.5 µs is due to photo-electric
production by S1 photons incident on the cathode grid (we find its probability to be broadly
consistent with the quantum efficiency of metals at VUV wavelengths). The exponential
trend observed away from the cathode is consistent with an electron attachment explanation
based on an independent lifetime measurement (23.2±1.5 µs for that day, obtained as
explained below). This suggests that S1-induced electron emission might enable a good
measurement of this parameter, provided that these electrons are uniformly distributed
in the liquid depth. Both the spatial distribution of energy depositions in the chamber
and the attenuation length for VUV light must be considered in determining whether the
VUV flux from scintillation is constant across the liquid. The small vertical dimension of
the chamber and the uniform horizontal distribution of this background ensure that this is
indeed the case. The photon mean free path for photoionisation was estimated in Ref. 
as ∼km, so a uniform VUV flux implies a constant probability for electron appearance with
depth, which translates to an exponential survival probability as observed in Figure 4.
This depth distribution should provide a measurement of the free electron lifetime in a
rather robust and expedite way, relying solely on the science waveforms themselves (as in
1This terminology does not preclude a radiation-induced origin for these events; its use in quotation
marks highlights that no event was detected within the maximum drift time of the time projection chamber.
– 6 –
/ ndf / ndf
68.04 / 38 68.04 / 38
Constant Constant 0.019 0.019
single electron drift time,
02468 101214 16
Figure 4. Drift time (i.e. depth) distribution of S1-induced single electron pulses for one day of
FSR data. The cathode grid, located at 14.5 µs drift time, produces an excess due to photo-electric
emission from the stainless steel wires caused by the scintillation VUV photons. The first 2 µs were
excluded since these are contaminated by PMT afterpulsing following large S1 pulses. The time
constant of the exponential fit gives an electron lifetime in the liquid τ=26.4±2.0 µs.
this instance) – rather than on dedicated calibration datasets. Typically, this calibration is
conducted by fitting the S2/S1 ratio as a function of drift time (S1-S2 time separation) in
response to57Co or other external γ-ray sources. In this instance it is not straightforward
to prevent (or correct for) saturation of the PMT readout for very large S2 pulses, which
may easily contain upwards of 105photoelectrons. The very high VUV photon rates in
the chamber may also affect the operation of these detectors in other, more subtle ways
(e.g. photocathode charging ). The single electron signature provides a mechanism
which involves only very small pulses which are anyway present in the data.
Figure 5 compares historical lifetime measurements with this method with those ob-
tained from the daily calibration with57Co for both science runs of ZEPLIN–III. The
agreement is very good in both cases. We anticipate that this new method may be es-
pecially useful for next-generation two-phase xenon and argon experiments, where routine
irradiation of the large WIMP targets with external sources will be even harder to achieve.
Even if not used on its own, this technique may be useful to assess any biases in the
2.2.2 ‘Spontaneous’ signals in the science runs
Another single-electron search was conducted in segments of the WIMP-search waveforms
preceding S1 pulses, totalling ∼200 s of live time. These events, like those found in the
– 7 –
0 20 40 6080100 120140160 180 200
electron lifetime, s
FSR SE FSR Co-57 SSR SESSR Co-57
Figure 5. Historical evolution of the free electron lifetime in the liquid xenon measured from single
electron signals (markers) and from the daily57Co calibration in the FSR and the first 200 days
of the SSR (lines). The latter data were corrected independently for PMT saturation for large S2
signals but were not scaled otherwise.
DSER, have no traceable correlation with particle interactions in the detector. The rate
for this population (within the 60 mm reconstructed radius) stabilised at ∼20 s−1approx-
imately one month into the FSR (starting out twice as high initially). This is higher than
the rate of 5.7 s−1measured in the DSER. However, we note that in this instance the
length of waveform available for analysis (16 µs) would not allow enforcing a 20 µs inhibit
time from a candidate pulse.
The experiment was upgraded after the first run, with new PMTs with considerably
lower radioactivity replacing the previous array, reducing the electron-recoil background
of the experiment by a factor of 18 . The >300-day second science run (SSR) started
in mid 2010. In these data, we observed a very significant reduction in the ‘spontaneous’
component, to a level of ∼1 s−1. However, the reduction in background was not the
only difference between the FSR and SSR datasets: the electrode voltage configurations
were also different, producing a slightly lower electric field in the drift region (13%) and
significantly lower at the cathode wire surface (see Table I). Therefore, one cannot conclude
for a background-related explanation for this reduction based solely on this observation.
A thorough study of the electric field dependence of ‘spontaneous’ emission was not
possible prior to decommissioning of the experiment at the Boulby mine. Nevertheless,
a short dedicated dataset had been acquired in a similar fashion to the DSER described
previously after the end of the SSR data-taking, but this time with a137Cs source located
above the detector; the energy deposition rate in γ-rays was some 300 times greater than
– 8 –
background. The resulting ‘spontaneous’ rate was 118 s−1. Significantly, reanalyses of
this dataset requiring clear 40 µs and 60 µs periods preceding the single electron cluster
(rather than the standard 20 µs) yielded lower rates of 55 s−1and 44 s−1, respectively.
We may conclude, therefore, that not only does the total ‘spontaneous’ rate depend very
significantly on the rate of energy deposition in the target, but it also decreases with
increasing time delay from those energy depositions.
2.3 Causes and implications of ‘spontaneous’ electron emission
This signal will provide a background for applications aiming to explore the ionisation
channel in the few-electron regime, and it is therefore important to ascertain its (possibly
multiple) causes. Amongst those we single out i) delayed emission due to lower-than-unity
cross-phase extraction probability and ii) field emission from the cathode grid.
The correlation between the ‘spontaneous’ emission and the γ-ray event rate in the
SSR and the137Cs datasets – acquired with similar field configurations – argues for a
delayed emission mechanism, which is further supported by the decrease in rate for pro-
gressively longer inhibit periods. The cross-phase emission probability  was 83% under
the FSR/DSER conditions and 66% in the SSR/137Cs runs. Most electrons heated by
the electric field to energies above the field-dependent surface potential barrier are emit-
ted promptly into the gas phase. Those left on the surface quickly thermalise with the
medium, but the most energetic ones can still be emitted as thermal electrons, albeit with
lower probability . Thermal emission is naturally curtailed by the finite electron lifetime
in the liquid, which was 45.4 µs for the137Cs dataset. The observed decrease in emission
rate is broadly consistent with this lifetime. Under this model, the ∼3× discrepancy be-
tween the rates observed in the FSR and DSER datasets can be attributed to the longer
inhibit period enforced in the latter case.
We also conclude that field emission from the stainless steel cathode wires (100 µm
diameter, 1 mm pitch) can contribute to the spontaneous single electron rate to some de-
gree. The field strength at the surface of the wires is actually comparable to the so-called
‘applied breakdown field’ which characterises the onset of macroscopic field emission in
metals (see, e.g., [20, 21]). This breakdown field is determined by electrode irregularities
and is some two orders of magnitude lower than the the critical breakdown field for the
material, which is determined by its work function (although the latter is, in this instance,
decreased by 0.67 eV due to immersion in the liquid xenon ). The electrode voltage
configuration changed between the first and second science runs; although the electric field
strength in the liquid xenon bulk was only 13% lower in the SSR, the field near the top of
the wires, where field lines connect with the anode, actually decreased from 60 kV/cm to
38 kV/cm  (this is mainly a consequence of the lower voltage applied to the cathode,
which also establishes a reverse field region to a second wire grid located underneath it
which shields the PMT input optics). The field dependence of the emission current is ex-
tremely steep (∝E2eEin the Fowler-Nordheim model ) and, being a quantum tunnelling
effect, no strict threshold can be defined. For example, the two emission sites studied in
 (caused by an insulating particle on the metal surface and by a surface imperfection)
would cause far higher rates than observed here, although no measurable emission would
– 9 –
result from the perfect wires. Therefore the 50% lowering of the field near the surface of
the wires between runs could easily explain a reduction in electron emission rates of several
orders of magnitude and may contribute to a baseline rate ?1 s−1.
Based on these findings, controlling single-electron emission will require a low back-
ground experimental set-up, achieving near-unity emission probability for hot electrons
(i.e. electric fields ?5 kV/cm below the surface) and perhaps maintaining a lower electron
lifetime (so as to limit the delayed emission of thermal electrons). The first (and possibly
second) of these requirements will be challenging for detectors operating in surface labora-
tories. Field emission from the cathode is also identified as a viable production mechanism,
but it is perhaps the more benign of the two since careful electrode design should be able
to avert significant spontaneous rates.
3 Sensitivity to coherent neutrino-nucleus scattering
We now assess the feasibility of measuring coherent neutrino-nucleus scattering using only
the low-threshold ionisation channel in a two-phase xenon detector, with ZEPLIN–III as the
working example. Having characterised the response to single electrons and identified the
foremost sources of background for this signature, we must consider the uncertain ionisation
yield for nuclear recoils in liquid xenon, which has not been measured experimentally below
a few keV. However, present data (see also, e.g., Fig. 5 in Ref. ) suggest that the energy
required to extract the first ionisation electron with appreciable probability is likely to be
<1 keV, and maybe significantly less.
For lack of experimental data at very low energies we resort to extrapolating existing
ionisation yields in an ad hoc manner. We adopt the yield curve obtained for the ZEPLIN-
III FSR  down to 4 keV, which is in good agreement with other data. This yields a
maximum of 6.5 e/keV at that energy, below which it is forced to inflect and vanish for zero
recoil energy along a 3rdorder polynomial. It takes 540 eV to create the first ionisation
electron in this parametrisation. (A more optimistic scenario was also considered which
matched the former above 6 keV but followed instead the last three data points from
Ref.  below that energy; this curve peaks at ≈10 e/keV for 2.7 keV, with the first
electron emitted at 350 eV. However, the conclusions of this study remained unchanged,
and we present only detailed results obtained with the former scenario.)
3.1 Coherent neutrino scattering
Coherent neutrino-nucleus elastic scattering is a predicted high-rate interaction of the
Standard Model whereby neutrinos interact with the nucleus as a whole through Z0ex-
change . This flavour-blind process measures the total neutrino flux and could have
important practical applications (e.g. nuclear reactor monitoring) as well as probe new
physics. For example, if this rate were observed to oscillate this could provide evidence
for the existence of sterile neutrinos. Existing detectors exploit the elastic scattering of
neutrinos off electrons or inelastic scattering from individual nucleons, in processes which
produce much higher energy depositions (but lower rates) for neutrinos of the same en-
ergy. Several studies have proposed to attempt the extremely challenging detection of
– 10 –
coherent neutrino scattering (e.g. [28–30]), and notably that in Ref.  addresses the type
of signature studied here. In these studies, xenon has been consistently pointed out as a
favourable detection medium when the combined effect of recoil energies and scattering
rates is considered.
The maximum recoil energy, Emax
, from a neutrino with energy Eν is inversely pro-
portional to the mass of the target nucleus (M):
M + 2Eν
The differential cross section is given by:
where GF is the Fermi constant, F(Q2) is the form factor at four-momentum Q and
QW=N −(1−4sin2(θW))Z ∼ N is the weak charge for a nucleus with N neutrons and
Z protons, with θW the weak mixing angle; Q2
coherence and favours heavier elements.
Wenhances the scattering rate through
3.2Signal rate estimation
Assuming a recoil energy threshold Eth=0.5 keV, Eq.(3.1) places a lower bound of 5.5 MeV
on the detectable neutrino energy for a xenon target. On the other hand, maintaining
scattering coherence requires small momentum transfer (qR < 1, where R is the nuclear
radius and q is the three-momentum), determining an upper bound of ∼50 MeV for the
neutrino energy. This range limits the neutrino sources that can be detected in this way.
Seeking those with highest flux, we consider the following – represented in Figure 6:
• Solar neutrinos: a fraction of the solar neutrino spectrum, namely the8B and ‘hep’
(3He + p →4He + e++ νe) contributions, delivers high flux in the interesting energy
range. We assume the Bahcall model for the neutrino spectra . (This case is
included mainly for reference, since the scattering rates are very small indeed.)
• Reactor antineutrinos: we address the possibility of placing a detector like ZEPLIN–
III some 10 m away from a 3 GW nuclear reactor, where the neutrino flux would be
∼4×1013cm−2s−1; we adopt spectra from Refs.  and . Several experiments
have operated at similar distances from a nuclear reactor core and new ones are being
• Stopped pion sources are promising for these studies . We consider neutrinos
produced at the 800 MeV proton beam at the ISIS facility (Rutherford Appleton
Laboratory), with a pulse repetition rate of 50 s−1and beam current of 200 µA .
The neutrino flux 10 m away from the target is estimated as ∼1×107cm−2s−1per
– 11 –
neutrino energy, MeV
neutrino flux, cm
Figure 6. Neutrino fluxes considered in this work; the solar flux includes8B and ‘hep’ contribu-
tions ; the reactor flux from Ref.  is adopted; the ISIS spectrum includes the beam-prompt
νµline at 29.8 MeV and the two continuum contributions from ¯ νµand νe (which follow a muon
decay timescale with τ=2.2 µs).
The integral event rate is given by:
R(Eth) = Nt
?Em a x
where Ntis the number of target atoms, Φ(Eν) is the neutrino flux and dσ/dEr is the
differential cross-section given by Eq.(3.2). Figure 7 shows the computed event rates of
coherent neutrino-nucleus scatters in xenon for the neutrino fluxes mentioned above.
From these event rates the neutrino signal induced in the detector is evaluated. We
consider 10 kg·year as a reasonable dataset (1.5-year run with the nominal ZEPLIN–III
fiducial mass of 6.5 kg). For each neutrino-nucleus interaction, very few (if any) S1 VUV
photons and some ionisation electrons would be generated, but the S1 signal is most likely
lost. However, due to the sensitivity achieved in the ionisation channel, a measurement
can be made even if only one electron is extracted from the interaction point. For S2-only
events the depth information normally afforded by the time projection chamber is lost (but
x,y positional information is still available) and so is particle discrimination by S2/S1 ratio.
For this reason, it is essential to record S1 pulses whenever present; crucially, this will also
help reject important backgrounds (e.g. radioactive contamination on the cathode grid).
We assume that external radioactivity neutrons and those associated with the reactor or
beam are suitably mitigated with sufficient hydrocarbon shielding combined with an anti-
– 12 –
detector threshold energy, keV
count rate, yr
Figure 7. Expected integral rate of coherent neutrino-nucleus scatters in liquid xenon as a function
of detector threshold for nuclear recoils.
coincidence system surrounding the xenon target – like that deployed in the second run of
ZEPLIN–III [39, 40]. A veto detector will also tag internal neutrons efficiently and reduce
the effect of cosmogenic neutrons to manageable levels.
A dominant background will arise from the single electron emission mechanisms dis-
cussed previously. We consider a rate f∼10 s−1, which is comparable, per unit volume,
to that observed (underground) for the SSR. Hopefully, a higher extraction field and a
longer inhibit period to preceding events can mitigate the potentially higher event rate
expected with a surface deployment. We include the probability of n-electron coincidences
according to nfn∆tn−1, where ∆t=1 µs is the typical single electron signal duration. We
point out that the coincidences rate could be lowered significantly (∼10 for a detector like
ZEPLIN–III) with more sophisticated position algorithms.
A more challenging background arises from low-energy electron recoils due to β and γ
radiation (internal and cosmogenic, assuming substantial γ-ray shielding). The SSR back-
ground rate of ∼1 event/kg/day/keV, measured and modelled in Ref. , is considered.
The average energy per emitted electron from an electron recoil is ∼50 eV – obtained from
the W-value for LXe at zero field  and relevant field-dependent extraction (from track)
and surface emission probabilities. This background represents 180 events/electron in a
10 kg·year dataset. Above ∼2 keV in S1 (corresponding to ∼50-electron S2 signals from
electron recoils) efficient discrimination by S2/S1 ratio will become possible.
This background can be suppressed significantly in an ISIS experiment by exploit-
ing the pulsed nature of the beam: a triggered measurement lasting for one drift length
(∼20 µs) per proton bunch (20 ms period) would effectively reduce most non beam-related
– 13 –
backgrounds by a factor of ∼1,000. In addition, the depth coordinate can still be recovered
with reasonable accuracy by replacing the S1 pulse by the trigger signal, enabling fiduciali-
sation and self-shielding of external backgrounds – this will work well for the beam-prompt
neutrinos; the continuum components will be delayed by a few µs, reducing the timing
resolution of the chamber. For a reactor experiment, ‘on/off’ background subtraction will
be far less effective.
3.4 Predicted observable spectra
In Figure 8 we present photoelectron spectra predicted for neutrino interactions and for
the two dominant backgrounds, as would be observed in ZEPLIN–III. Individual peaks
represent ionisation electrons detected by electroluminescence; we assume a yield of 30 pho-
toelectrons per electron and Poisson variance.
number of detected photoelectrons
differential rate, yr
Figure 8. Ionisation spectra expected from coherent neutrino scattering in ZEPLIN–III exposed
to different neutrino sources. Single electron and electron recoil backgrounds are also shown. The
peak structure reflects discrete numbers of ionisation electrons measured by electroluminescence.
As the figure suggests, the neutrino signal must be searched above ?3 electrons due
to the single electron background – although this will be improved with multiple-cluster
resolution in x,y using advanced position algorithms.
becomes significant above that threshold, but the reactor signal is clearly salient near
100 phe. Unfortunately, its spectrum does not extend to 1,500 photoelectrons in the S2
The electron recoil background
– 14 –
channel (50 electrons), which would be required for a detectable S1 pulse from an electron
recoil thus enabling discrimination by S2/S1 ratio.
For a reactor experiment, the number of events expected in a 10 kg·yr dataset above
a 75 phe threshold is of order 3,000 (1,000 above 90 phe). The electroninc background
is ∼200 events over the relevant range. These values are sensitive to the shape of the
antineutrino reactor spectrum and the ionisation yield for low energy recoils. The number
of signal events changes only by a few tens of percent when the antineutrino spectrum
of Ref.  is used instead. However, the optimistic ionisation yield scenario mentioned
previously would increase the signal rate ten-fold. This is therefore an appropriate level of
systematic uncertainty to frame these calculations as far as the signal is concerned. The
background in the reactor environment will depend critically on the shielding efficiency,
which must be higher than typically required for underground WIMP searches. We note
also that self-shielding will not be very effective in the absence of the depth coordinate. In
spite of this, the reactor experiment seems viable.
Signal rates at the stopped pion source are lower but the spectrum does extend to
considerable energies. Significantly, in this instance the electron recoil background can be
reduced by three orders of magnitude with a beam-coincident measurement. Discrimination
should be possible for approximately half of the events, when S1 pulses are expected.
3D position reconstruction should be achieved to a resolution of a few mm in the depth
coordinate by using the trigger signal to define zero drift time. The integrals above 75 phe
are ∼700 and ∼10 background events over the same energy range for a 10 kg·year exposure.
This result is not very sensitive to the ionisation yield at low energy. In conclusion, the
spallation source produces very encouraging numbers.
In this article we report studies of single electron emission using data from the ZEPLIN–III
dark matter experiment and assess two applications which exploit the ability of xenon emis-
sion detectors to sense the quantum of response in ionisation. Electroluminescence signals
due to single electrons emitted from the liquid xenon target were analysed. We showed
that such pulses, containing an average of ∼30 photoelectrons in the FSR configuration,
can be detected with very high signal-to-noise ratio and exhibit near-Poisson variance.
The source of single electrons following the scintillation generated by sizable energy
depositions in the liquid xenon is thought to be photoionisation of impurities by the VUV
photons. We demonstrated that this signature can be used to obtain a very robust mea-
surement of the free electron lifetime in the liquid phase from science data themselves.
In addition to this photon-induced population, ‘spontaneous’ electron emission was
also studied and attributed to delayed emission of thermal electrons trapped at the surface.
Clearly, the physics of the emission process at the liquid-gas interface is a topic deserving
further study. It was also concluded that field emission from cathode wire grids could be
significant and should be considered when designing these detectors. These single electron
pulses determine a ∼3 electron threshold for experiments exploiting the ionisation channel
below the scintillation threshold.
– 15 –
We assessed the feasibility of two such experiments related to the detection of coher-
ent neutrino-nucleus elastic scattering, a Standard Model process not yet observed, using
realistic signal characteristics and backgrounds. We found that the signal from the nuclear
reactor scenario considered in this study is salient above the electron recoil background,
with ?2,000 events/(10 kg·yr) expected above a ∼3-electron threshold. In this instance the
signal rate is very sensitive to the nuclear recoil ionisation yield assumed at low energies.
The prospects of detecting this elusive neutrino signature with a beam-coincident mea-
surement at a stopped pion source such as ISIS are also very encouraging: owing to a harder
energy spectrum, a sizable fraction of events should benefit from electron-nuclear recoil
discrimination; three-dimensional position reconstruction should be possible; backgrounds
would be significantly lower. ?700 events/(10 kg·yr) are expected above ∼3 emitted elec-
trons. Even higher neutrino fluxes are likely to be reached in the coming years: SNS at
Oak Ridge  is expected to achieve a flux several times higher than that considered here,
and ISIS itself may have its capability improved in a forthcoming upgrade .
The UK groups acknowledge the support of the Science & Technology Facilities Council
(STFC) for the ZEPLIN–III project and for maintenance and operation of the Boulby un-
derground laboratory. LIP-Coimbra acknowledges support from Funda¸ c˜ ao para a Ciˆ encia
e a Tecnologia (FCT) through project grant CERN/FP/116374/2010 and postdoctoral
grants SFRH/BPD/27054/2006, SFRH/BPD/47320/2008 and SFRH/BPD/63096/2009.
The ITEP group acknowledges support from the Russian Foundation of Basic Research
(grant 08-02-91851 KO a) and Rosatom (H.4e.188.8.131.529 from 10-03-2011). We are also
grateful for support provided jointly to ITEP and Imperial from the UK Royal Society.
ZEPLIN–III is hosted by Cleveland Potash Ltd (CPL) at the Boulby Mine and we thank
CPL management and staff for their long-standing support. We also express our gratitude
to the Boulby facility staff for their dedication. The University of Edinburgh is a charitable
body registered in Scotland (SC005336).
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