Observation of Anti-correlation between Scintillation and Ionization for
  MeV Gamma-Rays in Liquid Xenon
Observation of Anti-correlation between Scintillation and
Ionization for MeV Gamma-Rays in Liquid Xenon
E. Aprile, K.L. Giboni, P. Majewski∗, K. Ni†, and M. Yamashita
Physics Department and Columbia Astrophysics Laboratory,
Columbia University, New York, New York 10027
(Dated: November 4, 2018)
Abstract
A strong anti-correlation between ionization and scintillation signals produced by MeV γ-rays in
liquid xenon has been measured and used to improve the energy resolution by combining the two
signals. The improvement is explained by reduced electron-ion recombination fluctuations of the
combined signal compared to fluctuations of the individual signals. Simultaneous measurements
of ionization and scintillation signals were carried out with 137Cs, 22Na and 60Co γ rays, as a
function of electric field in the liquid. A resolution of 1.7%(σ) at 662 keV was measured at 1
kV/cm, significantly better than the resolution from either scintillation or ionization alone. A
detailed analysis indicates that further improvement to less than 1%(σ) is possible with higher
light collection efficiency and lower electronic noise.
PACS numbers: 29.30.Kv, 34.80.Gs, 95.55.Ka
Keywords: gamma-ray astronomy, dark matter, liquid xenon
∗ Current address: Department of Physics and Astronomy, University of Sheffield, UK.
† Current address: Physics Department, Yale University, New Haven, CT 06511.
http://arxiv.org/abs/0704.1118v1
I. INTRODUCTION
Liquid xenon (LXe) is an excellent medium for radiation detection, with high stopping
power, good ionization and scintillation yields. Currently liquid xenon detectors are being
developed for several fundamental particle physics experiments, from neutrinoless double
beta decay [1] and dark matter weakly interactive massive particles (WIMPs) detection
[2, 3, 4, 5], to spectroscopy and imaging of gamma-rays in physics, astrophysics and nuclear
medicine [6, 7, 8, 9]. A more precise energy measurement than currently demonstrated
with liquid xenon ionization and scintillation detectors would largely benefit all these exper-
iments. The best experimental energy resolution is not only orders of magnitude worse than
that expected from the Fano factor [10] but even worse than that predicted by the Poisson
statistics, based on the measured W-value of 15.6 eV [11], as average energy to produce
an electron-in pair. The reason for the discrepancy is yet to be fully understood but fluc-
tuations in electron-ion pair recombination rate are known to play a dominant role. Both
electron-ion pairs and excitons are produced by the passage of an ionizing particle in liquid
xenon. In the presence of an electric field, some of the electron-ion pairs are separated before
recombination, providing the charge signal as electrons drift freely in the field (positive ions
do not contribute as their drift velocity is several orders of magnitude slower). Recombina-
tion of the remaining electron-ion pairs lead to excited xenon molecules, Xe∗2. Excitons that
are directly produced by the incident particle also become Xe∗2 molecules. De-excitation of
these molecules to the ground state, Xe∗2 → 2Xe + hν, produce scintillation photons with a
wavelength of 178 nm [12]. The ionization and scintillation signals in liquid xenon are thus
complementary and anti-correlated as the suppression of recombination by the external field
results in more free electrons and less scintillation photons. This anti-correlation was first
observed by Kubota et al. [13]. Large fluctuations in the number of collected electrons due to
their reduction by recombination lead to poor energy resolution of the ionization signal. A
way to increase the ionization signal and thus the energy resolution via the photo-ionization
effect in LXe doped with triemethylamine (TEA) yielded good results, but only at low elec-
tric fields [14]. Another way to improve the energy resolution is to reduce recombination
fluctuations by combining ionization and scintillation signals. Since recombination also pro-
duce scintillation photons, fluctuations of the combined signal should be reduced. This was
originally suggested by Ypsilantis et al. many years ago [15], but the simultaneous detection
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��� 3.
Signal line
Vacuum Pump
Cathode
Radiation Source
Grid Anode Screening mesh at ground
1.9LED
PMT PMT
Gas Out
Anode signal redout
Opening for Pumping and Gas Filling
Cathode and grid HV 
feedthroughs
Vacuum Insulation
HV connection
LXe level
FIG. 1: The detector schematics (see text for details).
of scintillation and ionization in LXe has been hard to realize because of the difficulty to
efficiently detect VUV light under the constraints of efficient charge collection. In the Liquid
Xenon Gamma-Ray Imaging Telescope (LXeGRIT) [7], which we developed for Compton
imaging of cosmic γ-rays, both ionization and scintillation were detected, but the fast scin-
tillation signal merely provided the event trigger, while the ionization signal provided the
energy measurement, with a resolution of 4.2%(σ) at 1 MeV. The fair resolution has been
a major limitation of the LXe time projection chamber (TPC) technology for astrophysics.
In recent years, the development of VUV-sensitive photomultiplier tubes (PMTs), capable
to operate directly in the cryogenic liquid and to withstand overpressure up to 5 atm, has
enabled to significantly improve the Xe scintillation light collection efficiency with good
uniformity across the liquid volume. A light readout based on these novel PMTs, coupled
with a lower-noise charge readout, was proposed to measure both signals event-by-event and
thus to improve the energy resolution and the Compton imaging of the LXeGRIT telescope
[16]. The work presented here was carried out with two of the first PMTs developed for
operation in LXe and is our first attempt in this direction. Further optimization of these
VUV PMTs has continued, driven largely by our XENON dark matter detector develop-
ment [2, 17]. These improved PMTs, along with other VUV sensor technologies such as
Large Area Avalanche Photodiodes (LAAPDs) and Si photomultipliers (SiPMs), which we
are also testing for LXe scintillation detection [18, 19], promise further energy resolution
improvement.
II. EXPERIMENTAL SET-UP AND SIGNALS
The detector used for this study is a gridded ionization chamber with two VUV sensitive
PMTs (two-inch diameter Hamamatsu R9288) viewing the sensitive liquid xenon volume
from the anode and cathode side. The two PMTs, and the transparent meshes serving as
anode, cathode and shielding grid, are mounted in a structure made of Teflon for its VUV
reflectivity [20] (Fig. 1). The drift gap, between cathode and grid, is 1.9 cm while the
distance between grid and anode is 3 mm. Separate high voltage is supplied to the cathode
and the grid, keeping a ratio between the field in the drift gap and the field in the collection
gap such as to maximize electron transmission through the grid. The electrons collected
on the anode are detected by a charge sensitive amplifier (ClearPulse Model 580). The
charge signal is subsequently digitized with 10 bit resolution and a sampling time of 200 ns
(LeCroy Model 2262). The scintillation signal from each of the two PMTs is recorded with
a digital oscilloscope (LeCroy Model LT374) with 1 ns sampling time. The time difference
between the scintillation and ionization signals is the electron drift time which gives the
event depth-of-interaction information. The coincidence of the two PMT signals is used as
event trigger. Fig. 2 shows the scintillation and ionization waveforms recorded at 1 kV/cm
for a 662 keV γ-ray event from 137Cs. The number of photoelectrons, Npe, detected by the
PMTs is calculated based on the gain calibration with a light emitting diode (LED). The
charge waveform is well described by the Fermi-Dirac threshold function in equation 1, as
shown in [21]The pulse height A, drift time td, rise time tr and fall time tf are determined
from fitting equation 1 to the charge waveform. A known test pulse is used to calibrate the
charge readout system, and the number of collected electrons, Ne, is calculated from the
pulse height of the charge waveform.
Q(t) = A ·
e−(t−td)/tr
1 + e−(t−td)/tf
The Teflon structure holding the PMTs and the meshes is mounted in a stainless steel
vessel filled with liquid xenon at about –95oC during the experiment. A vacuum cryostat
surrounds the vessel for thermal insulation. The xenon gas filling and purification system, as
well as the “cold finger” system used for this set-up is described in a previous publication[21].
The set-up was modified for these measurements by adding a gas recirculation system [17]
in order to purify the xenon continuously until sufficient charge collection is reached.
0 100 200 300 400 500
Time [ns]
0 20 40 60 80 100 120
Time [µs]
FIG. 2: Waveforms of scintillation signal (left, sum of two PMTs) and ionization signal (right) of
a 662 keV γ-ray event from 137Cs at 1 kV/cm drift field.
Field [kV/cm]
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Field [kV/cm]
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Light
Charge
Combine
FIG. 3: Light and charge yield as a function of drift field for 662 keV γ-rays from 137Cs. The
uncertainty for charge measurement is due to the uncertainty in pre-amplifier calibration. The
light yield is relative to that at zero field, for which the systematic uncertainty is negligible.
III. RESULTS AND DISCUSSION
A. Field dependence of scintillation and ionization
Fig. 3 shows our measurement of the field dependence up to 4 kV/cm of the light and
charge yield for 662 keV γ rays from 137Cs. With increasing drift field, the charge yield
increases, while the light yield decreases. This behavior has been known for a long time,
and was originally reported in [13].
A parametrization of the field dependence of the light yield, S(E)/S0, was proposed by
Doke et al. [22] introducing the model of escaping electrons to explain the scintillation
light reduction at low LET(linear energy transfer). In this parametrization, expressed by
equation 2, the light yield S(E) at drift field E, normalized by the light yield at zero field,
S0, depends on the charge yield Q(E) normalized to the charge at infinite field, Q0, and
on the ratio Nex/Ni of the number of excitons and ion pairs produced by a γ-ray. χ is
the fraction of escaping electrons, i.e. the fraction of Ni electrons which do not recombine
with positive ions for an extended time (>ms) even at zero field, when the probability of
recombination is highest.
1 +Nex/Ni −Q(E)/Q0
1 +Nex/Ni − χ
Nex/Ni and χ can be determined from a fit of equation 2 to the charge and light yields data,
knowing Q0 which is given by Eγ/W , where Eγ is the γ-ray deposited energy and W = 15.6
eV [11] is the average energy required to produce an electron-ion pair in liquid xenon.
Fig. 4 shows the result of such a fit to our 662 keV data which gives Nex/Ni = 0.20±0.13
and χ = 0.22 ± 0.02. The errors are from the uncertainty on charge collection only. A
ratio of 0.06 for Nex/Ni was originally estimated from the optical approximation, using
the absorption spectrum of solid rare gases [23]. In [22], Nex/Ni = 0.20 and χ = 0.43 as
estimated from 1 MeV conversion electrons data in LXe. This Nex/Ni value is consistent
with that obtained from our data. The difference in χ might be due to the limited range of
electric fields used in our study.
The charge and light signals can be combined by the following equation,
C(E) = a
with a = 1/(1 + Nex/Ni) and b = 1 − aχ, which gives a constant C(E) = 1, regardless of
applied field. The proportion of charge and light is different at different fields but their sum
is constant, as verified by our data in in Fig. 3. Note that at very low fields, equation 2 and
3 are not valid as escaping electrons are not fully collected.
B. Combined Energy from Scintillation and Ionization
The observed field dependent anti-correlation between charge and light signals and its
linear relationship offers a way to improve the energy resolution by combining the two signals
with proper coefficients. This was first shown in a measurement of energy loss of relativistic
Charge Yield Q(E)/Q
0 0.2 0.4 0.6 0.8 1 1.2
Charge Yield Q(E)/Q
0 0.2 0.4 0.6 0.8 1 1.2
=0.20i/NexN
 =0.22χ
FIG. 4: Correlation between light yield and charge yield for 662 keV γ rays.
La ions in liquid argon [25]. More recently, Conti et al. [26] applied the same method to
improve the energy measurement of relativistic electrons in a liquid xenon detector using a
single UV PMT to detect the scintillation signal. For 570 keV γ-rays from 207Bi, an energy
resolution of 3%(σ) was measured at 4 kV/cm, by combining the charge and light signals.
In our study, the improved light collection efficiency with two PMTs immersed in the liquid
gives even better results.
Fig. 5 shows the strong anti-correlation of charge and light signals measured with our
detector for 662 keV γ-rays from 137Cs at 1 kV/cm. The energy resolution inferred from
the light and the charge signals separately is 10.3% (σ) and 4.8%(σ), respectively. The
resolution from the charge signal is consistent with previously measured values [7] and [24].
The charge-light correlation angle, θ, also shown in Fig. 5 is defined as the angle between the
major axis of the charge-light ellipse and the X-axis for light. θ can be roughly calculated
as tan−1(Rq/Rs), where Rs and Rq are the energy resolutions of the 662 keV peak from
scintillation and ionization spectra separately. θ can also be found by a 2D gaussian fit to
the charge-light ellipse of the 662 keV peak. A better energy resolution can be achieved by
combining the charge and light signals as,
sin θ · εs + cos θ · εq
sin θ + cos θ
where εc is the combined signal, in unit of keV. εs and εq are scintillation light and charge
based energy in units of keV. The charge-light combined energy resolution of 662 keV line
Energy from Light [keV]
0 100 200 300 400 500 600 700 800 900 10000
662 keV
Energy from Charge [keV]
0 100 200 300 400 500 600 700 800 900 10000
662 keV
Charge-Light Combined Energy [keV]
0 100 200 300 400 500 600 700 800 900 10000
662 keV
Energy from Light [keV]
0 200 400 600 800 1000 1200 1400 1600
662 keV
FIG. 5: Energy spectra of 137Cs 662 keV γ-rays at 1 kV/cm drift field in liquid xenon. The top
two plots are from scintillation and ionization separately. The strong charge-light anti-correlation
is shown in the bottom-right plot. The straight line indicates the charge-light correlation angle. A
charge-light combined spectrum (bottom-left) shows a much improved energy resolution of 1.7%(σ).
is significantly improved to 1.7%(σ).
The energy resolution from the charge-light combined spectrum, Rc, can be derived from
equation 4 as [27],
R2c =
sin2 θ · R2s + cos
2 θ · R2q + 2 sin θ cos θ · Rsq
(sin θ + cos θ)2
where Rs and Rq are the energy resolutions from scintillation and ionization spectra sep-
arately. The covariance Rsq is the contribution from the correlation of the two signals.
The magnitude of Rsq indicates the strength of anti-correlation (or correlation) between the
scintillation and ionization signals. It is usually expressed in terms of correlation coefficient
ρsq = Rsq/(RsRq) (6)
A value of ρsq close to -1 (or 1) indicates a very strong anti-correlation (or correlation) of
scintillation and ionization signals, while a zero ρsq means no correlation. In equation 5, Rs
and Rq can be expressed as,
2 = R2si +R
sg +R
ss ≈ R
si +R
ss (7)
≈ R2qi +R
qe (8)
where Rsi and Rqi are the energy resolution of scintillation and ionization, respectively
contributed by liquid xenon itself. They include the liquid xenon intrinsic resolution and
the contribution from fluctuations of electron-ion recombination. Rsg is from the geometrical
fluctuation of light collection. It is negligible in our result since only events in the center
of the detector were selected for the analysis. Rss is from the statistical fluctuation of
the number of photoelectrons Npe in the PMTs. Rss can be calculated roughly as Rs =
[1 + (
)2]/Npe, which includes the statistical fluctuations of the number of photoelectrons
and the PMTs gain variation (σg/g ∼ 0.67, based on the single-photoelectron spectrum).
Rqe is from the noise equivalent charge (ENC) of the charge readout. ENC was measured to
be between 600 and 800 electrons, depending on the drift field, from a test pulse distribution.
Rqe = ENC/Ne, where Ne is the number of collected charges from the 662 keV peak. We
note that we have neglected other contributions to the resolution of the charge measurement,
such as from shielding grid inefficiency or pulse rise time variation, as they are sub-dominant
compared to the electronic noise contribution.
Table I lists the energy resolution of the 662 keV γ-ray peak inferred from ionization,
scintillation, and charge-light combined spectra at different drift fields. The quoted errors
are statistical only. The correlation angle and the correlation coefficient at each field are also
presented. The energy resolution improves with increasing field for both scintillation and
ionization, while the charge-light combined energy resolution is about the same at different
fields. The best value achieved in this study is 1.7%(σ) at 1 kV/cm drift field. We should
mention that during this work, we observed improvement of the energy resolution from both
light and combined energy spectra with improved light collection efficiency by using Teflon,
while the energy resolution from the charge spectrum did not change.
The different value of the charge-light correlation coefficient at different fields indicates a
more fundamental correlation coefficient between ionization and scintillation in liquid xenon.
In fact, the energy resolution Rc from charge-light combined signals comes from two factors.
One is the liquid xenon intrinsic energy resolution Rci. Another factor, Rce, is contributed
by external sources, such as the fluctuation of light collection efficiency on the light signal
and fluctuation of electronic noise on the charge signal. The charge-light combined energy
Field [kV/cm] Rs(%) Rq(%) Rc(%) θ ρsq
0 7.9±0.3
1 10.3±0.4 4.8±0.1 1.7±0.1 24.8o -0.87
2 10.5±0.3 4.0±0.1 1.8±0.1 20.8o -0.80
3 10.0±0.3 3.6±0.1 1.9±0.1 19.7o -0.74
4 9.8±0.3 3.4±0.1 1.8±0.1 19.1o -0.74
TABLE I: Measured energy resolutions (σ) and correlation coefficients for 662 keV gamma rays at
different electric field values.
resolution can be written as below,
R2c = R
ci +R
ce (9)
R2ci =
sin2 θ · R2si + cos
2 θ · R2qi + 2 sin θ cos θ ·Rsqi
(sin θ + cos θ)2
R2ce ≈
sin2 θ · R2ss + cos
2 θ · R2qe
(sin θ + cos θ)2
In these equations Rsi, Rqi are the liquid xenon energy resolution from scintillation and ion-
ization separately, as previously discussed. Rsqi indicates the correlation between ionization
and scintillation signals in liquid xenon. We can define the intrinsic correlation coefficient,
ρsqi, of liquid xenon scintillation and ionization, similar to equation 6 for the measured
charge-light correlation coefficient, but without instrumental noise contributions.
ρsqi = Rsqi/(RsiRqi) (12)
The energy resolution for scintillation, Rsi, and ionization, Rqi, can be calculated based
on equation 7 and 8, from the measured values of correlation angle θ, statistical fluctuation
of light detection Rss and electronic noise contribution Rqe. The calculated values are listed
in Table II. Table II also shows the intrinsic and external contributions, Rci and Rce, to
the charge-light combined energy resolution. The values of Rci and Rce are calculated from
equation 9-11. The intrinsic correlation coefficients from equation 12 are also shown.
The intrinsic energy resolution in liquid xenon from the combined scintillation and ion-
ization signals is estimated to be less than 1%. Only upper limits are given here since the
uncertainties become large at such small values. The intrinsic correlation coefficients are
Field [kV/cm] Rsi(%) Rqi(%) Rce(%) Rci(%) ρsqi
0 6.0±0.3
1 9.9±0.4 4.3±0.1 1.6±0.1 < 1.0 −1.00
2 10.1±0.3 3.5±0.1 1.7±0.2 < 1.2 −0.98
3 9.5±0.3 3.0±0.1 1.8±0.2 < 1.2 −0.98
4 9.3±0.3 2.8±0.1 1.8±0.2 < 1.0 −1.00
TABLE II: Predicted achievable energy resolutions in liquid xenon for light (Rsi), charge (Rqi) and
combined (Rci) measurements, and charge-light correlation coefficient by removing instrumental
noise contributions.
closer to -1 than those measured from the experimental data including instrumental noise-
contributions. This indicates near-perfect anti-correlation between ionization and scintilla-
tion in liquid xenon. We therefore expect that further improvement in the combined signal
energy resolution can be achieved by increasing light collection efficiency and by minimizing
electronic noise.
C. Energy dependence of resolution
The improvement of the energy resolution by combining scintillation and ionization sig-
nals was studied at 3 kV/cm drift field as a function of γ-ray energy, using radioactive sources
such as 22Na (511 keV and 1.28 MeV), 137Cs (662 keV) and 60Co (1.17 MeV and 1.33 MeV)
(Fig. 6). The energy resolution from charge, light and charge-light combined spectra is
shown in Fig. 7. The data was fitted with an empirical function, σ/E = α/
(E/MeV ),
yielding for the parameter α (8.6±0.4)%, (3.0±0.4)% and (1.9±0.4)% for light, charge and
combined spectra separately.
IV. CONCLUSION
We have shown that the energy resolution of MeV γ-rays in liquid xenon can be signifi-
cantly improved by combining simultaneously measured scintillation and ionization signals.
The best resolution achieved is 1.7% (σ) for 662 keV γ-rays at 1 kV/cm. This value is
0 500 1000 1500 2000
Energy [keV]
511 keV
1.27 MeV
Na−22, 3 kV/cm
0 500 1000 1500 2000
Energy [keV]
1.17 MeV
1.33 MeV
Co−60, 3 kV/cm
FIG. 6: Energy spectra of 22Na and 60Co γ ray sources at 3 kV/cm, by combining charge and light
signals.
Energy [keV]
400 600 800 1000 1200 1400
Energy [keV]
400 600 800 1000 1200 1400
Light
Charge
Combined
FIG. 7: Energy dependence of resolution measured from 22Na, 137Cs, and 60Co at 3 kV/cm drift
field.
much better than that measured from scintillation [10.3% (σ)] or from ionization [4.8%(σ)],
separately. By summing the two signals, which are strongly anti-correlated, recombination
fluctuations are reduced, resulting in improved energy resolution. At present, the energy
resolution of the combined signal is still limited by external factors, such as light collection
efficiency, PMT quantum efficiency and charge readout electronic noise. By reducing the
contribution from these factors, we estimate that the intrinsic energy resolution of MeV
gamma-rays in liquid xenon from charge-light combined signal should be less than 1%. The
simultaneous detection of ionization and scintillation signals in liquid xenon therefore pro-
vides a practical way to improve the energy measurement with a resolution better than the
Poisson limit, and possibly closer to the Fano limit [10]. On the other hand, the limit to
the energy resolution of LXe might well be not determined by Fano statistics but rather
connected to the liquid phase, for instance to microscopic density non-uniformities of the
liquid itself. It has been shown by Bolotnikov and Ramsey [28] that the energy resolution
deteriorates as the density of Xe gas increases. The behavior was attributed to the formation
of molecular clusters in high pressure and liquid xenon, but a more quantitative explana-
tion is needed. Despite the limitation of energy resolution, the liquid phase offers far too
many advantages for high energy radiation detection. The development of a LXeTPC which
combines millimeter spatial resolution with 1% or better energy resolution, within a large
homogeneous volume, is very promising for particle physics and astrophysics experiments.
V. ACKNOWLEDGMENTS
This work was supported by a grant from the National Science Foundation (Grant No.
PHY-02-01740) to the Columbia Astrophysics Laboratory. The authors would like to express
their thanks to Tadayoshi Doke and Akira Hitachi for valuable discussions.
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http://arxiv.org/abs/astro-ph/0407575
http://arxiv.org/abs/physics/0702078
	Introduction
	Experimental Set-up and Signals
	Results and Discussion
	Field dependence of scintillation and ionization
	Combined Energy from Scintillation and Ionization
	Energy dependence of resolution
	Conclusion
	Acknowledgments
	References
