22Research Report of Laboratory of Nuclear Science, Tohoku University Vol. 41 (2008)(LNS Experiment : #2620)

Energy Resolution of an SF-5 Lead Glass Čerenkov Counter
M. Sato, T. Ishikawa, S. Kuwasaki, H. Fujimura, R. Hashimoto, H. Shimizu,
K. Suzuki, and H. Yamazaki
Laboratory of Nuclear Science, Tohoku University, Sendai 982-0826

A new electro-magnetic (EM) calorimeter complex FOREST consists of three independent calorimeters [1], covering a solid angle of about 4π sr in total. An SF-5 lead glass Čerenkov counter array Rafﬂesia II is employed to cover backward angles from 110 to 170 degrees of FOREST. The energy resolutionof the SF-5 counter has been measured using a positron beam with energies up to 800 MeV.

§ 1. Experimental setup
The energy resolution of the SF-5 lead glass Čerenkov counter was measured at the electron/positron
beamline dedicated to testing detectors at LNS. It consists of an SF-5 lead glass with a size of 150 mm(W) × 150 mm (H) × 300 mm and a 5 inch photo-multiplier tube (Hamamatsu R1250) directly connectedto the lead glass, and it was manufactured by Ohara Optical Company [2]. The SF-5 lead glass is amixture of 55% PbO2 and 45% SiO2 by weight, its density is 4.07 g/cm3 , and its radiation length (X0 ) is
25.4 mm. The thickness of the counter corresponds to 11.8X0 .
Momentum-analyzed positrons were used as an incident beam with the energy ranging from 100 to800 MeV . A beam proﬁle monitor (BPM) was used to specify the position of the incident positrons. BPM
consists of two layers of scintillating ﬁber (SciFi) hodoscopes. Each hodoscope is composed of 16 SciFiswith a cross section of 3 × 3 mm2 . The upstream and downstream layers determine the x and y positionsof the incident positron, respectively. Figure 1 shows the experimental setup for measuring the energy
resolution of the SF-5 counter.
The trigger condition for the data acquisition system is described as[x ﬁber OR] ⊗ [y ﬁber OR],(1)

where ⊗ means coincidence of signals. The maximum singles rate of the SF-5 counter was 4 kHz and afraction of accidental coincidence events was negligibly small. The energy resolution was measured byusing positrons bent with a RTAGX current from 50 to 450 A ( about 100–800 MeV/c) [3] injected on tothe central region (9×9 mm2 ).

§ 2. Energy Response
The measured energy E is determined by subtracting the mean of the pedestal distribution Apedfrom the ADC value A as
E = A − Aped .

(2)

23SF-5 Lead Glass

1616 Fibers

e+ BeamFig.1. Experimental setup for measuring the energy resolution of the SF-5 counter. The 16 ×16 scintillating ﬁber hodoscopes are placed in front of the calorimeter to determine theposition of incident positions.

The unit of the measured energy E is arbitrary. The positrons injected on to the central region (9×9 mm2 )were selected in the energy measurement to suppress the energy leakage out of the SF-5 counter in thelateral direction. The linearity of the energy response was checked with the ratio of the mean of themeasured energy distribution to the incident positron energy Ee+ . Figure 2 shows the ratio as a functionof the incident energy. The difference of the ratio is less than 1% for Ee+ < 0.6 GeV and 5% for all thedata.
The measured energy distribution for each incident positron energy was ﬁtted with a Gaussianfunction, and the mean (μ) and width (σ) of the distribution was determined. The energy resolution isobtained asσEσ=.
Eμ(3)The energy spread of the positron beam and the smearing of the pedestal distribution is much smaller
than the energy resolution of the SF-5 counter, and they do not affect the obtained resolution. Figure 2shows the energy resolution as a function of the incident positron energy.
The energy resolution σE /E may be expressed asσE=E a 22E+a√1E

21/2+ a20(4).

The function (4) is ﬁtted to the data to give the result,σE(Ee+ ) =E



0.51 ± 0.07
Ee+

2

+4.06 ± 0.01
√
Ee+

2

1/2+ (2.70 ± 0.14)

2,

(5)

where the energy resolution and Ee+ are given in % and in GeV, respectively. The energy resolution for
1 GeV positrons corresponds to 4.9%. The energy resolution of the SF-5 counter is much higher thanthat of lead scintillating ﬁbers (7.2%) [4]. The details of the analysis are described elsewhere [5].
Rafﬂesia II was constructed on the 11th June in 2008, and 10 SF-5 counter are used in it. The
details of construction of Rafﬂesia II are reported [6].

Measured Energy/ Incident Positron Energy [channel / GeV]

24

1000

800

600

400

200000.2
0.4
0.6
0.8Incident Positron Energy (GeV)

1Fig.2. Ratio of the mean of the measured energy distribution to the incident positron energy.
The measured energy is given by subtracting the mean of the pedestal distribution fromthe ADC value, and its unit is arbitrary.

0.16Energy Resolution σ/μ0.140.120.1

0.08

0.06

0.04

00.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Incident Positron Energy (GeV)

1Fig.3. The energy resolution as a function of the incident positron energy. The resolution is
given by the width (σ) divided by the mean (μ) of the measured energy distributions.
The solid curve shows the ﬁtted function by the equation (4).

25References[1]

T. Ishikawa et al.: Research Report of LNS, Tohoku University 39 (2006) 35.

[2]

A. Ando et al.: KEK Report, KEK-79-21 (1979).

[3]

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

[4]

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).

[5]

M. Sato: Internal GeV-γ analysis note No. 86 (2008).

[6]

T. Ishikawa et al.: in this Research Report of LNS, 41 (2008) 7.