arXiv:nucl-ex/0108019v1 20 Aug 2001
Measurements and Simulations of Cherenkov
Light in Lead Fluoride Crystals⋆
P. Achenbacha,1, S. Baunacka, K. Grimma, T. Hammela,
D. von Harracha, A. Lopes Ginjaa, F.E. Maasa, E. Schillinga,
H. Str¨ oherb
aInstitut f¨ ur Kernphysik, Johannes Gutenberg-Universit¨ at, Becherweg 45, 55099
bInstitut f¨ ur Kernphysik, Forschungszentrum J¨ ulich GmbH, 52425 J¨ ulich,
The anticipated use of more than one thousand lead fluoride (PbF2) crystals as a
fast and compact Cherenkov calorimeter material in a parity violation experiment at
MAMI stimulated the investigation of the light yield (L.Y.) of these crystals. The
number of photoelectrons (p.e.) per MeV deposited energy has been determined
with a hybrid photomultiplier tube (HPMT). In response to radioactive sources
a L.Y. between 1.7 and 1.9 p.e./MeV was measured with 4% statistical and 5%
systematic error. The L.Y. optimization with appropriate wrappings and couplings
was investigated by means of the HPMT. Furthermore, a fast Monte Carlo sim-
ulation based on the GEANT code was employed to calculate the characteristics
of Cherenkov light in the PbF2 crystals. The computing time was reduced by a
factor of 50 compared to the regular photon tracking method by implementing de-
tection probabilities as a three-dimensional look-up table. For a single crystal a L.Y.
of 2.1 p.e./MeV was calculated. The corresponding detector response to electrons
between 10 and 1000 MeV was highly linear with a variation smaller than 1%.
Key words: Cherenkov counters; lead fluoride; light yield; photoelectron
distributions; Monte Carlo simulations
PACS classification: 24.10 – Lx; 29.40 – Ka
⋆This work is part of the doctoral thesis of P. Achenbach.
1Corresponding author. Tel.: +49 6131 39 22958; fax +49 6131 39 22964; e-mail:
Preprint submitted to Elsevier Preprint8 February 2008
The A4 collaboration is preparing a measurement of the parity violating asym-
metry A0in elastic scattering of right and left handed electrons on an unpo-
larized proton target at the Mainz Microtron MAMI . An electromagnetic
calorimeter was built in the years 1999 and 2000 to carry out the precise
measurement with a total accuracy of δA0< 5%. In order to obtain a clear
separation of events in the low energy tail of the elastic peak to a background
of photons from π0decays, soft electrons and pions an energy resolution of
∆E/E ≤ 3.5%/
E[GeV] in arrays of 3×3 detectors and a fast online calibra-
tion are needed. This energy resolution not only depends on intrinsic shower
and leakage fluctuations but also on the effective light yield (L.Y.). There-
fore the number of photoelectrons (p.e.) per MeV deposited energy at a given
quantum efficiency of a photocathode is of great interest. Additionally, the
effect of non-linearities in the response, which might produce a degradation of
the energy resolution, should be taken into account.
In the early nineties lead fluoride in its cubic lattice form (β-PbF2) was dis-
covered as a Cherenkov radiator for electromagnetic calorimetry [2–4] because
of its high transparency and compactness. The optical transmittance of the
β-PbF2crystals extends below 270 nm, their radiation resistance is moder-
ate  and the A4 collaboration decided to use them in order to exploit their
excellent time response (< 20 ns). Since the L.Y. of β-PbF2is low compared
to scintillating crystals a search for scintillation in doped and orthorhombic
PbF2was performed in recent years [6,7]. The measurements presented in this
paper have proved that the L.Y. of good quality crystals is sufficient for their
application in medium and high energy physics experiments. Two methods of
accessing the L.Y. will be presented: on the one hand the use of low energy
radioactive sources to measure photoelectron distributions and on the other
hand a Monte Carlo code to simulate the Cherenkov photon production and
detection in the crystals.
One has to consider that PbF2only emits few photons per MeV of deposited
energy, which complicates conventional laboratory measurements. The detec-
tion of single photons is usually performed by means of regular photomulti-
plier tubes (PMTs) as well as by ultraviolet-sensitive multi-wire proportional
chambers (MWPCs). Both types of photon sensors are limited in their intrin-
sic resolution by fluctuations in the number of secondary electrons produced
at the first dynode of a PMT or in the avalanche around the anode wire of a
MWPC. This limitation favors the use of the recently reinvented hybrid pho-
tomultiplier tube (HPMT) with its excellent multiple photon separation and
high efficiency. A HPMT consists of a reversely biased silicon P-I-N diode, in
which highly accelerated photoelectrons create a few thousand electron-hole
pairs with much smaller statistical fluctuations. In Section 2 of this paper it
will be shown that a HPMT allows to study the effective L.Y. and related
properties of PbF2crystals.
To realize the second method, the GEANT 3.21 Monte Carlo code  was
used. The transport of Cherenkov photons from the location of their produc-
tion to the photocathode requires a step by step tracking through uniform
attenuating media to the nearest boundaries. Usually, large computing times
are required because photons are refracted or reflected and the tracking has to
continue until either absorption, detection or escape of the photons will occur.
In Section 3 of this paper, a method is described that avoids the tracking as
soon as a look-up table is generated, which tabulates the detection probabili-
ties of a photon depending on its wavelength, its angle relative to the primary
particle’s direction and its longitudinal location of production.
Section 4 provides the summary of the L.Y. measurements and simulations.
2 Measurements of the Light Yield
2.1 Experimental Arrangements
For the laboratory measurements at Mainz an electrostatically focused HPMT
manufactured by DEP2with a photocathode of 19 mm useful input diameter
was employed. The S20 photocathode featured a high quantum efficiency in
the ultraviolet region with 27% at 270 nm and 25% at 400 nm. The HPMT
was operated at −15 kV accelerating voltage and with an applied reversed-
bias voltage of +90 V. Two electrodes at a potential of −11 kV provided
the focusing of the released photoelectrons onto a silicon P-I-N diode. Each
bombarding photoelectron led to the creation of ≈ 3500 electron-hole-pairs,
causing an electrical current in the diode. This output signal was subsequently
amplified by a low-noise charge pre-amplifier, which was built in the HPMT
housing to avoid any unnecessary cabling capacitances by a direct charge cou-
pling. Coincidences between the HPMT signal and a scintillating counter were
used to detect the cascading γ-decay of60Co isotopes. The number of p.e. re-
leased from the HPMT photocathode on a quartz window were counted to
obtain the L.Y. of the crystal. The block diagramme in Fig. 1 (a) illustrates
the geometry of the detectors as well as the applied electronic components.
The PbF2crystal was read out by the HPMT whereas the plastic scintilla-
tor opposite to the crystal was read out by a regular PMT. The source was
placed between the two detectors. Most of the measurements were done with
the60Co source, but during parts of the data taking a90Sr source was used.
2Delft Electronic Products BV, Roden, The Netherlands
Then the scintillator was read out by two coincidence detectors to define the
trigger, see Fig. 1 (b). This set-up allowed to measure events in which no
particle has hit the PbF2crystal. A blue LED was used in separate calibra-
tion measurements to obtain the HPMT characteristics. All detectors were
located in a light-tight box. The crystal and the plastic scintillator were cou-
pled with silicone rubber pads of Elastosil RT 601 with a high transparency
and good coupling reproducibility. The pre-amplifier signals have been shaped
by a commercially available spectroscopy equipment. The energy spectra were
recorded by Constant Fraction Discriminators (CFDs) and Analog-to-Digital
Converters (ADCs) accessed by a CAMAC bus. The coincidence measure-
ments exhibited almost no background, but dark counts contributed to false
coincidences, i.e. random signals fell accidentally into the measurement gate.
The dominant contribution to those counts is the thermal emission of electrons
off the photocathode. Its rate depends on the temperature and the stabiliza-
tion time of the HPMT. Thirty minutes after switching the high voltage on
the rate of dark pulses had decreased exponentially to 5% of the initial rate
to about 75 counts per second. After some hours of stabilization the rate had
further decreased to about 50 counts per second.
2.2 Performance of the HPMT
Measured photoelectron spectra such as the one shown in Fig. 2 have been
obtained with very short and highly attenuated LED pulses. The photoelec-
tron distributions are composed of Gaussian shaped peaks corresponding to
the overlap of an integer number of released photoelectrons and a contin-
uum. More than 10 photoelectron peaks are clearly separated. A calibra-
tion of the obtained spectra in numbers of photoelectrons versus channels
of the ADC was possible with an accuracy of 0.026%, since the peak po-
sitions showed a very high degree of linearity. The contrast function f =
(Peak − Valley)/(Peak + Valley) calculated from the photoelectron peaks of
the shown photoelectron distribution is presented in Fig. 3. The straight
solid line at 0.03, which is commonly defined as the limit of peak resolu-
tion, crosses the exponentially fitted data points at 14 p.e., demonstrating the
excellent resolving power of the HPMT. Photon counting measurements with
HPMTs of up to fifteen resolved photoelectron peaks have been reported by
C. d’Ambrosio . In contrast, PMTs could resolve only two or three photo-
The photoelectron peaks have been fitted and single photoelectron resolutions
σmeas= 10.7% (≈ 1.60 keV) were found almost independent on the peak po-
sition. Two effects contribute to this variance: the fluctuations in the number
of electron-hole pairs σdiodeand the electronic noise σnoise. The latter must not
be neglected in HPMT measurements, because the total gain of a HPMT is
of the order of a few thousand whereas the PMT gain is usually of the order
of 106−107. The set-up with the strontium source and the plastic scintillator
as a trigger allowed to measure the width of the pedestals in the ADC distri-
butions of the HPMT spectra. The obtained variance of 9.5% (≈ 1.43 keV) of
the pedestal peak corresponds to the electronic noise σnoiseand can be sub-
tracted in quadrature from the measured variance, resulting in the intrinsic
resolution σdiode= 0.75 keV. The continuum in the spectrum is explained by
backscattering of the accelerated photoelectrons off the diode surface which
re-enter the diode at a smaller angle or with lower energy . The ohmic
contact being responsible for the backscattering effect is ion implanted and
its thickness amounts to only 0.05 µm. The fraction of backscattered events
could be estimated by calculating the ratio of the continuous area to the peak
area, which was about 80%.
2.3Analysis of the Photoelectron Distributions
In the first part of this study, several small PbF2samples of the dimensions
25 × 25 × 25 mm3were used. The samples have been polished on all faces by
the manufacturer SICCAS. The average number of p.e. detected by the HPMT
was determined from the photoelectron distributions using the expression:
where qm is the calibrated channel number in p.e. and Nm the number of
counts per channel. The number ?n?measaveraged over a series of measurements
amounted to (1.55±0.06) p.e. with a good reproducibility. Some of the emit-
ted γ-rays of the cobalt source undergo Compton scattering and transfer their
energy to electrons which produce Cherenkov light. The maximum electron
energy can be calculated by using Emax
where m0c2is the rest mass of the electron. Electrons with velocities below
the Cherenkov threshold of βthr= 1/n ≈ 0.54 cannot contribute to the L.Y.;
this limit is equivalent to a minimum electron energy Emin
the number of emitted Cherenkov photons increases with the electron energy,
a mean electron energy ?E? ≈ 800 ± 40 keV can be used for evaluating the
detector response. Because significant changes have not been observed when
comparing the cobalt source spectra with the β-excited strontium source spec-
tra, the assumed systematic error in the electron energy of 5% was confirmed.
By dividing the mean number ?n?measof p.e. by the mean energy ?E? a L.Y.
of 1.9 p.e./MeV was obtained. The calculated statistical error of the effective
L.Y. of 4% is one order of magnitude larger than the one in the calibration
measurements. This is due to the low count rates using the Cherenkov radiator
PbF2and could be improved by longer measurements.
= Eγ[1−(1+Eγ/m0c2)−1] = 890 keV,
= 608 keV. Since
In the second part of the study large size 302×150 mm3crystals were investi-
gated. Fig. 4 shows a typical photoelectron distribution where the scale is given
in numbers of photoelectrons. Their mean number ?n?meas= (1.38±0.05) p.e.
corresponds to 1.7 p.e./MeV. The difference between the result of the sample
and the one of the large crystal is explained by the different light collection
efficiency, since this is a function of the crystal’s size, shape and surface finish.
The use of a small sample reduces uncertainties in the light collection process
due to imperfections of the surface, because most of the light produced inside
a sample directly reaches the photocathode.
2.4 Optimization of the Light Yield
Since only a small fraction of the produced Cherenkov photons is detected,
the wrapping of the crystals could enhance their L.Y. However, the Cherenkov
light is peaked in the forward direction with respect to the primary particle’s
direction and the improvement is small compared to scintillation counters. The
light collection efficiency for different wrappings was measured with the de-
scribed set-up and the cobalt source. Wrapping materials investigated were a
high density, porous, chalk-loaded polyethylene fleece Tyvek3in two different
thicknesses (≈ 75 µm and ≈ 150 µm), two types of PTFE Teflon (≈ 25 µm and
≈ 80 µm), a nitrocellulose membrane4and a polyvinylidene fluoride named
Immobilon-P5(≈ 140 µm), which is commonly used as a transfer membrane.
The reference L.Y. for the comparison was determined using the unwrapped
crystal. The light detected in this measurement is assumed to originate from
internal reflections at the polished crystals’ faces. Then, consecutive layers of
the different reflectors have been added on all five faces. However, it is known
that further layers of material compromise the gain in L.Y. due to the increas-
ing amount of dead material between the crystals, which makes it possible for
shower particles to escape the detector. The measured photoelectron distribu-
tions have been analyzed according to the method described in the previous
section and the results are presented in Table 1. Using two layers of Teflon tape
or one layer of Immobilon-P gave the highest effective L.Y., confirming earlier
results obtained with a prototype PbF2calorimeter at the MAMI Microtron.
Both wrapping materials resulted in a 12% increase compared to a crystal
without wrapping. For this reason the membrane Immobilon-P was chosen for
use in the final detector assembly of the A4 calorimeter. The membrane has
a nominal pore size of 0.45 µm, its mechanical strength is barely sufficient.
It is hydrophobic, but it looses its reflectivity when exposed to moisture or
3Du Pont de Nemours, Le Grand Saconnex, Switzerland
4Biometra biomedizinische Analytik GmbH, G¨ ottingen,Germany
5Millipore GmbH, Eschborn, Germany
Since the number of p.e. is strongly affected by the wavelength-dependent
reflectivity of the wrapping material, a comparative measurement has been
carried out with the commercial double beam spectrophotometer Shimadzu
UV-2101 PC. In Fig. 5 the diffuse reflectance R is shown as a function of the
wavelength. The reflectivity of the Immobilon-P membrane reached 100% in
the visual area of the spectrum and started decreasing at about 310 nm.
To detect the propagating photons, they have to be transmitted through an
air gap, an optical grease or a glue to the photocathode. The reflection losses
at these boundaries strongly depend on the difference in reflection indices of
the PbF2 crystal and the optical coupling. To find the coupling with mini-
mum losses in effective L.Y., the properties of different optical oils, greases
and glues were studied in the laboratory measurements. The best result has
been obtained with the two-component silicone rubber Elastosil RT 6016. The
compound has a viscosity of 5000 mPa s, can be poured on the crystal, and
cures at room temperature during 12 hours. Its refractive index (n = 1.41) is
somewhat lower than that of the entrance window (n = 1.48) and significantly
lower than that of PbF2(n ≈ 1.82 at 400 nm). Curing a silicon layer of 0.1 mm
thickness in direct contact with the PMT and the crystal not only provided a
good optical coupling but also some adherence of the PMT and its base.
3 Monte Carlo Simulations
3.1 The Geometrical Set-up and the Detection Method
For the requirements of the A4 experiment the Cherenkov light production and
detection in PbF2crystals have been simulated using the Monte Carlo code
GEANT 3.21 . The geometrical set-up used was a matrix consisting of a 3×3
array of tapered PbF2crystals with 26×26 mm2front faces and 30×30 mm2
readout faces and lengths of 150, 155 and 160 mm, all nine crystals pointing
to the interaction vertex at a distance of about 105 cm. Air gaps of 300 µm
between adjacent crystals have been implemented. The number of photons de-
tected by the photon sensor has to be evaluated from their interactions at the
crystals’ surface. The reflection coefficient of the surface finish parameterizes
its reflectivity from perfect smoothness to maximum roughness. A reasonable
number of 90−91% was found by a comparison with measurements compris-
ing PbF2crystals at the MAMI electron beam. This value includes the diffuse
reflectance of the Immobilon-P transfer membrane. The characteristics of 11
inch diameter Philips XP2910 PMTs with borosilicate entrance windows and
bi-alkali cathodes have been used to simulate the photon detection. The in-
6Wacker-Chemie GmbH, Burghausen/Obb., Germany
ternal transmittancies of the crystals and of the entrance windows have been
measured with the above mentioned spectrophotometer.
To simulate the Cherenkov photon production and detection the GTCKOV
tracking routine of the GEANT code can be used, wherein the photons are
subject to in flight absorption and medium boundary action . This photon
transport mechanism requires an evaluation of the length that the individual
photon can travel in the current medium before each of the possible pro-
cesses will occur. These numbers are the different interaction lengths and the
minimum among these defines the step length over which the photon will be
transported. In addition, the distance from the photon’s location to the near-
est boundary has to be calculated and compared with the interaction lengths.
This method usually consumes large computing time, since huge amounts of
produced Cherenkov photons have to be tracked along small steps to the pho-
In order to accelerate the Monte Carlo simulation, the characteristics of the
Cherenkov photons have been investigated. First, the number of generated
photons has been determined as a function of the photons’ wavelength λ, their
angle θ to the primary particle’s direction and their longitudinal location of
production z. This simulation was done with a full tracking of the Cherenkov
photons by the GTCKOV routine and three-dimensional spectra of produced
and detected photons were obtained. The two-dimensional projection λ vs. z of
the produced photons inside the 3×3 array of PbF2is shown in Fig. 6 (a). The
spectrum of the subset of these photons detected at the photocathode is shown
in Fig. 6 (b). The shape of the latter distribution along the λ-direction reflects
the transmission of the bulk crystal, the surface properties, the transmission
of the entrance window and finally the quantum efficiency of the PMT. The
distribution exhibits a steep rise at 270 nm, followed by a maximum at 330 nm,
and a slower decrease up to a wavelength of about 600 nm. The shape of
the distribution along the z-direction corresponds to the longitudinal profile
of the Cherenkov photon shower. To obtain the detection probability p the
three-dimensional spectrum of detected photons was divided by the spectrum
of produced photons. The resulting probability distribution is shown in Fig. 7.
The full tabulated probability distribution p(λ,θ,z) has been implemented as
a look-up table in the simulation code, so that for subsequent simulations
the probability p of all produced Cherenkov photons could be compared with
a randomly generated number. If p was larger than the random number, it
was assumed that the photon could be detected, otherwise it was supposed
to be absorbed. This method avoids the tracking of photons, and this reduces
the computing time by a factor of fifty, which allows to simulate the detector
response and more complex geometries in reasonable time scales.
3.2 Simulated Properties of the Cherenkov Light
The half-angle θCh= arccos(1/nβ) of the Cherenkov cone is a characteristic
observable for a particle with velocity v = βc in a medium with the index
of refraction n. Depending on the lateral development of the electromagnetic
shower particles an angular distribution of the emitted Cherenkov photons as
shown in Fig. 8 was evaluated. The maximum of the distribution at 56◦is
clearly pronounced, which corresponds to the half-angle θCh= 57◦of relativis-
tic leptons, but tails of the distribution reach 0 and 180 degrees. The calcu-
lated number of radiating leptons per event was ?n?lep≈ 219 lep./GeV. The
distribution of the number of photons produced per centimeter path length
extended from only few photons up to a limit of dN/dx ≈ 900 photons/cm.
The strong rise to the limit is due to the low rest mass of the electrons and
positrons. The value of the obtained limit is in accordance with the theoretical
number, which can be calculated by the following equation :
The lateral distribution of the Cherenkov photons was found to be narrower
than the distribution of the energy deposition in the electromagnetic shower.
This is caused by the decreasing fraction of energy which is carried by the
leptons with increasing depth inside the crystals  and due to the larger
fraction of leptons with increasing lateral extension that have energies below
the Cherenkov threshold of 608 keV. This results in an apparent Moli` ere radius
RM≈ 1.8 cm which is smaller than the nominal radius RM= 2.2 cm (see e.g.
3.3 Light Yield and Detector Response
Cherenkov radiators are characterized by their effective L.Y. and their intrinsic
non-linearity. The best energy resolution will be achieved when the L.Y. is
large and proportional to the energy of the primary particle. Since ?n?lepis
small, its fluctuations δnlep= 6% at 734 MeV contribute considerably to the
energy resolution of the crystals. The total number of produced Cherenkov
photons amounted to nCh≈ 20,000 photons at 855 MeV, which is equivalent
to 23.4 photons/MeV. This number, however, is of low significance, because
the photons are subject to a multitude of processes reducing the number by
about 90%. For that reason it is more interesting to determine the number of
p.e. detected by a photon sensor of given type and sensitivity. This effective
L.Y. is a function of nChand depends on the light collection efficiency, the
quantum efficiency and the efficiency of the photoelectron collection. In a
3 × 3 array the simulated L.Y. at 855 MeV was ?n?sim = (2163 ± 2) p.e.
which corresponds to an effective L.Y. of 2.53 p.e./MeV. By using a set-up
consisting of only a single crystal a L.Y. of 2.10 p.e./MeV was calculated. This
value was simulated at energies above 10 MeV and could be compared with
the low energy measurements, but one has to be aware that the simulation
does not include small imperfections in the light and photoelectron collection.
In contrast, the real crystals exhibited minor defects in the bulk material and
on the surface. In addition, the detector response is degraded at such low
electron energies. Together both facts presumably explain the small difference
between the simulated and measured L.Y.
Calculations using different electron energies provided a measure of the detec-
tor response and its differential non-linearity, which is defined by the variation
in the L.Y. as a function of the energy of primary particle. At energies be-
tween 10 and 1000 MeV the L.Y. increased monotonically between 2.52 and
2.54 p.e./MeV. The projection of the detection probability distribution on the
axis of the photon’s longitudinal location of production p(z) is interesting in
terms of the non-linearity of the L.Y. As can be inferred from Fig. 7., its slope
in z-direction is 0.12% per cm at the position of the shower maximum at 5 cm
inside the crystal (z ≈ 110 cm).
The L.Y. of the Cherenkov radiator PbF2has been studied, because the parity
violation experiment at MAMI requires a good energy resolution of its elec-
tromagnetic calorimeter and a high L.Y. of their crystals. It is shown that a
HPMT can be used to obtain the effective L.Y. Measurements with a low en-
ergy γ-source as well as with a β-source revealed a number of 1.7−1.9 p.e./MeV
with 4% statistical and 5% systematic error. The L.Y. was increased by us-
ing appropriate wrappings on the crystal and a well adapted coupling to the
photon sensor. The latter results confirmed that the Immobilon-P membrane
is the best wrapping material to be used with Cherenkov crystals.
Monte Carlo simulations have been performed in order to evaluate the L.Y. of
an electromagnetic calorimeter consisting of 3×3 PbF2crystals. By establish-
ing a method to accelerate the GEANT code a computing time reduction by
a factor of fifty was achieved. Nevertheless, a simulation with full Cherenkov
photon tracking was still needed to obtain the detection probability distribu-
tion. This approach was used to simulate various experimental implications
and geometrical effects. An effective L.Y. of 2.1 p.e./MeV for a single PbF2
crystal was calculated, which agrees fairly well with the HPMT measurements,
taking small imperfections of the crystal and a lower detector response at very
low energies into account. The L.Y. is very high compared to other Cherenkov
radiators and is needed to obtain the good energy resolution required by the
parity violation experiment. Besides, the simulations predicted a very high
linearity of the response in the energy range between 10 and 1000 MeV with
a variation smaller than 1%. This promising result confirms that PbF2is very
well suited for its use as a calorimeter material, since larger non-linearities
would have degraded the energy resolution.
The authors would like to thank J. Garcia from University of Valencia for his
help during parts of the HPMT measurements.
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(a) Set-up during measurements
HPMT and the
counter triggered the readout.
(b) Set-up during measurements
with a strontium β-source. The
two coincidence counters trig-
gered the readout.
Fig. 1. HPMT detector set-up and block diagrammes of the readout electronic com-
ponents for the light yield measurements. Standard CAMAC electronics was used,
CFD abbreviates Constant Fraction Discriminator, ADC Analog-to-Digital Con-
Number of Photoelectrons
Fig. 2. Photoelectron distribution of highly attenuated LED pulses that have been
measured with the HPMT. The distribution is composed of Gaussian shaped peaks
and a continuum. Note the large peak-to-valley ratio of the first photoelectron peak.
02468 1012 14
Fig. 3. The HPMT contrast function f which was calculated from the photoelectron
peaks of the LED pulse measurements. The straight solid line at 0.03, which is
commonly defined as the limit of peak resolution, crosses the exponentially fitted
data points at 14 p.e.
Number of Photoelectrons
Fig. 4. A typical photoelectron distribution of a PbF2 crystal from the series of
measurements with the60Co γ-source. The distribution corresponds to the mean
number of photoelectrons ?n?meas = (1.38 ± 0.05) p.e. from which a L.Y. of 1.7
p.e./MeV was derived.
Diffuse Reflectance [%]
Fig. 5. Diffuse reflectance of wrapping materials. The different types of material
are encoded as follows: solid line = Immobilon-P (Millipore); dot-dashed = Tyvek
(Du Pont); narrow dots = office paper; dashed = Teflon; wide dots = nitrocellulose
(a) Distribution of photons produced inside the
(b) Distribution of photons detected in the pho-
Fig. 6. Two-dimensional spectra of the Cherenkov photon simulation. The location
z of the photons’ production along the longitudinal axis is plotted versus their
Detection Probability [per cent]
Fig. 7. Detection probability of the produced Cherenkov photons as a function of
the location of the photon’s production and their wavelengths. At the position of
the maximum of the electromagnetic shower at 5 cm inside the crystal (z ≈ 110 cm)
the slope along the z-direction is 0.12% per cm.
Fig. 8. Simulated spectrum of the Cherenkov photon’s angle θ with respect to the
direction of the primary particle. The peak at 56◦agrees well with the half-angle
θCh≈ 57◦of the Cherenkov cone for relativistic particles.
Table 1 Download full-text
Effective light yield (L.Y.) of a PbF2crystal wrapped in several layers of different
reflective materials. The thickness of the wrapping defines the dead material between
Wrapping MaterialNo. of LayersThickness [µm]L.Y. [%]
Teflon + Al4 + 1100 + 35111.5
Teflon + Al3 + 175 + 35108.0