Research Report of Laboratory of Nuclear Seience, Tohoku University Vol. 40 (2007)

15(LNS Experiment : #2536, #2582)

Performance of a Test Calorimeter of Lead Scintillating
Fiber Modules
K. Mochizuki, T. Ishikawa, R. Hashimoto, T. Ishida, S. Kuwasaki, K. Nawa,
Y. Okada, Y. Onodera, H. Shimizu, K. Suzuki, and H. Yamazaki
Laboratory of Nuclear Science, Tohoku University, Sendai, 982-0826

A new electro-magnetic (EM) calorimeter complex FOREST comprises three independent calorimeters, covering a solid angle of about 4π sr in total. The Backward Gamma detector brought from SPring8/LEPS is employed to cover the central part of FOREST. Backward Gamma consists of lead scintillatingﬁber (Lead/SciFi) detector modules. The performance of a test calorimeter made up with 9 Lead/SciFi
detector modules of Backward Gamma has been studied by using a positron beam with energies up to800 MeV.

§ 1. Experimental Setup
The performance study of a test calorimeter was made at the electron/positron beamline dedicatedto testing detectors at LNS. The test calorimeter is made up with Lead/SciFi detector modules stackedin a 3 × 3 array, which is a small portion corresponding to a polar angle from 60◦ to 90◦ of the Backward Gamma detector. Momentum-analyzed positrons were used as an incident beam with the energy
ranging from 200 to 800 MeV . A beam proﬁle monitor (BPM) was used to specify the position of theincident positrons. BPM consists of two layers of scintillating ﬁber (SciFi) hodoscopes. Each hodoscopeis composed of 16 SciFi modules with a cross section of 3 × 3 mm2 . The upstream and downstream layers
determine the x and y positions of the incident positron, respectively. Figure 1 shows the experimental
setup for the performance study of the calorimeter.
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 trigger rate was 2 kHz and a fraction of accidental
coincidence events was negligibly small. The energy calibration for the Lead/SciFi detector modules wasmade by using 300, 460, 590, and 800 MeV positrons injected on to the central region (6×6 mm2 ) of each
module one by one. The detector module has the shape of a truncated pyramid. Therefore the position
and the tilted angle of the calorimeter were set so that the beam axis was perpendicular to the front faceof the module of interest. Then the gain of each detector module was adjusted.

16

33 Lead/SciFi modules
33 Lead/SciFi modules
1616 fibers

1616 fibers
Beamline

Fig.1. Experimental setup for the performance study of a test calorimeter comprised of 9Lead/SciFi detector modules. The 16 × 16 scintillating ﬁber hodoscopes are placed infront of the calorimeter to determine the position of incident positions.

§ 2. Energy Response
The deposited energy in the calorimeter is obtained by summing up the measured energies with 9detector modules as
E=9


Ej .

(2)

j=1

The positrons injected on to the central region (6×6 mm2 ) were selected in the energy measurement tosuppress the energy leakage out of the detector modules in the lateral direction. The linearity of theenergy response was checked with the ratio of the reconstructed energy to the incident positron energy.
Figure 2a) shows the ratio as a function of the incident energy. The normalization of the reconstructedenergy is arbitrary. A linear function rμ (Ei ) of the incident energy Ei was ﬁtted to the measured ratiorμ . The ﬁtted result is expressed asrμ (Ei ) = (1.1307 ± 0.0022) − (5.0769 ± 0.3433) × 10−5 Ei ,(3)where Ei is in MeV. The non-linearity of the energy response was found to be less than 6% for theincident beam energies from 200 to 800 MeV.
The energy resolution σE /E can be evaluated with a Gaussian mean μ and a width σ of the reconstructed energy distribution as 2 1/2
2σEσbσ−,=Eμbμ(4)where the effect of beam energy spread σb /μb [3] is subtracted. Figure 2 b) shows the measured energy
resolution as a function of the incident energy. The energy resolution σE /E may be expressed as
1/2

2

a1
σEa2 22+ √+ a0.
(5)=EEEThe function (5) is ﬁtted to the data to give the result,1/2
2 2σE1.93 ± 0.11
6.91 ± 0.082√++ (0.00 ± 0.92),(Ei ) =EiEEi(6)1.20
1.18a)
Energy Resolution (%)

ADC Peak Position/Incident Energy

17

1.16
1.14
1.12
1.10
1.08
1.06
0200 400 600
800Incident Energy E (MeV)2018 b)16
14121086
4
200
0.2
0.4
0.6
0.8
Incident Energy E (GeV)

Fig.2. The energy response as a function of the incident positron energy. a) The ratio of
the reconstructed energy to the incident energy. The normalization factor is arbitrary.
The data are ﬁtted with a linear parametrization 1.1307 − 5.0769 × 10−5 Ei . b) The
measured energy resolution. The data are well expressed with the parametrization√222(1.93/Ei ) + 6.91/ Ei + (0.00) .

where the parameters a0 , a1 , and a2 are given in % and Ei in GeV, respectively. The energy resolution for
1 GeV positrons corresponds to 7.2%. The details of the analysis for the energy resolution are described
elsewhere [4].

§ 3. Position Resolution
The incident position of positrons on the calorimeter was reconstructed by the energy weighted
average of the position vectors xi of 9 modules asxr ∝9

Cj Ej xj ,(7)j=1where the origin of the position vectors was the common center of a circumscribed sphere for front facesof the modules. The normalization was made in such a way that the length of the reconstructed position
vector should be the radius of the sphere (300 mm). Since the energy deposit to the central module wasmuch larger than that to the peripheral modules, the weight for the signal from the central module wasset to be smaller by using an extra factor Ci :⎧⎨ Cfor the central module0Cj =⎩ 1
for the peripheral modules(8)

The factor C0 was determined for each incident energy so that the mean of the difference between thereconstructed position and the incident position determined by BPM would be 0. The determined valuesof C0 are 0.01765±0.00002, 0.02684±0.00001, 0.02484±0.00001, 0.02123±0.00001, 0.02562±0.00001,
and 0.02473 ± 0.00001 for the incident energies of 300, 400, 500, 590, 670, and 800 MeV, respectively.
The difference distribution has a Gaussian shape whose mean is 0 by using the determined C0 . The x (y)position resolution is estimated with the width σx (σy ) which is obtained by ﬁtting a Gaussian function

18

Position resolution (mm)20181614121086420x Component
00.2

0.4

y Component

0.6 0.8 0 0.2 0.4 0.6Incident Energy E (GeV)

0.8

Fig.3. The position resolution as a function of the incident energy. The left and rightpanels show x and y components, respectively. The data are ﬁtted with the form√
222(a2 /Ei ) + a1 / Ei + (a0 ) .

to the difference distribution in x (y) direction. Figure 3 shows the position resolution as a function of
the incident energy. The position resolution σx and σy may also be represented with a similar function
to Eq. (5). The ﬁtted result are
⎧
1/2

2 
2
⎪
⎪
0.00
±0.00
8.27±0.03⎪
2⎪ σx (Ei ) =√++ (6.18 ± 0.07)
and⎪
⎨
Ei
Ei
1/2
2 
2
⎪
⎪
0.00
±0.00
8.53±0.03⎪2⎪√++ (5.68 ± 0.07),⎪ σy (Ei ) =
⎩Ei
Ei(9)

where the position resolution σx (σy ) and Ei are given in mm and GeV, respectively. The x and yposition resolutions for 1 GeV positrons correspond to 10.3 mm and 10.2 mm, respectively. The detailsof the analysis for the position resolution are described elsewhere [5].

Acknowledgment
We appreciate Dr. T. Matsumura for fruitful discussions on the energy and position resolutions for
the Lead/SciFi modules.

References[1]

T. Ishikawa, LNS Experiment #2536 (2005).

[2]

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

[3]

T. Ishikawa, Internal GeV-γ analysis note No.43 (2007).

[4]

K. Mochizuki, Internal GeV-γ analysis note No.44 (2007).

[5]

K. Mochizuki, Internal GeV-γ analysis note No.46 (2007).