Research Report of Laboratory of Nuclear Science, Tohoku University Vol. 41 (2008)

11(LNS Experiment : #2577)

Energy Resolution of a Prototype EM Calorimeter withBSO Crystals
S. Kuwasaki, T. Ishikawa, R. Hashimoto, J. Kasagi, Y. Okada, M. Sato,
H. Shimizu, K. Suzuki, and H. Yamazaki
Laboratory of Nuclear Science, Tohoku University, Sendai 982-0826

A new high resolution electro-magnetic (EM) calorimeter with a large solid angle is planned forthe precise study of nucleon resonances via π 0 and η photo-production. A BSO crystal is a candidateof modules which comprise the EM calorimeter. The performance of a prototype EM calorimeter madeup with 4 BSO crystals has been studied by using positron beams with energies ranging from 100 to800 MeV. The energy resolution for 1 GeV positron corresponds to 1.75%. The decay time is roughly
estimated to be 136 ns from a pulse shape taken with an oscilloscope. The energy resolution for the0.662 MeV photons from 137 Cs has also been measured, and it is found to be 16.6%±0.2%.

§ 1. A New Large Solid Angle EM CalorimeterA new EM calorimeter complex FOREST with a solid angle of about 4π in total has been constructedin the GeV-γ experimental hall [1] to study nucleon resonances via π 0 and η photo-production. It consists of three calorimeters: a forward one with CsI crystals, a middle one with lead scintillating ﬁber(Lead/SciFi) modules, and a backward one with lead glass Čerenkov counters. The π 0 and η mesons areidentiﬁed as a peak in the γγ invariant mass distribution. Thanks to the large solid angle of FOREST,a background due to wrong combinations of γ’s is strongly suppressed, which do not form a peak of π 0nor η in the mass distribution. The resolutions of the EM calorimeters with Lead/SciFi and lead glass
modules are 7.2% [2] and 4.9% [3] for 1 GeV positrons, respectively. The resolution of each calorimeteris poorer than that of nominal inorganic scintillator crystals. A high resolution EM calorimeter with alarge solid angle is desired for the further precise study of nucleon resonances.
Since photons with an energy of several hundred MeV are mainly produced, inorganic scintillator
crystals with a good energy resolution in this energy region are required. A fast response is also required
to suppress pile-up events, and a short radiation length and no hygroscopicity are preferable. A BSOcrystal [5] is a candidate which satisﬁes the requirements among the available crystals. The BSO is abismuth silicate Bi4 Si3 O12 , produced by replacing Ge in BGO with Si.

§ 2. Experimental Setup
The performance measurement of a prototype BSO EM calorimeter was carried out by using positron
beams for testing detectors at LNS. The prototype EM calorimeter was constructed with a 2 × 2 arrayof BSO crystals. Each crystal was 210 mm long with a cross section of 40 × 40 mm2 , and was connected

12to a 1-inch photo-multiplier tube (Hamamatsu H7415MOD). Semi-monochromatic positrons with energies ranging from 100 to 800 MeV were used as incident beams. To determine the incident position of
the positrons, a beam proﬁle monitor (BPM) was used. The BPM consists of two layers of scintillatingﬁber (SciFi) hodoscopes and 16 SciFi’s with a cross section of 3 × 3 mm2 were aligned in each hodoscope.
The upstream and downstream layers determine x and y positions from responding ﬁbers, respectively.
Figure 1 shows the experimental setup for the energy resolution measurement of the calorimeter.

BPM

BSO
Positron Beam

Fig.1. Experimental setup for the performance measurement of a prototype BSO EM calorimeter. The 16 × 16 scintillating ﬁber hodoscopes are placed in front of the calorimeter todetermine incident positions of positrons.

The trigger condition of the data taking system was described as[x ﬁber OR] ⊗ [y ﬁber OR],(1)

where ⊗ stands for the coincidence of signals. The maximum trigger rate was 3 kHz and a fraction ofaccidental coincidence events was negligibly small. The energy calibration for the BSO modules wasmade by using 300, 460, 590, and 750 MeV positrons injected onto the central region (3×3 mm2 ) of eachcrystal one by one, and the gain of each crystal was adjusted so that peak positions for the same incident
energy should be the same.

§ 3. Energy Resolution
The energy of the calorimeter was reconstructed by the sum of 4 crystal energies asE=4i=1Ei .

(2)

13The events that positrons were injected onto the central region (3×3 mm2 ) of the EM calorimeter wereselected to suppress the energy leakage in the lateral direction. Figure 2 shows energy distributions forCounts

all the incident positron energies.

150
100
500150100
500150100
500150100
500101 MeV

302 MeV

675 MeV

152 MeV

401 MeV

747 MeV

202 MeV459 MeV

806 MeV

252 MeV

591 MeV

0500

00500

500
Energy (MeV)

Fig.2. Energy distributions for all the incident positron energies together with the ﬁtted function (3).

The energy distributions were ﬁtted with a logarithmic Gaussian [3] 2σ 20
1x−μ,F (x) = N exp −log 1 −−
ησ
22σ 20where σ0 is described with a constant ξ = 2σ0 =(3)log4 asηξ
2sinh−1.
ξ2(4)The parameters μ, σ, and η show a mean, a width, and an asymmetry, respectively. One gets a nominal
Gaussian function taking the limit of Eq. (3) as η becomes inﬁnitely small.

14The linearity of the energy response was checked by the ratio of the reconstructed energy to theincident positron energy. Figure 3a) shows the ratio as a function of the incident energy. The normalization of the reconstructed energy is arbitrary. The non linearity of the energy response was less than 2%
for all the incident beam energies. The asymmetry parameter as a function of the incident energy wasalso checked, and it was a constant within errors. Figure 3b) shows the asymmetry as a function of the

3.80.5a)b)0.4
Asymmetry Parameter ηMeasured Energy / Incident Energy (a.u.)incident energy.

3.73.63.50200400600
Energy (MeV)

0.30.20.100800

200400600
Energy (MeV)

800Fig.3. The energy response as a function of the incident positron energy. a) The ratio of thereconstructed energy to the incident energy. The normalization factor is arbitrary. b)
The asymmetry parameter. Both the values are almost constant for all the incidentenergies.

The energy resolution σE /E was estimated from the mean μ and width σ of the reconstructedenergy distribution, the beam energy spread σb /μb [4], and the width σp of the pedestal distribution asσE=Eσμ2−σbμb2−σpμ21/2(5).

Figure 4 shows the energy resolution as a function of the incident energy. The energy resolution σE /Eas a function of the incident energy Ei was ﬁtted withσE(Ei ) =E



0.000 ± 0.233
Ei2

+1.466 ± 0.032√
Ei

21/22+ (0.977 ± 0.115),(6)

where the units of the resolution and Ei were % and GeV, respectively. The energy resolution is muchhigher than that measured for an EM calorimeter consists of nine BSO crystals, 22 × 22 × 180 mm3 [5]:σE(Ei ) =E



2.3 ± 0.3√
Ei21/22+ (1.7 ± 0.2).

(7)

The energy resolution for 1 GeV positron corresponds to 1.74%, and it is extremely high. The details ofthe analysis for the energy resolution are described elsewhere [7, 8].

157Resolution (%)

654σ/μ3σΕ/Ε

2
100.1

0.2

0.3

0.4

0.5

0.6

0.7

Energy (MeV)

0.8

0.9

1Fig.4. The energy resolution as a function of the incident positron energy. The open circles
show σ/μ and the ﬁlled ones show σE /E. The data points for σE /E are ﬁtted with the√ 222parametrization (0.000/Ei ) + 1.466/ Ei + (0.977) .

§ 4. Decay Time
The decay time of the BSO crystal has been estimated from pulse shapes taken with a digital
phosphor oscilloscope (Tektronix DPO4104: 5 GHz sampling and 1 GHz bandwidth). The trigger fortaking pulse shapes is a coincidence signal of the central x and y BPM ﬁbers to select the positrons
which inject onto the central region (3×3 mm2 ) of the crystal. Figure 5 shows the pulse shapes for somepositron energies.
The pulse shape from 0 to 800 nsec are ﬁtted with an exponential function, and the obtained decay
times are 133.9, 136.4, and 137.2 ns for positron energies of 800, 670, and 500 MeV, respectively. The
ﬁtting error is less than 0.1 ns, and the average value is 136 ns. The obtained decay time is longer thanthat of a BSO crystal with a size of 22 × 22 × 180 mm3 (∼100 ns) measured by a single photo-electron
method [5]. The measured value from the pulse shape depends on how the EM shower grows in the BSO
crystal and where scintillation photons are produced. The details of the analysis for the decay time aredescribed elsewhere [8].

§ 5. Energy Resolution for 137 Cs
The energy of the photons from 137 Cs is 0.662 MeV and is so low that electron and positron paircreation does not take place. The energy deposit of electrons generated by the photoelectric effect forms
a bump in the energy distribution. The energy resolution is given by the number of detected scintillation
photons.

16Pulse Height (mV)

0−200−400−600−800−1000450A−12000250500

750350A

1000 0250500750

1000 0250A
250500750

1000Timing (ns)Fig.5. The pulse shape taken by an oscilloscope for positron energies of 800, 670, and 500 MeV(RTAX currents of 450, 350, and 250 A) together with the ﬁtted exponential functions.

The energy of 137 Cs photons were measured with a BSO crystal with a size of 40 × 40 × 210 mm3 .
A 2-inch photo-multiplier tube (Hamamatsu H6522) was connected to the crystal. Figure 6 shows theADC distributions taken with 137 Cs together with a background distribution measured without the 137 Cs
source which is normalized by a data taking time and a data taking efﬁciency. A net ADC distribution
for the 137 Cs photons is obtained by subtracting the background distribution from the ADC distribution
with 137 Cs.

Counts103800Source

2600
Counts

10BG

10400200

101000 2000 3000
ADC Channel

4000

00500
1000
1500
ADC Channel

2000

Fig.6. The measured ADC distributions. The left panel shows the ADC distributions taken with137Cs together with a background measured without the 137 Cs source which is normalized
by a data taking time and a data taking efﬁciency. The right panel shows the net ADC
distribution for the 137 Cs photons together with the ﬁtted Gaussian.

The mean μ and width σ of the net ADC distribution was estimated by ﬁtting with a Gaussianfunction. The energy resolution for the 137 Cs photons are estimated asσEσ,=Eμ − μp(8)17where μp stands for the mean of the pedestal distribution. The width of the pedestal distribution is negligibly small as compared with that of the net ADC distribution. The energy resolution of 16.6%±0.2%
has been obtained, which corresponds to about 40 detected photons with the photo-multiplier tube. Theresolution is much higher than that of the ﬁrst manufactured small BSO with a diameter of 20 mm
and a thickness of 39 mm (∼32% [9]). The details of the analysis for the energy resolution for the 137 Cs
photons are described elsewhere [10].

References[1]

T. Ishikawa et al.: Research Report of LNS, Tohoku University 39 (2006) 35;
T. Ishikawa et al.: Research Report of LNS, Tohoku University 40 (2007) 19;
T. Ishikawa et al.: in this Research Report of LNS, 41 (2008) 7.

[2]

K. Mochizuki and T. Ishikawa et al.: Research Report of LNS, Tohoku University 40 (2007) 15.
K. Mochizuki: Internal GeV-γ analysis note No.44 (2007).

[3]

M. Sato and T. Ishikawa et al.: in this Research Report of LNS, 41 (2008) 22.;
M. Sato: Internal GeV-γ analysis note No. 86 (2008).

[4]

T. Ishikawa et al.: Research Report of LNS, Tohoku University 40 (2007) 6.

[5]

H. Shimizu et al.: Nucl. Instrum. and Meth. A 550 (2005) 258.

[6]

H.Ikeda et al.: Nucl. Instrum. and Meth. A 441 (2000) 401.

[7]

S. Kuwasaki: Internal GeV-γ analysis note No.62 (2007).

[8]

S. Kuwasaki: Internal GeV-γ analysis note No.68 (2007).

[9]

M. Ishii et al.: Optical Materials 19 (2002) 201.

[10] S. Kuwasaki: Internal GeV-γ analysis note No.74 (2007).