Performance Evaluation of Silicon Drift
Detectors for a Precision Spectroscopy ofKaonic Helium-3 X-rays
K 中間子ヘリウム 3 原子の X 線精密分光実験に用いるシリコンドリフト検出器の性能評価

Tadashi Hashimoto橋本 直
Department of Physics, School of Science
University of Tokyo
February 2011

Abstract
A new precise measurement of kaonic helium-3 x-rays is going to be
performed as the first experiment at the K1.8BR beamline in the J-PARC
hadron experimental facility. The experiment aims to determine the stronginteraction-induced 2p shift with a precision below 2 eV, which provides
crucial information on the K̄-nucleus strong interaction in the low energy
limit.
For the detection of the ∼ 6.2 keV x-rays from the 3d → 2p transitions inkaonic helium-3, 8 silicon drift detectors (SDDs), which have good resolutions
in both timing and energy, will be used.
The operation of the SDD was established under the experimentally required condition; SDDs at low temperatures and their preamplifiers also inthe vacuum. In the optimized temperature conditions, the energy resolutionwas ∼150 eV in FWHM at 6 keV and the time resolution was ∼500 ns in
FWHM. The operation under the realistic beam condition was also confirmedwith a good energy resolution and a good signal-to-noise ratio.
Furthermore, The response function of the SDD was studied to minimize
the systematic error in the fitting of the obtained spectrum. Pileup eventswere successfully removed and the eﬀect of the diﬀerent incident angle wasinvestigated. The validity of the energy scale at 6 keV in our system wasestimated to be better than 1 eV.

Contents
1 Introduction
1.1 Kaonic Atom X-rays . . . . . . . . . . . . . . . . . . . . . . .
1.2 History of Kaonic Helium X-ray Studies . . . . . . . . . . . .
1.2.1 “Kaonic Helium Puzzle” . . . . . . . . . . . . . . . . .
1.2.2 Connection to “Kaonic Nuclear Bound States” . . . . .
1.2.3 KEK-PS E570 . . . . . . . . . . . . . . . . . . . . . . .
1.2.4 SIDDHARTA Experiment . . . . . . . . . . . . . . . .
1.3 Present Experiment J-PARC E17 . . . . . . . . . . . . . . . .
1.3.1 Experimental Strategy . . . . . . . . . . . . . . . . . .
1.3.2 Precision Goal . . . . . . . . . . . . . . . . . . . . . . .

9
9
10
10
10
11
14
18
18
21

2 Silicon Drift Detectors
24
2.1 Basic Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2 Operational Requirement in E17 . . . . . . . . . . . . . . . . . 26
3 Optimization of Operational Conditions
3.1 Measurement Setup . . . . . . . . . . . . . . . . . . . . . . . .
3.1.1 Test Cryostat . . . . . . . . . . . . . . . . . . . . . . .
3.1.2 PIPS Detector . . . . . . . . . . . . . . . . . . . . . . .
3.1.3 Signal Readout . . . . . . . . . . . . . . . . . . . . . .
3.1.4 Trigger Logic and Data Acquisition . . . . . . . . . . .
3.1.5 X-ray Sources . . . . . . . . . . . . . . . . . . . . . . .
3.2 Temperature Control . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 SDD Temperature Control . . . . . . . . . . . . . . . .
3.2.2 Preamplifier Temperature Control . . . . . . . . . . . .
3.3 Optimization of Bias and Substrate Voltages . . . . . . . . . .
3.4 Optimal Temperature Search . . . . . . . . . . . . . . . . . . .
3.4.1 Preamp Temperature . . . . . . . . . . . . . . . . . . .
1

27
27
28
30
30
32
34
34
34
35
36
38
39

CONTENTS

2

3.4.2

SDD Temperature . . . . . . . . . . . . . . . . . . . . 39

4 Response Function of SDDs
4.1 Response Function . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Energy Dependent Energy Resolution . . . . . . . . . . . . . .
4.3 Pileup Rejection . . . . . . . . . . . . . . . . . . . . . . . . . .
4.3.1 Pre-pileup Event . . . . . . . . . . . . . . . . . . . . .
4.3.2 Post-pileup Event . . . . . . . . . . . . . . . . . . . . .
4.4 Response at Diﬀerent Detection Rates . . . . . . . . . . . . .
4.4.1 X-ray Detection Rate . . . . . . . . . . . . . . . . . . .
4.4.2 Charged Particle Detection Rate . . . . . . . . . . . .
4.5 Response to Diﬀerent Incident Angles . . . . . . . . . . . . . .
4.6 Validity of the Calibration Method . . . . . . . . . . . . . . .

44
44
47
47
47
51
52
52
53
56
59

5 SDD Commissioning with the Beam
5.1 J-PARC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.1 J-PARC . . . . . . . . . . . . . . . . . . . . . . . . . .
5.1.2 K1.8BR Beamline in the Hadron Experimental Facility
5.2 Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.1 Beamline Detectors . . . . . . . . . . . . . . . . . . . .
5.2.2 SDD & Liquid-3 He Target System . . . . . . . . . . . .
5.2.3 Trigger Scheme & Data Acquisition . . . . . . . . . . .
5.2.4 Experimental Condition . . . . . . . . . . . . . . . . .
5.3 Data Summary . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4 Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.4.1 Cut Condition . . . . . . . . . . . . . . . . . . . . . . .
5.4.2 Spectral Fitting . . . . . . . . . . . . . . . . . . . . . .
5.4.3 Characteristic X-ray Yields . . . . . . . . . . . . . . .
5.4.4 Signal to Noise Ratio . . . . . . . . . . . . . . . . . . .

68
68
68
69
71
71
73
74
79
81
84
84
85
87
88

6 Conclusion

90

Acknowledgement

92

A Asymmetry in Characteristic X-ray Lines

94

List of Figures
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
2.1
2.2
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9

Akaishi’s coupled-channel calculation for the 2p shifts in kaonic
He atoms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Kaonic 4 He spectrum obtained in E570. . . . . . . . . . . . . .
Calibration spectra obtained in SIDDHARTA. . . . . . . . . .
Kaonic 3 He spectrum obtained in SIDDHARTA. . . . . . . . .
All the measured values of the 2p shifts in kaonic He atoms . .
All the measured values of the 2p widths in kaonic He atoms .
Experimental setup for E17 . . . . . . . . . . . . . . . . . . .
Recent measurements of the 2p shifts in kaonic He and our
precision goal. . . . . . . . . . . . . . . . . . . . . . . . . . .

11
13
15
15
17
17
20
22

Schematic drawing of an SDD specialized for an x-ray measurement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Typical potential distribution in an SDD. . . . . . . . . . . . . 25
Schematic drawing of the test cryostat . . . . . . . . . . . . .
PIPS detector . . . . . . . . . . . . . . . . . . . . . . . . . . .
Flow of the SDD signal. . . . . . . . . . . . . . . . . . . . . .
Trigger logics for the measurements at the test cryostat. . . .
Close-up view around SDDs. . . . . . . . . . . . . . . . . . . .
Close-up view around a preamplifier. . . . . . . . . . . . . . .
Results of the scans of the bias voltages and the substratevoltage. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Typical 55 Fe spectrum with optimized voltages. . . . . . . . .
Preamplifier temperature dependence of (a) the energy resolution at Mn Kα (b) Mn Kα peak position . . . . . . . . . . .

3

29
30
31
33
35
36
37
38
39

LIST OF FIGURES
3.10 (a) Correlation of the signal height and the timing after theslewing correction and the event selection. (b) Typical TDC
spectrum at diﬀerent SDD temperatures. . . . . . . . . . . . .
3.11 SDD temperature dependence of (a) the energy resolution at
Mn Kα (b) the time resolution . . . . . . . . . . . . . . . . . .
3.12 Electron mobilities in SDDs . . . . . . . . . . . . . . . . . . .
3.13 SDD temperature dependence of Mn Kα peak position . . . .

4

40
41
42
43

Typical 55 Fe spectrum fitted with the response function . . . . 46
Timing relation of FOUT, OUT ( shaping time = 0.2 µs ) andOUT ( shaping time = 3.0 µs ) . . . . . . . . . . . . . . . . . 48
4.3 Timing relation of OUT, delayed XOUT and the ADC gate . . 48
4.4 Correlation between the baseline and the signal height before
the optimization of the veto widths. . . . . . . . . . . . . . . . 50
4.5 55 Fe spectrum w/ and w/o the baseline cut (before the optimization of the veto widths). . . . . . . . . . . . . . . . . . . . 50
4.6 Base line histograms were fitted to estimated the ration of theremained pileup events after 3-sigma cut. . . . . . . . . . . . 50
4.7 Ratios of the remained pileup events after the baseline 3-sigma
cut. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.8 Correlation between the baseline and the signal height after
the veto widths optimization. . . . . . . . . . . . . . . . . . . 51
4.9 Histograms of the baselines in diﬀerent conditions. . . . . . . . 51
4.10 Comparison of the x-ray spectra at diﬀerent incident x-ray rates. 52
4.11 Comparison of the x-ray spectra at the diﬀerent electron-backgroundrates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.12 Dependence on the 90 Sr electron hit rate. . . . . . . . . . . . . 55
4.13 Close up view around the E17 target. . . . . . . . . . . . . . . 56
4.14 Schematic of the setup for angle measurements. . . . . . . . . 56
4.15 Comparison of the x-ray spectra to the diﬀerent incident angle 57
4.16 Dependence on the incident angle. . . . . . . . . . . . . . . . . 58
4.17 Obtained spectra for the study of the validity of the calibration
method. (a) 55 Fe: 0 degree, (b) 55 Fe 60 degree. Residuals of
the fittings are also shown with ±2 σ lines. . . . . . . . . . . . 61
4.18 Energy deviations of the x-ray peaks. . . . . . . . . . . . . . . 67
4.19 Energy dependent energy resolution. . . . . . . . . . . . . . . 67
4.1
4.2

LIST OF FIGURES

5

5.1

Schematic drawing of K1.8BR beam line in the J-PARC hadronexperimental facility. . . . . . . . . . . . . . . . . . . . . . . . 70
5.2 Side view of the detector alignment downstream the D5 magnet. 71
5.3 T0 counter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
5.4 Defining Counter. . . . . . . . . . . . . . . . . . . . . . . . . . 73
5.5 Front and side views of the SDD & liquid-3 He target system. . 74
5.6 Second level trigger circuit . . . . . . . . . . . . . . . . . . . . 76
5.7 DAQ scheme in the SDD beam commissioning. . . . . . . . . . 78
5.8 (a) SDD temperatures and (b) preamplifier temperatures during the beam time. . . . . . . . . . . . . . . . . . . . . . . . . 80
5.9 Scaler counts of each discriminator for each SDD. . . . . . . . 83
5.10 Common cut conditions. (a) select the events which madethe triggers, (b) baseline cut, (c) OUT-FOUT correlation, (d)OUT-FOUT correlation cut. . . . . . . . . . . . . . . . . . . . 85
5.11 Typical spectrum in the beam commissioning (condition #3).
χ2 /ndf = 161.2/176. . . . . . . . . . . . . . . . . . . . . . . . 86
5.12 (a) Energy resolutions obtained in the fitting. (b) Energy
deviations from the energy scale calibrated by Ti and Ni Kα1
peaks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
5.13 Characteristic x-ray yields at the diﬀerent beam rates. . . . . 88
5.14 Comparison with the E570 calibration spectrum. . . . . . . . 89
5.15 Signal-to-noise ratio at the diﬀerent beam rates. . . . . . . . . 89
A.1
A.2
A.3
A.4
A.5

Measured Ti Kα line shape . . . . . . . . . . . . . . . . . . . . 95
Measured Ni Kα line shape . . . . . . . . . . . . . . . . . . . . 95
Generated line shape of Ni Kα with satellite peaks. . . . . . . 96
The generated spectrum was smeared by the detector resolution. 96
Energy deviations between the fitting results and the values
used to generate the spectra. . . . . . . . . . . . . . . . . . . . 96

LIST OF FIGURES

6

List of Tables
1.1

Calculated x-ray energy of the kaonic 3 He 3d → 2p transition.

2.1

Comparison of x-ray detectors used for kaonic x-ray measurements. KpX and DEAR were the experiments for kaonic hydrogen. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.1
3.2
3.3
3.4
3.5

Numbering of SDDs and preamplifiers . . . . . . . . . . . . .
Specifications of CAEN N568B shaping amplifier outputs . . .
Obtained data in the test cryostat measurements. . . . . . . .
Energies of characteristic x-rays used for the present study . .
Optimized values for the bias and the substrate voltages . . .

4.1
4.2

4.7
4.8
4.9

Definitions of the parameters in the response function. . . . . 46
Comparison of the parameters in the response function at thediﬀerent x-ray detection rates. . . . . . . . . . . . . . . . . . . 53
G
Obtained parameters by the “Best Fit”. Ni Esc Fesc
was fixed
since the Ni Esc peaks overwrap with Mn Kα peak. . . . . . . 62
Energy deviations for symmetric and asymmetric Gauss. χ2 /ndf
is represented by the values of 60 degrees (same in the following tables). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Diﬀerence in the energy deviations by the treatment of the
T ail slope β. . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Diﬀerence in the energy deviations by the treatment of theG
Shelf intensity (Fshelf−height ) . . . . . . . . . . . . . . . . . . . 64
Diﬀerence in the energy deviation by the background shape. . 65
Diﬀerence in the energy deviation by the fitting range. . . . . 65
Obtained white noises and Fano factors. . . . . . . . . . . . . 66

5.1

Parameters of K1.8BR beam line as of November, 2010. . . . . 70

4.3
4.4

4.5
4.6

7

21

27
31
33
34
38

LIST OF TABLES
5.2
5.3
5.4
5.5

Settings for the gate and delay generators in the second level
trigger circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thresholds of the discriminators and veto widths for the SDD
trigger circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Obtained data in the beam commissioning. . . . . . . . . . . .
Data summary of the SDD beam commissioning. . . . . . . .

A.1 Parameters used to generate the spectrum with satellite lines.

8

77
77
81
82
97

Chapter 1
Introduction
1.1

Kaonic Atom X-rays

Hadronic atoms reveal the eﬀect of the strong interaction in terms of shifts
and broadenings of their low-lying atomic states compared to the pure electromagnetic values. Experimentally, they can be produced by stopping negative hadrons such as π − , p̄, K − , Σ− in the target. The negative hadron√ isM∗

initially captured at highly excited state with a principal number ∼ mXe ,where MX∗ denotes the reduced mass of the hadronic atom system, then deexcite by emitting Auger electrons and x-rays. The spectroscopy of the x-rays
feeding “last orbit”, where the hadron-nucleus strong-interaction width become larger than the radiative transition width, is therefore a unique tool to
precisely determine the hadron-nucleus strong interaction in the low energy
limit.
Although a wide range of pionic atom data with high precisions are available, the data of kaonic atom x-rays are poor in both quality and quantity
mainly due to the lack of the intense kaon beam [1]. Especially, in lightkaonic atoms with targets Z≤2 , there were confusing “puzzles” in the past
century and the precisions of the measurements are still not satisfactory.

9CHAPTER 1. INTRODUCTION

1.2

10

History of Kaonic Helium X-ray Studies

First of all, the definition of the energy level shift (∆E) in this thesis should
be clarified. The shift is defined by∆E = −(E strong − E e.m. ),(1.1)

where E strong is a strong-interaction-aﬀected (i.e. actual) energy level which
can derive from measured x-ray energies and E e.m. is a calculated energy
level assuming only the Coulomb interaction. In this definition, a positive∆E means an attractive shift.

1.2.1“Kaonic Helium Puzzle”

In the last century, three experiments observed kaonic 4 He 3d → 2p x-rays [2–4]. 2p level is the “last orbit” in the kaonic He atom. All of these experiments
reported a relatively large repulsive 2p shift and a large width. Their average
is
old
∆E2p
= −43 ± 8 eV,

Γold
2p = 55 ± 34 eV(1.2)

In contrast, optical model calculations result in very small shifts and widths[5, 6], for example [5],opt
= 0.13 ± 0.02 eV,
∆E2p

Γopt
2p = 1.8 ± 0.05 eV(1.3)

The diﬀerence in the shifts between the experiments and the theory was asmuch as 5σ, and this situation was called the “kaonic helium puzzle”.

1.2.2

Connection to “Kaonic Nuclear Bound States”

The atomic level shift become more attractive as the attractive interaction
between K̄-nucleus increases, until the interaction become suﬃciently strong
to confine the atomic wave function in the local potential. Then, the atomic
wave function acquires a node in the nuclear surface, which pushes the atomic
state to the repulsive side. [7, 8] (for example, Fig. 1.1).
Therefore, the observed repulsive shift in the kaonic 4 He 2p state can beinterpreted as an evidence of the existence of p-wave kaon-nuclear bound state[9, 10]. But in the optical model, the observed large shift can be reproduced

CHAPTER 1. INTRODUCTION

11

eV
10

attractive

only when the imaginary part of the potential is much smaller than the value
obtained from the global fit of kaonic atom data for Z≥3 [5].
In the late 1990’s, the attractive K̄N strong interaction was establishedby the KpX experiment at KEK [11]. It motivated Akaishi and Yamazaki
to predict an unconventionally deep phenomenological K̄-nucleus potential
which accommodates narrow deeply-bound kaonic nuclei. They treated theΛ(1405) as a K̄N bound state and used g-matrix method [12]. Their framework was also applied to kaonic He atoms [13]. Akaishi used a coupledchannel potential to avoid the diﬃculty in the imaginary part of the opticalpotential, then he showed the 2p shift in Kaonic 4 He and 3 He can be |∆E| ≤11 and 15 eV, respectively, if K̄-nucleus potentials are deep as Akaishi and
Yamazaki predicted (Fig. 1.1).
Even though the much larger shifts in the experiment cannot be explained,“kaonic helium puzzle” attracted renewed interest.
Ucoupl = 120 MeV.

3He-K -Δ E2p

5300 U0 MeV
0

100

200

-10
-1
-15

repulsive-5

4He-K -

Figure 1.1: Akaishi’s coupled-channel calculation for the 2p shifts in kaonic
He atoms [13]1.2.3

KEK-PS E570

The situation triggered to carry out a new high precision measurement ofkaonic 4 He x-rays. KEK-PS E570 collaboration measured them, by using aliquid target and sophisticated techniques described in the following [14].

CHAPTER 1. INTRODUCTION

12• High energy resolution using Silicon Drift Detectors (SDDs)• Background suppression by a target volume cut with information ofparticle tracks• In-beam absolute energy calibration
The detailed explanations of these techniques will appear in Sec 1.3 as we
also employ them for the present kaonic 3 He experiment.
As a result, they achieved 2 times better resolution, 3 times higher statistics and 6 times better signal-to-noise ratio compared to the past experiments. Figure 1.2 shows the obtained spectrum in E570. The resulting 2p
shift wasE570
∆E2p
= 2 ± 2 ± 2 eV,(1.4)

which obviously diﬀers from the previous experiments and is consistent to
the theoretical calculations.

CHAPTER 1. INTRODUCTION

13

Figure 1.2: (a) Calibration spectrum (SDD self trigger) (b)(c) Kaonic 4 He
spectra (stopped-K events) obtained in KEK-PS E570 [14].

CHAPTER 1. INTRODUCTION

1.2.4

14

SIDDHARTA Experiment

Soon after E570, another measurement on kaonic 4 He X-ray was reported by
SIDDHARTA at DAΦNE, Italy [15]. The original purpose of SIDDHARTA
is to precisely measure X-rays from kaonic hydrogen and deuterium. Since
the x-ray energies of the 2p → 1s transitions in these atoms and the 3d →2p transitions in both isotopes of kaonic helium atoms lies between 6 and 8
keV, they can also measure kaonic helium x-rays just replacing their target.
They eﬀectively used gaseous target since the incident kaons from theφ decays are low momentum and almost mono energetic. 144 SDDs werearranged around the target and background was suppressed by using the
SDD timing information. 55 Fe sources and titanium foils provided in-situ
energy calibration in their case. The observed 2p shift in kaonic 4 He was
4He(test)∆E2p= 0 ± 6 ± 2 eV,(1.5)

which confirmed the E570 result.
Very recently, the first measurement on kaonic 3 He was reported by SIDDHARTA together with a preliminary result of new kaonic 4 He data [16].
3∆E2pHe = −2 ± 2 ± 4 eV
4 He(new)∆E2p= 5 ± 3 ± 4 eV(preliminary)

(1.6)
(1.7)

which are consistent with ∼ 0 eV shift. A large shift, initially seen in the
kaonic 4 He 2p state, was not observed also in kaonic 3 He.
The experimental method was basically same as before except for the calibration method. This time, characteristic x-rays from titanium and copper
foils induced by an x-ray tube provided the energy calibration. Note thatthe calibration data were obtained separately from the data taking of kaonic
helium x-rays and at much higher intensity, which resulted in larger systematic errors. The obtained calibration spectra and kaonic 3 He spectrum areshown in Fig. 1.3 and Fig. 1.4.
It is worth mentioning that the diﬀerence between Eq. 1.6 and Eq. 1.7 is
7 eV ± 3.6 eV (stat.) which may be an indication of the finite isotope shift.
Since these measurements were performed in the almost same condition, theisotope diﬀerence should be less aﬀected by the systematic eﬀects.

CHAPTER 1. INTRODUCTION

count  /  30  eV

x  106
6

15(a)

Cu  K_

5

Ti  K_

4
3
2
1

x  104
count  /  30  eV

30

(b)

28

Cu  K_

26
24

Au  L_

22
20
18

4

5

6

7

8

9

10

11

Energy  [keV]

Figure 1.3: (a) A high statistics calibration spectrum with an x-ray tube(b) An in-beam spectrum without a kaon coincidence in the SIDDHARTA
kaonic 3 He experiment. [16]Figure 1.4: Kaonic 3 He spectrum (required a kaon coincidence) obtained in
the SIDDHARTA experiment. [16]

CHAPTER 1. INTRODUCTION

16

All the results of the 2p shifts and widths in kaonic He obtained in thepast experiments are plotted in Fig. 1.5 and Fig. 1.6, respectively. The error
bars were defined by quadratic sum of the statistical error and systematic
error.

∆E2p [eV]CHAPTER 1. INTRODUCTION

17

SHIDDHARTA

0
E570[16]
test[17] new[18]

-20

-40

Old Average

BT79[3]-60
BR83[4]-80-

K -4He-K -3He

WG71[2]Γ 2p [eV]

Figure 1.5: All the measured values of the 2p shifts in kaonic He atoms

140
120
-

100

BR83[4]K -4He80
average60
40
BT79[3]20
0

Figure 1.6: All the measured values of the 2p widths in kaonic He atoms

CHAPTER 1. INTRODUCTION

1.3

18

Present Experiment J-PARC E17

A new precision measurement of kaonic 3 He balmer series x-rays is going
to be performed at J-PARC, Japan Proton Accelerator Research Complex.
This experiment has been approved as E17 [17] and is the first experiment
to be done at K1.8BR beamline in the Hadron Experimental Facility.

1.3.1

Experimental Strategy

Figure 1.7 shows the experimental setup. Incident kaons identified by the
Lucite Cherenkov counters are degraded to stop inside the liquid-3 He target
and resultant x-rays from the 3d → 2p transition in kaonic 3 He are measured
by 8 Silicon Drift Detectors (SDD).
To determine the x-ray energy as precisely as possible, we use and refine
the techniques which were successful in E570.
Silicon Drift Detectors (SDDs)
An SDD has a good time resolution of sub µs in addition to a good energy
resolution ∼ 150 eV at 6.2 keV. It also have a thin active layer of 450 µm in
spite of the 100 mm2 large eﬀective area, which reduces Compton backgroundinduced by high-energy γ-rays mainly from the π 0 and hyperon decays. The
solid angle of 8 SDDs is ∼ 1 %.
Since a performance evaluation of SDDs is the main subject of this thesis,
a detailed description of the detector will appear in the next chapter.
Background suppression by the target volume cut
Since the kaon is absorbed to nucleus after the atomic de-excitation and emit
secondary charged particles, we can reconstruct reaction point by tracking
both incident kaon and secondary charged particle. In E17, incident kaons
are detected by the Small Drift Chamber (Small DC). Secondary charged particles are detected by the Cylindrical Detector System (CDS) which covers∼ 60 % solid angle with a cylindrical drift chamber (CDC) and scintillation hodoscope counters (CDH). These detectors enables us to select x-rays
originated only in the liquid 3 He target volume.
But in-flight decay or reaction events in the target cannot be rejected by
the fiducial volume cut. Therefore, we additionally apply a correlation cut

CHAPTER 1. INTRODUCTION

19

between the energy deposit on the E0 counters and the z-vertex position to
reduce these events. As a result we can expect a good signal-to-noise ratio
in the kaonic helium x-ray spectrum.
In-beam absolute energy calibration
An in-beam calibration is essential for this kind of precision measurement
since it oﬀsets various eﬀects which come from the changes in the condition,such as a gain drift. In E17, characteristic x-rays from titanium and nickel
foils, induced mainly by contaminating pions in the kaon beam, provide thein-situ and absolute energy calibration. The kaonic 3 He Lα line lies between
the two Kα lines.
We will discuss validity of this calibration method in Sec 4.6.

CHAPTER 1. INTRODUCTION

20
CDH

chargedparticles

CDC

carbondegrador

SDD

K-

X-raysLC

E0

liq.-3He target

Ti & Ni foil

Small DC

050 cm

Figure 1.7: Experimental setup for E17

The pure-electromagnetic energy of the x-rays calculated in the framework of Klein-Gordon equation (K.G.) with the vacuum polarization eﬀect(V.P.) from the first-order term of the Uehling potential are presented inTable 1.1.

CHAPTER 1. INTRODUCTION

21

Table 1.1: Calculated x-ray energy of the kaonic 3 He 3d → 2p transition [16]Level
K.G. [eV]2p-11179.63d-4968.6
3d → 2p
6211.0

1.3.2

V.P. [eV]
-15.4
-1.9
13.5

Total [eV]-11195.0-4970.5
6224.6

Precision Goal

Previous measurements of kaonic He x-rays were overviewed in the previous
section. Although the long-standing “kaonic helium puzzle” has been solved,
the precision is not satisfactory especially for kaonic 3 He and important questions still remain. They are• Are the 2p shifts ∼ 0 eV or non-zero (|∆E| > 2 eV) ?
• Are the 2p shifts attractive or repulsive ?
• Is there a finite isotope shift?
These questions are essential to discuss the K̄-nucleus interaction and the“kaonic nuclear bound state”. Then, our precision goal in E17 is set to below
2 eV in both statistics and systematics and we aim to improve them up to 1
eV if possible. Since the detector resolution is ∼ 150 eV in FWHM, ∼ 1 eVseems to be the limit of the suppression of the systematic error. Furthermore,
now we are thinking about re-measuring the kaonic 4 He x-rays in the same
setup as the kaonic 3 He measurement to examine the indication of the finite
isotope shift by the SIDDHARTA experiment.
Our precision goals are plotted with the results of recent measurements
in Fig. 1.8.

∆E2p [eV]CHAPTER 1. INTRODUCTION

22-

K -4HeK -3HeIsotope shift
Syst. error

10

5

0

E570

proposal± 2(stat.) ± 2(syst.)

-5

-10

test
new
SIDDHARTA

J-PARC E17
Precision goal

Figure 1.8: Recent measurements of the 2p shifts in kaonic He and our
precision goal.

In addition to the precise determination of the 2p shift, information on
the 2p width and the yields of x-rays are important. Therefore we will also
determine these quantities. As for the 2p width, however, we may be able
only to set a upper limit since the expected width is much smaller than thedetector resolution.
Possible improvements from E570 for a better systematic error are as
follows.
• Further optimization of operational conditions of SDDs (Chapter 3)• Better understanding of response function of SDDs (Chapter 4)• Wave form analysis with FADC data
• Beam information for the calibration x-rays with a second level trigger
schemeCHAPTER 1. INTRODUCTION

23• Higher beam quality, especially in K− /π − ratio, which improves signalto-noise ratio
Latter three points were tested and studied in the realistic beam conditionand partially described in Chapter 5.

Chapter 2
Silicon Drift Detectors
2.1

Basic Concept

The basic concept of silicon drift detectors (SDD) was originally developed
by Gatti and Rehak [18] based on the principle of sideward depletion; alarge volume of high-resistivity n-type silicon is fully depleted by a smallsized n+ ohmic substrate contact. If the p+ junctions covering both surfaces
are designed to produce an electric field parallel to the surface with proper
reverse-bias voltages, all the electron induced by particle injection drift tothe n+ substrate contact acting as a collecting anode.
Although this mechanism was originally developed for a position sensitive
detector by using the drift time information, we use SDDs specialized for xray spectroscopies [19].
In this case, one side of an SDD is made of uniform p+ junction as ahomogeneous radiation entrance window. In the opposite surface, concentric
ring-shaped p+ junction stripes are placed to produce electric field in theradial direction toward small n+ ohmic substrate contact in the center, whichacts as a collecting anode. A schematic view of the SDD configuration andthe typical potential distribution produced by the reverse-bias voltages areshow in Fig. 2.1 and Fig. 2.2.

24

CHAPTER 2. SILICON DRIFT DETECTORS

Figure 2.1: Schematic drawing ofan SDD specialized for an x-ray
measurement [19].

25

Figure 2.2: Typical potential distribution in an SDD [19].

As a result, an SDD can have a large eﬀective area while keeping a small
anode size and a thin active layer. The small anode size is vital for a goodenergy resolution and the thin active layer reduces the Compton backgroundproduced by high-energy γ-rays. The time resolution of an SDD reflects thedrift time distribution of electrons in silicon, which is typically sub micro
second at low temperatures.
They are now commercially available and we use SDDs and corresponding
preamplifiers manufactured by KETEK [20].
Comparison with Previous Detectors
Here we compare the x-ray detectors used for x-ray spectroscopies of lightkaonic atoms. A conventional Si(Li) detector cannot realize large eﬀective
area and thin active layer keeping a good energy resolution, whereas a charge
coupled device (CCD) have no time resolution as summarized in Table 2.1.
Thus, SDDs are the best devices among them for an x-ray spectroscopy oflight kaonic atoms.

CHAPTER 2. SILICON DRIFT DETECTORS

26

Table 2.1: Comparison of x-ray detectors used for kaonic x-ray measurements.
KpX and DEAR were the experiments for kaonic hydrogen.

Detector
2

Eﬀective area (mm )Thickness (mm)Energy resolution (FWHM)@ 6 keV (eV)Temperature (K)Time resolution (FWHM) (ns)Reference

2.2

Si(Li) CCD
KpX DEAR
200
724
5
0.03

E570
100
0.26

SDD
Siddharta
100
0.45

E17
100
0.45

410

170

185

150

150

?
290
[11]

165
[21]

83
430
[14]

170
690
[22]

∼130
∼500
this thesis

Operational Requirement in E17

For a larger acceptance, SDDs are placed very close to the liquid-3 He target
which will be held at ∼ 1.5 K. Therefore, low-temperature operation of SDDs
are crucial to reduce thermal eﬀect to the target. We put SDDs in a liquidnitrogen cooled aluminum housing (∼ 80 K) for this reason.
As for the preamplifiers, they should be placed close to the corresponding
SDDs to minimize the cable lengths for the better resolution. Since ourtarget cell, consequently SDDs are placed in the center of the cylindricaldetector system, there is no space around the SDDs except for inside thetarget vacuum chamber. That’s why we will operate the preamplifiers inside
the vacuum unlike in the case of E570. They will be also placed inside a box
cooled with liquid nitrogen.

Chapter 3
Optimization of Operational
Conditions
As will be described in the chapters to follow, we performed various studies with 9 SDDs and 10 preamplifiers. Among them, 2 SDDs come from adiﬀerent manufacturing lot and somehow showed diﬀerent behavior for thebias-voltage. We distinguish them as “old” SDDs against other 7 “new”
SDDs according to the order of purchases. 10 preamplifiers are considered to
be basically identical. Table 3.1 shows the numbering of SDDs and preamplifiers.
The studies were performed at KEK (High Energy Accelerator Research
Organization) and later at the J-PARC hadron experimental facility.
Table 3.1: Numbering of SDDs and preamplifiers

SDD
Preamplifier

3.1

Number Remark
1 ∼ 6, 9 “new”
7, 8
“old”
1 ∼ 10Measurement Setup

To study the operational conditions of SDDs and other systematic eﬀects, socalled test cryostat was prepared. It can provide the temperature conditions
27

CHAPTER 3. OPTIMIZATION OF OPERATIONAL CONDITIONS

28

for SDDs and their preamplifiers described in the previous chapter with amuch easier operation than the real experimental cryostat.

3.1.1

Test Cryostat

A schematic view of the test cryostat is shown in Fig. 3.1. The test cryostat
was evacuated with a rotary pump and a turbo-molecular pump (TMP) torealize a thermal insulation vacuum. Then, liquid nitrogen was transferredto the 8 L tank. A copper support and a copper finger, which were directly
connected to the liquid-nitrogen tank, were cooled down to below 80 K. An
SDD and a preamplifier were mounted on the copper finger and the copper
support, respectively. The SDD was irradiated to the x-rays from outside
the vacuum through a 188 µm Mylar window ( changed to 250 µm later ).
A typical vacuum pressure with liquid-nitrogen cooling was of the orderof 10−6 torr and a typical consumption time of fully-filled liquid nitrogen in
the 8 L tank was around 14 hours.

CHAPTER 3. OPTIMIZATION OF OPERATIONAL CONDITIONS

Figure 3.1: Schematic drawing of the test cryostat

29

CHAPTER 3. OPTIMIZATION OF OPERATIONAL CONDITIONS

3.1.2

30

PIPS Detector

For a timing measurement, we used a PIPS detector (passivated implemented
planar silicon detector, manufactured by Canberra [23]) as a start counter.
Even low energetic electrons from a 90 Sr source can easily penetrate the
PIPS for its thinness of 300 µm. The time resolution of the PIPS detector
was measured by using 90 Sr electrons and a scintillation counter to be ∼ 50
ns in FWHM.

Figure 3.2: PIPS detector

3.1.3

Signal Readout

A schematic diagram of the signal flow from the SDD is shown in Fig. 3.3.
High voltages supplied by KIKUSUI was divided to 3 voltages for R1 ( mostinner ring ), RX ( most outer ring ), BACK ( back contact ) of an SDD(seeFig. 2.1). These bias voltages fully deplete the silicon bulk and make potential like Fig 2.2. For a preamplifier +12 V/ -12 V were supplied by an
external voltage supplier.
A detected charge pulse was integrated by the reset-type charge-sensitive
preamplifier separated by ∼ 40 cm from an SDD. Then, the ramped signal
was taken out from the vacuum chamber and divided into two lines to input
to a CAEN N568B shaping amplifier, where the signal was amplified andshaped. The preamplifier also generates so-called reset signal just after the
reset timing.
The CAEN shaping amplifier has 16 channel inputs and 3 types of outputs
for each 16 channel input. The features of these outputs are summarizedCHAPTER 3. OPTIMIZATION OF OPERATIONAL CONDITIONS

31

in Table 3.2. We used 2 channels for each SDD. One of the outputs was
negative with a 0.2 µs shaping time which was used for the trigger logic andthe other one was positive output with 3 mus shaping time for a peak-hightmeasurement.
The CAEN N568B was also used for the PIPS detector.
Back
SDD chip

-70 V

SDD
HV
-20 V BoxRX
R1
Feedback
Drain
Bulk(SUB)KIKUSUI-200 V PMC-0.2A-130 V

ChargeSensitive
Preamplifier±12 V Power

SourceResetsupplyPreamp
LV BoxRampedSignal

CAEN
N568B

Reset

SDD
Vacuum Chamber

Outside

1~5 m

<1m

SDD HV Box
Preamplifier

Preamp LV Box~40 cm<1m

KIKUSUI PMC-0.2A
power supply

reset
ramped signal
LEMO cable ( 1~3 m )SDD

CAEN 16CH
Spectroscopy Amplifier
Model N568B

Test Cryostat

to the counting room
15 m BNC cable (KEK)
8 m LEMO +50 m BNC cable (J-PARC)

Figure 3.3: Flow of the SDD signal.

Table 3.2: Specifications of CAEN N568B shaping amplifier outputs
Name
OUT
XOUT
FOUT

Description
shaping time (0.2/1.0/3.0/6.0 µs) and polarity selectable
further 10x fixed amplification of the OUT value
100 ns diﬀerentiation time constant. Risetime: 25 ns typically.

CHAPTER 3. OPTIMIZATION OF OPERATIONAL CONDITIONS

3.1.4

32

Trigger Logic and Data Acquisition

At the very beginning of our study, we defined the trigger as (Figure 3.4 (a))
SDD ⊗ Reset.
Since the reset sometimes made fake signals and the baseline of the signal
became unstable after a reset , Reset was introduced with a typical width ofseveral hundreds µs.
In the timing measurement, a hit on PIPS detector was additionally required(Figure 3.4 (b)).
SDD ⊗ Reset ⊗ P IP S,
where we selected only rapid rising signal for P IP S by using a narrow coincidence window for two discriminators with diﬀerent thresholds.
For the x-ray measurements with 90 Sr electron background, we used another discriminator and rejected large signals produced by electron directhits.(Figure 3.4 (c))
SDD ⊗ Reset ⊗ HighT h
The pulse data (height/charge) of the signals and various timing information
were fed into the PHADC, CHADC and TDC modules of the TKO standard.
Then, they were read from VME-SMP via TKO SCH to record on the PC.
The recorded signals in each measurement are summarized in Table 3.3.

CHAPTER 3. OPTIMIZATION OF OPERATIONAL CONDITIONS

33

(a)
SDD

preamplifier

CAEN OUT 0.2 μs (-)
N568B

DiscriFixed Delay

Reset Discri

Gate & Delay

Trigger(b)
SDD

preamplifier

CAEN FOUT (-)
N568B

Discri

Gate & Delay

Reset Discri

Gate & Delay
Trigger

PIPS

preamplifier

CAEN XOUT 0.2 μs (-)
N568B

(c)

SDD

OUT 0.2 μs (-)

preamplifier

HighTh Discri
PIPS timing
LowTh Discri

Gate & Delay

CAEN

HighTh Discri

Gate & Delay

N568B XOUT 0.2 μs (-)(OUT 0.2 μs (-))

LowTh Discri

Fixed Delay

Reset Discri

Gate & Delay

Trigger

Figure 3.4: Trigger logics for the measurements at the test cryostat.

Table 3.3: Obtained data in the test cryostat measurements. (∗) data werepartially available.
Name
Sh. Amp (µs) polality
moduleremark(a) SDD ADC
OUT
3.0 positive
PHADC(b) SDD ADC
OUT
3.0 positive
PHADC
SDD Timing
FOUT
negative TDC (5 µs) PIPS HighTh start
PIPS ADC
XOUT
3.0 positive
PHADC
TDC
PIPS LowTh
XOUT
0.2 negative
PIPS HighTh start
Timing(100 ns )(c) SDD ADC
OUT
3.0 positive
PHADC
Baseline
XOUT
3.0 positive
PHADC∼ 3.0 µs delay∗ FOUT
FOUT
positive
PHADC∼ 800 ns delay
TDC (5 µs)∗ Reset Timing∗ Next Timing
OUT
0.2 negative TDC (5 µs) Discri Vth =30 mV∗ Tail Charge
OUT
0.2 negative
CHADC

CHAPTER 3. OPTIMIZATION OF OPERATIONAL CONDITIONS

3.1.5

34

X-ray Sources

As an x-ray source, an 55 Fe is suitable in our case since the manganese xray lines are close to kaonic 3 He Lα line. Thus, an 55 Fe was used for various
studies of the response of SDDs . A 90 Sr was used for the timing measurement
and to obtain calibration lines of nickel and titanium fluorescence x-rays.
The reference energies of these characteristic x-rays are listed in Table 3.4.
Fe x-rays were used only in the beam commissioning (Chapter 5).
Table 3.4: Energies of characteristic x-rays used for the present study [24].
Metal
Ti

X-ray name
Kα1
Kα2
Kβ1
Mn
Kα1
(55 Fe)
Kα2
Kβ1
Fe
Kα1
Kα2
Kβ1
Ni
Kα1
Kα2
Kβ1

Energy (eV)4510.904504.92
4931.835898.805887.69
6490.596404.01
6391.037058.18
7478.257461.038264.78

3.2

Temperature Control

3.2.1

SDD Temperature Control

As mentioned above, SDDs were placed inside housings cooled down to liquid
nitrogen temperature. But, SDDs themselves should be a bit warmed up as
studies described in this section revealed.
Figure 3.5 shows the close-up drawing around the SDDs. Thermal contact
between the base of the SDD housing and a SDD rod was reduced by a SUS
bolt and a Teflon washer. Then, a film-type heater (120 Ω) attached on
the rod could heat up a minimal region including the SDD itself when aCHAPTER 3. OPTIMIZATION OF OPERATIONAL CONDITIONS

35

DC voltage was applied. A temperature sensor (LakeShore Pt-100) was also
mounted on the rod and the temperature of the rod was defined as the SDD
temperature.

Figure 3.5: Close-up view around SDDs. As for the temperature sensors,
two types of Pt-100s were used.

3.2.2

Preamplifier Temperature Control

Although we succeeded in operating our preamplifiers in the vacuum, one
preamplifier was broken in the low-temperature operation at ∼ 150 K. We
therefore decided to operate preamplifiers at the temperature over 200K to
avoid such trouble although the direct cause of the breakdown was not clear.
A circuit board of a preamplifier was set in a housing with materials
which optimize the heat conductance (Figure 3.6). An aluminum support
for the preamplifier housing equipped a heater and a temperature sensor forthe temperature control and mounted on the cold copper support with Teflon
washers to reduce heat conductance. The temperature was controlled with a
PID (Proportional-Integral-Derivative) feedback unit (Lakeshore 340). Another temperature sensor was attached on one of the chips of the preamplifier,whose temperature was adopted as the temperature of the preamplifier.

CHAPTER 3. OPTIMIZATION OF OPERATIONAL CONDITIONS

36

Figure 3.6: Close-up view around a preamplifier.

3.3

Optimization of Bias and Substrate Voltages

After roughly optimized operational temperatures of SDDs and their preamplifiers, optimal values of the bias voltages and the substrate voltage (SUB)of the FET were studied. We scanned around the values recommended by
KETEK for R1/RX/BACK (-20V/-130V/-60V). Since we had to change SUB
by the potentiometer on the preamplifier, we took out the preamplifier outside the vacuum for the SUB measurement.
As for R1 and RX, the recommended values were located in the stableregions. However, we found that the gain became smaller and resolution got
worse just below the recommended value for BACK for “new” SDDs. Thus
we adopted higher voltages for BACK. Although diﬀerence between “new”
and “old” SDDs appeared in the behavior for the BACK voltage, they canshare the same optimal voltages including the SUB voltage.
The results are shown in Fig. 3.7 together with arrows which indicate theCHAPTER 3. OPTIMIZATION OF OPERATIONAL CONDITIONS

37

adopted values. The energy resolutions were obtained by the fitting of 55 Fe
spectra. The adopted voltages are summarized in Table 3.5 and a typical
spectrum is shown in Fig. 3.8.
Although there were some diﬀerences in energy resolutions among SDDs,
they were not characteristics of the detectors. The noise level usually changed
when we open the cryostat for some modifications.
Resolution FWHM at Mn Kα (eV)Resolution FWHM at Mn Kα (eV)

152

154

SDD7 ("old")

152

SDD7 ("old")

150

SDD1 ("new")

SDD1 ("new")

148

150

set

set

146

148

144

146

142

144

140

142
140
5

10

15

20

25

30

35

138
100

110

120

130

140

R1 Voltage (V)Resolution FWHM at Mn Kα (eV)

210

175

SDD7 ("old")
SDD1 ("new")
SDD4 ("new")200

SDD7 ("old")
SDD8 ("old")
SDD1 ("new")

170

190

165

180

set

160

170

155

set

160

150

150

145

140
130

160

180

Resolution FWHM at Mn Kα (eV)

220

150

RX Voltage (V)

140
45

50

55

60

65

70

75

80

85

90

Back Contact Voltage (V)

135
0

1

2

3

4

5

6

7

8

9

Substrate Voltage (V)Figure 3.7: Results of the scans of bias voltages and a substrate voltage. The
voltages except for the objective one were fixed to the optimized values.

CHAPTER 3. OPTIMIZATION OF OPERATIONAL CONDITIONS

38

Table 3.5: Optimized values for the bias and the substrate voltages

Counts

R1
-20 V

102

RX
-130 VBACK SUB-70 V -6.5 V

Mn K α Gauss
Mn K β Gauss
Mn K α Tail
Mn K β Tail

1011200 1400 1600 1800 2000 2200 2400
ADC channel

Figure 3.8: Typical 55 Fe spectrum obtained in the measurements for the
optimization of the voltages. Only Gauss and T ail were used for the fitting(see Sec. 4.1).

3.4

Optimal Temperature Search

Now that optimal voltages were found, we systematically studied the optimal
operational temperatures for preamplifiers and SDDs.

CHAPTER 3. OPTIMIZATION OF OPERATIONAL CONDITIONS

3.4.1

39

Preamp Temperature

At temperatures between 240 K and 290 K, we found energy resolutions
are stable and Mn Kα peak positions moves 0.5 eV equivalent every 1 Kchange (Fig. 3.9). This peak shift is not so a large problem because thein-situ energy calibration compensates it in E17. Nevertheless, it is better tooperate preamplifiers with stable temperatures.
The most severe constraint on preamplifiers’ temperatures are related
to the Reset veto time. The discharging time accompanied by reset has
negative correlation on preamp temperature. When the discharging time
becomes suﬃciently longer, a large bump appears after reset in the shaped
signal, which made us Reset veto time considerably long (an order of ms ormore). To avoid such a long veto time, preamplifiers should be kept at >270 K including some safety margin.
(a)(b)
slope : -0.16± 0.01 ch / K(1 ch ~ 3 eV)

1833.5152

Mn Kα peak center (ch)Energy resolution FWHM (eV)

154

150

1832.5

148
146

1832

1831.5

144
142
140

1831

1830.5

138

1830

136
240

1833

250

260

270

280

290

300

Preamp Temperature (K)1829.5

265

270

275

280

285

Preamp Temperature (K)Figure 3.9: Preamplifier temperature dependence of (a) the energy resolution
at Mn Kα (b) Mn Kα peak position

3.4.2

SDD Temperature

Time Resolution Measurement
Timing diﬀerence between electron hit on a PIPS and a penetrated electron
hit on an SDD were measured to derive the time resolution of an SDD. A

CHAPTER 3. OPTIMIZATION OF OPERATIONAL CONDITIONS

40

slewing eﬀect of PIPS was corrected using parameters obtained in a measurement with a scintillation counter. Then, the slewing of SDD was corrected(Fig 3.10 (a) ). After cutting oﬀ low signals, a timing histogram was fittedwith a Gaussian and the time resolution of an SDD (∆ESDD ) was defined as√∆ESDD = 2 2 ln 2 × σGaus
where σGaus is the Gaussian sigma obtained in the fitting.
1000
103k
170k

500

1000

Counts / 20 ns

SDD Timing (ns)

1200

0

600
400

-500

accept
-1000
0

800

200

←fast
500 1000 1500 2000 2500 3000 3500 4000

SDD ADC (ch)

0

-500

late→
0

500

1000

1500

SDD timing (ns)Figure 3.10: (a) Correlation of the signal height and the timing after theslewing correction and the event selection. (b) Typical TDC spectrum at
diﬀerent SDD temperatures.
Optimal Operational Temperature
Measured energy and time resolution dependence on the SDD temperaturesare shown in Fig. 3.11. It shows the energy resolution got worse at temperatures lower than 130 K. Below 100 K, we sometimes could not obtain x-ray
signals. Usually, semiconductor detectors are operated at a low temperature(< 150 K) to suppress the current noise caused by thermally excited carriers
and the frequent reset caused by leakage current. However, the performanceof an FET is known to become poor at such low temperatures. Our result
may be explained by a such behavior of the FET on the SDD.
In the higher temperature region > 150 K, diﬀerent tendencies were observed for diﬀerent SDDs. However, this region is out of our interest for theoperation and we can neglect the diﬀerence.

CHAPTER 3. OPTIMIZATION OF OPERATIONAL CONDITIONS

41

Considering that the time resolution becomes better at a lower temperature, 110 K - 130 K is the optimal operational temperature for the SDD. A
further fine tuning will be done in the final setup.
1200

SDD5
170

Time resolution FWHM (ns)Energy resolution FWHM (eV)

180

1000

SDD9

160

150

140

130

100

120

140

160

180

SDD Temperature (K)

200

800

600

400

200

100

120

140

160

180

200

SDD Temperature (K)Figure 3.11: SDD temperature dependence of (a) the energy resolution at
Mn Kα (b) the time resolution

Time Resolution and Electron Drift Time in Silicon
The observed temperature dependence of the time resolution can be well
explained by the temperature dependence of electron mobility in silicon since
the SDD time resolution reflects the electron drift time distribution in silicon.
We calculated electron mobilities in SDDs from the measured time resolutions
assuming the drift time from the outer-most ring to center anode corresponds
to the resolution (FWHM), that is,µe =L2
F W HM × (VRX − VR1 )(3.1)

where µe is an electron mobility, L is a length from the outer-most ring to
the center anode, F W HM is the measured time resolution, VRX and VR1 are
the applied voltages to the outer-most ring and inner-most ring, respectively.
Figure 3.12 shows the estimated electron mobilities in SDDs are consistent
with well-known data [25].

CHAPTER 3. OPTIMIZATION OF OPERATIONAL CONDITIONS

mobility (cm2/V/s)

106

42

Si - electron [27]mark: measurement
line : theoretical fit

105

104

1

J-PARC E17
KEK E570 [16]SIDDHARTA [24]10210Temperature (K)103

Figure 3.12: Electron mobilities in SDDs

Gain and Electron-Hole Creation Energy
We also found that Mn Kα peak position moves ∼0.5 eV equivalent every 1 Kchange, which is mainly due to the temperature dependence of the electronhole pair creation energy [26].

CHAPTER 3. OPTIMIZATION OF OPERATIONAL CONDITIONS

1842

slope : 0.19±0.00 ch / K( 1 ch ~ 3 eV )Mn K α peak center (ch)

1840
1838
1836
1834
1832
1830
1828
1826
100

120

140

160

180

200

SDD Temperature (K)Figure 3.13: SDD temperature dependence of Mn Kα peak position

43

Chapter 4
Response Function of SDDs
As already mentioned in the introduction, most part of the systematic error
in E570 came from the uncertainty of the response function of SDDs. The
rest part of the systematic error in E570, which came from the validity ofthe energy scale, was also closely related to the response function. Therefore, studies of response function in various conditions are crucial for the
suppression of the systematic error in E17.

4.1

Response Function

It is well known that the response of semiconductor detecter for monochromatic energy x-rays does not simply result in a symmetric Gaussian peak
represented by the detector resolution. Following the E570 case, we use a
response function based on that of conventional Si(Li) detectors intensely
studied in many literatures [27].
We define the response function for characteristic x-rays as a summationof following 4 components.
(

)

Gain
(E − E0 )2
Gauss(E) = √
exp −
2σ 2
2πσ
(
)
G
· GainFtail
1
E − E0T ail(E) =
exp
+ 2
2βσ
βσ
2β
)
(
1
E − E0
√
+√
·erfc
2σ
2β

44

(4.1)

(4.2)

CHAPTER 4. RESPONSE FUNCTION OF SDDS
(

45
)

G
Fshelf
E − E0−height · Gain√
erfc
Shelf (E) =
2
2σ
(
)
G
Fesc · Gain
(E − (E0 − ESiKα )2√
Esc(E) =
exp −
2σ 2
2πσ
2 ∫ ∞ −t2where,
erfc(x) = √
e dt
π x

(4.3)
(4.4)
(4.5)

As a main peak, a Gaussian is used (Gauss) since the natural widths ofcharacteristic x-rays are much smaller than the energy resolution of an SDD.
Incomplete charge collections result in the structures in the low energy side,
represented by T ail and Shelf in our case. T ail is a convolution of an
exponential, a step function and a Gaussian, while Shelf is a convolutionof a step function and a Gaussian. Escapes of a silicon K x-ray make apeak (Esc) which have indeed more complicated line shape than a simple
Gaussian.
The definitions of the parameters appeared in above equations are described in Table 4.1. ESiKα is not a parameter but the energy of silicon Kα
x-ray. Note that a P ileup component, which was appeared in E570, is notincluded in our response function since we succeeded to reject pileup events
as will be described in Sec. 4.3. Figure 4.1 shows typical result of spectrum
fitting with the response function defined here.
For some reason, we observed a peak just located at the Ti Kα energy. The
peak seem to be actually Ti x-rays originated around the 55 Fe source since
the peak disappeared when we attached a thick attenuator on the source.
Therefore, we usually included Ti K x-rays represented by Gaussians in thefitting function for the 55 Fe spectrum.

CHAPTER 4. RESPONSE FUNCTION OF SDDS

46

Table 4.1: Definitions of the parameters in the response function.

structureGaussparameter
Gain
E0
σ

T ail

G
Ftail
β

Shelf
Esc

G
Fshelf−heightG
FescCounts / 20 eV

105

104

Description
Area of Gaussian
Mean value of the Gaussian
Width of the Gaussian.
√
FWHM(=2 2 ln 2) was often used instead.
Area ratio between the T ail and the Gauss
Slope of the T ail structure
Ratio between the Shelf height and the Gauss area
Area ratio between the Esc and the Gauss

Total
Main Gaussian
Tail
Shelf
Escape peak

MnK α
MnK β

103

102

3500 4000 4500 5000 5500 6000 6500 7000

X-ray energy (eV)Figure 4.1: Typical 55 Fe spectrum fitted with the response function

CHAPTER 4. RESPONSE FUNCTION OF SDDS

47

To precisely evaluate these parameters in the response function is the
purpose of the studies in the following sections.

4.2

Energy Dependent Energy Resolution

The energy resolution of a semiconductor detector is known to derive fromnoise and the statistical fluctuation in the number of created electron-hole
pair. Therefore it can be given by√∆E(E) = 2.35ω WN2 +

FE
ω

(4.6)

where ω is the electron-hole creation energy in silicon, WN and F denote a
white noise and the Fano factor respectively.
The energy dependence of the energy resolution described by Eq. 4.6 will
be used and confirmed later.

4.3

Pileup Rejection

To reject pileup events is important not only for the suppression of the systematic error in the fitting of the final spectrum, but also for the study of
response function. Since pileup events disturb the spectrum, we cannot study
detailed line shape without rejecting them.

4.3.1

Pre-pileup Event

To understand the pileup events, we first observed the signal baseline height
just before an x-ray detection and checked the correlation with the signal
height. The observation of the signal baseline was realized by a ∼ 3 µs cabledelay to be in time for the trigger. The timing relation of the trigger, signal
and the delayed signal for the observation of the baseline is shown in Fig. 4.2
and Fig. 4.3. Since the baselines lay around the ground level, we set some
oﬀset in the CAEN shaping amplifier and used XOUT to enlarge the narrow
distribution.

CHAPTER 4. RESPONSE FUNCTION OF SDDS

FOUT

48

Trigger timing
OUT(0.2 μs)

OUT(3.0 μs)

Figure 4.2: Timing relation of FOUT, OUT ( shaping time = 0.2 µs ) andOUT ( shaping time = 3.0 µs )OUT(3.0 μs)

XOUT(3.0 μs)

ADC Gate

Figure 4.3: Timing relation of OUT, delayed XOUT and the ADC gate
55

Fe x-ray were observed in the background of 90 Sr electrons which real-CHAPTER 4. RESPONSE FUNCTION OF SDDS

49

ized a similar condition to an in-beam condition. The obtained correlation
between the signal height and the baseline height is shown in Fig 4.4. Pileup
events were clearly seen as tail structures toward higher baseline side and the
x-ray spectrum became clean by removing those events with high baselines(Figure. 4.5). The data were obtained at the HighTh rate of ∼ 500 Hz.
However, the tail structure of the pileup events continues even beneaththe gaussian peak in the baseline histogram. We estimated these events
by fitting the baseline histograms with a Gaussian and a exponential tailstructure ( T ail(x): a convolution of a Gaussian, an exponential and a step
function ). The line shapes were well represented by this fitting function as
3σcut
shown in Fig. 4.6. Then the ratios of the remained pileup events Fpile
werederived by a simple formula,∫ Gmean +3σ
3σcut
Fpile
=

0

T ail(x)dx
Gaussian area

(4.7)

The resulting ratio had linear dependence on the HighTh rate and it was ∼1% at the HighTh rate of several hundreds Hz, which is an expected rate in
the realistic beam condition.

50

4000
105
3500

pileup events × 10

counts / 20 eV

3000
2500
2000
1500
1000

Mn K αtotal
pileup-rejected

Pileup Events

Baseline Height (ch)CHAPTER 4. RESPONSE FUNCTION OF SDDS

Mn K β

104

103

500
0
0

3500 4000 4500 5000 5500 6000 6500 7000 7500

500 1000 1500 2000 2500 3000 3500 4000

Energy(eV)

Signal Height (ch)Figure 4.5: 55 Fe spectrum w/ andw/o the baseline cut (before the optimization of the veto widths).
Remained pileup ratio

CountsFigure 4.4: Correlation between thebaseline and the signal height before
the optimization of the veto widths.

103

102

0.05
0.045
0.04
0.035
0.03
0.025
0.02

10

0.015
0.01
1
0

0.005
500 1000 1500 2000 2500 3000 3500 4000

SDD baseline (ch)Figure 4.6: Base line histograms
were fitted to estimated the rationof the remained pileup events after
3-sigma cut.

0
0

500

1000

1500

2000

2500

HighTh rate (Hz)Figure 4.7: Ratios of the remained
pileup events after the baseline 3sigma cut.

Actually, most of these pre-pileup events occurred after vetoed signals
induced by electron hits. Since a large signal sometimes takes more than 100µs to recover the original baseline, the veto time for them should be set long

CHAPTER 4. RESPONSE FUNCTION OF SDDS

51

4000

CountsBaseline Height (ch)enough. Then, we became almost free from pre-pileup events as shown in
Fig. 4.8 and the baseline histograms are compared in Fig. /refbaseline. The
HighTh rates were ∼500 Hz in both Figures.
In this method, there should be no remained pileup events unlike thecase before the veto width optimization. It can be confirmed by analyzing
Flash-ADC wave-form data obtained in the beam commissioning (Sec. 5).

3500
3000

104
90

103

No Sr
VETO Width NOT optimized
VETO Width optimaized

2500
2000

102

1500
1000

10

500
0
0

500 1000 1500 2000 2500 3000 3500 4000

Signal Height (ch)1
0

500 1000 1500 2000 2500 3000 3500 4000

Baseline Height (ch)Figure 4.8: Correlation between thebaseline and the signal height after
the veto widths optimization.

4.3.2

Figure 4.9: Histograms of the baselines in diﬀerent conditions.

Post-pileup Event

A rejection of post-pileup events is much more complicated because they aremuch rarer than the pre-pileup events and the criteria of the pileup are notso clear. We recorded the charge of the signal tail and the timing of thenext signal, then checked the correlation with the signal height. Although
we could pick up some candidates of post-pileup events, we could not see
whether or not they really disturbed the spectrum.
Again, Flash-ADC data should be useful to identify the post-pileup events.

CHAPTER 4. RESPONSE FUNCTION OF SDDS

52

4.4

Response at Diﬀerent Detection Rates

4.4.1

X-ray Detection Rate

First, we checked the responses at diﬀerent injection rates of x-rays by using
two diﬀerent intensity 55 Fe sources. Typical detection rates were ∼5 Hz and3.2 kHz. Although the detection rate diﬀered by 3 orders of magnitude andthe relative intensities of Ti contamination and Mn Kβ were diﬀerent, we cannot see diﬀerences in the spectral shape around Mn Kα peak (Fig. 4.10). The
fitting results also showed no significant diﬀerence (Table. 4.2). The energy
scale was determined by the Mn Kα and Mn Kβ peaks and the conversion
between an energy and an ADC channel was done via

Counts (arbitrary)

ADC channel = E2ch × energy + Intercept.

104

103

Mn Kα
Mn Kβ

Fe 3 kHzFe 5 Hz
Ti Kα

102

10

1
1000

1200

1400

1600

1800

2000

2200

ADC channel

Figure 4.10: Comparison of the x-ray spectra at diﬀerent incident x-ray rates
normalized by the height of the Mn Kα peak.

CHAPTER 4. RESPONSE FUNCTION OF SDDS

53

Table 4.2: Comparison of the parameters in the response function at thediﬀerent x-ray detection rates.
Parameter
E2ch
Intercept
Mn Kα Gain
Mn Kβ GainTi Kα Gain
Mn Kα FWHM (eV)Mn Kβ FWHM (eV)G
Mn Kα Tail FtailG
Mn Kβ Tail Ftail
Mn Tail βG
Mn Shelf Fshelf−heightG
Mn Esc Fesc

4.4.2

High rate (3.2 kHz)Low rate (5Hz)
value
error
value
error
3.1462.E-01 9.3.E-05 3.1457E-01 6.3.E-06
3.722.E+01 5.5.E-01 3.699E+01 3.8.E-02
7.906.E+06 8.3.E+03 5.647.E+05 2.2.E+03
1.250.E+06 3.5.E+03 1.639.E+05 1.3.E+03
1.828.E+04 5.3.E+02 9.9.E+01 9.2.E+01
146.050.13
146.170.42
155.540.21
155.940.66
2.31.E-02
3.9.E-04
2.05.E-02
1.5.E-03
1.06.E-01
1.8.E-03
8.25.E-02
4.1.E-03
4.54
0.10
4.25
0.36
1.49.E-05
2.5.E-07
1.45.E-05
8.5.E-07
4.05.E-03
8.1.E-05
4.67.E-03
3.1.E-04

Charged Particle Detection Rate

The responses at diﬀerent detection rates of charged particles had investigated by changing electron hit rates from 90 Sr source while an 55 Fe source
position was fixed during the measurement. The electron hit rate was definedby a scaler count of HighT h, which ranged up to 3 kHz. A typical x-ray
detection rate was ∼ 50 Hz.
Because of the existence of the background induced by electrons as the
typical spectra shown in Fig. 4.11, we could not correctly extract all theparameters of response function by the global fitting. To minimize the bias
due to the background shape, local fits around the main peaks and the escapeGpeak of Mn Kα were performed to extract the energy resolution, the T ail Ftail
G. T ail β was fixed in the fitting. The obtained parameters
and the Esc Fesc
are plotted against the detection rate of electrons in Fig. 4.12, which shows
no systematic correlation.

Counts (arbitrary)

CHAPTER 4. RESPONSE FUNCTION OF SDDS

54

Mn Kα

105

Sr 200 Hz
Sr 1 kHzMn K β

Sr 3 kHz

4

10

103

102
800

1000

1200

1400

1600

1800

2000

2200

2400

ADC channel

Figure 4.11: Comparison of the x-ray spectra at the diﬀerent electronbackground rates. Oﬀsets were adjusted by the integral between 2200 and
2800 channel, and the spectra were normalized by the height of the Mn Kαpeak.

CHAPTER 4. RESPONSE FUNCTION OF SDDS

Ka Tail Ratio

Resolution at Mn Kα

152
151

150
149

55

0.04
0.038
0.036
0.034

148

0.032

147

0.03

146
0.028
145
0.026
1440

500

1000 1500 2000 2500 3000

Esc Ratio

X-ray Incident Rate (Hz)05001000 1500 2000 2500 3000

X-ray Incident Rate (Hz)0.00640.00620.006
0.00580.00560.00540.00520.005
0.00480.004605001000 1500 2000 2500 3000

X-ray Incident Rate (Hz)Figure 4.12: Dependence on the 90 Sr electron hit rate.

As we employ the in-situ calibration method, the rate dependence of the
response function make little trouble for us even if it existed. But thesemeasurements guarantee that the parameters obtained in the source measurements can be applied for the spectrum under the beam condition.

CHAPTER 4. RESPONSE FUNCTION OF SDDS

4.5

56

Response to Diﬀerent Incident Angles

Because of the low statistics of kaonic helium x-rays, the parameters of their
response function cannot be determined by themselves. One possible method
to estimate them is an interpolation from the parameters of the calibrationlines. However, the incident-angle distributions of the calibration x-rays andkaonic helium x-rays are completely diﬀerent in E17 as shown in Fig. 4.13.
In this context, the response of SDDs to diﬀerent incident angles are of greatinterest.
The measurement was performed for the incident angle from 0 to 80
degrees. 80 degrees is almost the acceptance limit of SDDs in the housing.
To cover this wide range of incident angle, the SDD housing was tilted by 45
degrees in the test cryostat and the incident angle was changed by the 55 Fe
source position (Figure 4.14).

Figure 4.13: Close up view aroundthe E17 target.

Figure 4.14: Schematic of the setup
for angle measurements.

Counts (arbitrary)

CHAPTER 4. RESPONSE FUNCTION OF SDDS

105

57

Mn Kα

0 degree50 degrees
70 degrees

Mn Kβ

104

103

102
1000

1200

1400

1600

1800

2000

ADC channel

Figure 4.15: Comparison of the x-ray spectra to the diﬀerent incident angle
normalized by the height of the Mn Kα peak.

The typical spectra are shown in Fig. 4.15 and the fitting results withthe response function are plotted in Fig. 4.16. Although the resolutions werestable for wide range of incident angle, significant dependences on incident
GGG
angle were observed for T ail Ftail, Shelf Fshelf−height , Esc Fesc .
A possible explanation of these tendencies is as follows. Almost all Incident x-rays (several keV in our case) are absorbed by the photoelectric eﬀect
in silicon. The generated low-energy photoelectrons distribute mainly in theperpendicular direction to the incident x-rays. In addition, the eﬀective surface become thicker as the incident-angle become larger. Thus, with a larger
incident angle, both electric charges and silicon x-rays are easy to escapefrom the sensitive region, resulting in higher intensities in the components inthe lower energy side of the main peak.
The eﬀect of diﬀerent incident angle to the peak center position ( meanvalue E0 of Gaussian ) will be discussed in the next section.

CHAPTER 4. RESPONSE FUNCTION OF SDDSGKα Tail Ftail

Resolution at Mn Kα

152
151

150

0.065
0.06

0.055

149

0.05

148

0.045

147

0.04

146

0.035

145

0.03

144

0.025

143

0.02

142

0

10

20

30

40

50

60

70

80

90

0

10

0.15

6.5

0.13

6

0.12

5.5

0.11

5

0.1

4.5

10

20

30

40

50

60

70

80

30

40

50

60

70

80

90

7

0.14

0

20

X-ray Incident Angle (degrees)

Tail βG

Kβ Tail Ftail

X-ray Incident Angle (degrees)

0.09

58

4

90

0

10

X-ray Incident Angle (degrees)

20

30

40

50

60

70

80

90

X-ray Incident Angle (degrees)

× 10

0.011

G

Esc FescG

Shelf Fshelf-height

-6

32
30

0.01

0.009

28

0.008
26
0.007
24
0.006
22

0.005

20
18

0.004
0

10

20

30

40

50

60

70

80

90

X-ray Incident Angle (degrees)

0.003

0

10

20

30

40

50

60

70

80

90

X-ray Incident Angle (degrees)

Figure 4.16: Dependence on the incident angle.

CHAPTER 4. RESPONSE FUNCTION OF SDDS

4.6

59

Validity of the Calibration Method“The Calibration Method” includes following elements here.
• Absolute energy calibration by using the characteristic x-rays of titanium and nickel.
• Response function as a fitting function for the x-ray spectrum• Diﬀerent incident-angle eﬀect• Linearity of the whole system
For the study of these things, we obtained the fluorescence x-ray lines oftitanium and nickel induced by 90 Sr electrons in addition to the manganeselines from 55 Fe.
For the two spectra with diﬀerent incident-angle manganese x-rays (0 and
60 degrees), various spectral fittings were performed to evaluate the energy
meas.
of Mn Kα1 peak center (EMnKα1 ) from the interpolated value from the Ti
Kα1 and Ni Kα1 peak positions and their known energies (Table. 3.4). Then,the Mn Kα1 energy deviation was defined by
ref
meas.
∆EM nKα1 = EMnKα1 − EM nKα1
refwhere EMnKα1 is the reference energy in Table 3.4.

Fitting Function and Parameters
As for a fitting function, the response function defined in Sec.4.1 was used forKα1 , Kα2 and Kβ lines of titanium, manganese and nickel. The backgroundwas estimated to be a second order polynomial function. Because the background shape become nontrivial in the low channel, the fitting ranges werelimited and thus Esc peaks for the titanium lines were omitted.
Best Fit
Figure 4.17 shows the fitting spectra which seem to give the most reliable
fitting parameters. They relatively well reproduced the parameters obtainedin Sec. 4.3. Therefore, we set this fitting condition as a standard, andexamined what happens if the fitting condition changed a bit.

CHAPTER 4. RESPONSE FUNCTION OF SDDS

60

Note that χ2 /ndf became bad with higher statistics spectrum (even in
an Fe spectrum with almost no backgound). It might be because the weakcomponents such as the RAE (radiative auger electron) peaks, the satellite
peaks and contaminating x-ray lines revealed their significance. Furthermore,
the response of the SDD is indeed much complicated than our relatively
simple description. However, our goal is to know the energy of the peak
centers which will be clearly observed. Therefore we do not necessarily fit
the whole spectrum well, although the statistical eﬀects from the bad fitting
should be carefully considered.
55

Counts / 8 ch

CHAPTER 4. RESPONSE FUNCTION OF SDDS

105

Ti

Mn

Ni

1500

2000

2500

61

(a)

104

Residual

103

1000
0
-1000
1000

3000

Counts / 8 ch

ADC channel

105

Ti

Mn

Ni

1500

2000

2500

(b)

104

Residual

103

1000
500
0
-500
-1000
1000

3000

ADC channel

Figure 4.17: Obtained spectra for the study of the validity of the calibration
method. (a) 55 Fe: 0 degree, (b) 55 Fe 60 degree. Residuals of the fittings arealso shown with ±2 σ lines.

CHAPTER 4. RESPONSE FUNCTION OF SDDS

62

G
Table 4.3: Obtained parameters by the “Best Fit”. Ni Esc Fesc
was fixed
since the Ni Esc peaks overwrap with Mn Kα peak.

Parameter
E2ch
Intercept
Mn Kα Gain
Mn Kβ GainTi Kα Gain
Ti Kβ GainNi Kα Gain
Ni Kβ Gain
Mn Kα 1Shift
Mn Kβ 1ShiftTi Kβ 1ShiftNi Kβ 1ShiftMn Kα FWHM
Ti Kα FWHM
Ni Kα FWHMG
Mn Kα FtailG
Mn Kβ FtailG
Ti Kα Ftail
G
Ti Kβ FtailG
Ni Kα FtailG
Ni Kβ Ftail
Mn Tail β
Ti Tail β
Ni Tail βG
Mn Shelf Fshelf−heightG
Ti Shelf Fshelf −heightG
Ni Shelf Fshelf−heightG
Mn Esc FescG
Ni Esc Fesc
BG p0
BG p1
BG p2
χ2
NDF

0 degree
value
error
3.03862.E-01 2.4.E-06
2.330.E+01
1.9.E-02
1.053.E+07
1.1.E+04
1.724.E+06
4.9.E+03
3.314.E+06
5.4.E+03
7.894.E+05
2.7.E+03
3.666.E+06
5.8.E+03
6.895.E+05
2.9.E+03-1.79.E-01
1.1.E-01-3.01.E+00
2.1.E-01-1.41.E+00
2.9.E-01-3.81.E+00
3.7.E-01
150.220.12
137.540.21
164.090.20
2.04.E-02
6.8.E-04
1.16.E-01
3.3.E-03
3.31.E-02
1.3.E-03
2.04.E-01
6.2.E-03
3.21.E-02
1.6.E-03
2.42.E-01
1.6.E-02
3.49
0.16
6.30
0.20
10.85
1.22
2.98.E-05
6.4.E-05
1.00.E-09
3.1.E-06
4.06.E-05
8.7.E-07
3.07.E-03
1.6.E-04
3.00.E-03
fixed
3.288.E+03
6.1.E+00
4.53.E-01
1.8.E-03-8.93.E-05
9.1.E-07752.4
244

60 degrees
value
error
3.0423.E-01 1.8.E-05
2.360.E+01 1.1.E-01
4.068.E+06 7.5.E+03
8.023.E+05 5.3.E+03
3.484.E+06 6.7.E+03
8.395.E+05 4.1.E+03
3.716.E+06 6.3.E+03
6.929.E+05 3.7.E+03-3.54.E-01
1.7.E-01-3.89.E+00 4.4.E-01-1.28.E+00 3.4.E-01-3.94.E+00 4.5.E-01
149.170.23
136.560.23
162.690.23
2.84.E-02
2.9.E-03
1.33.E-01
9.3.E-03
3.05.E-02
2.4.E-03
2.10.E-01
2.1.E-02
3.71.E-02
2.7.E-03
2.40.E-01
2.5.E-02
3.95
0.62
7.46
0.86
10.02
1.36
2.82.E-05
6.3.E-05
1.01.E-09
6.5.E-06
4.75.E-05
1.7.E-05
5.87.E-03
5.2.E-04
3.00.E-03
fixed
3.90.E+03
2.3.E+02
7.43.E-02
1.7.E-01-8.35.E-06
3.2.E-05
562.4
244

CHAPTER 4. RESPONSE FUNCTION OF SDDS

63

Asymmetric GaussianCharacteristic x-ray lines are known to have asymmetric shape due to theexistence of satellite lines which resulted from the possible existence of additional holes in the outer shell. The additional holes can be created by the
charged particle hits, thus asymmetric shapes appear for the titanium andnickel lines and not for manganese line.
The asymmetric Gaussian peak made the peak energy ∼ 0.3 eV lower
compared to the symmetric Gaussian case, which is consistent with theMonte Carlo study described in Appendix A. Although the energy deviation became larger for the present spectra, the asymmetric one was adopted
in the following fittings.
Table 4.4: Energy deviations for symmetric and asymmetric Gauss. χ2 /ndf
is represented by the values of 60 degrees (same in the following tables).
∆EM nKα1 (eV)Gaussian
0 degree 60 degrees
Asymmetric
-0.18
-0.35
Symmetric
0.16
-0.02

χ2 /ndf
562.4/244
561.9/244

Treatment of Tail Slope
The energy deviation became significantly larger with common T ail slope β
for all 6 peaks. As the “best fit” implies β depends on the energy, we should
check it.
Individual βs for all 6 peaks gave some unrealistic β values although theenergy deviation and the reduced chi-square became better.

CHAPTER 4. RESPONSE FUNCTION OF SDDS

64

Table 4.5: Diﬀerence in the energy deviations by the treatment of the T ail
slope β.
T ail βTail β
Ti/Mn/Ni
Kα /Kβindividual common
commoncommonindividual individual∆EM nKα1 (eV)
0 degree 60 degrees
-0.18
-0.35
-0.59
-0.76
+0.07
-0.20

χ2 /ndf
562.4/244
580.7/245
554.0/241

Shelf component
It is hard to correctly separate the weak Shelf components from the background. However a treatment of them changed the peak position up to 0.2
eV.
Table 4.6: Diﬀerence in the energy deviations by the treatment of the Shelf
G−5intensity (Fshelf/ 2.5×10−5 for 0 degree−height ) . fixed values were 2.0×10/ 60 degrees.

G
Shelf Fshelf−height

free
0
fixed

∆EM nKα1 (eV)
0 degree 60 degrees
-0.18
-0.35
-0.42
-0.54
-0.34
-0.50

χ2 /ndf
562.4/244
566.5/247
567.1/247

Background Shape
We changed the background shape to a linear one and a constant one. The
diﬀerence of the obtained energy deviation was small ( < 0.1 eV ).

CHAPTER 4. RESPONSE FUNCTION OF SDDS

65

Table 4.7: Diﬀerence in the energy deviation by the background shape.
∆EM nKα1 (eV)
Background 0 degree 60 degrees
pol2
-0.18
-0.35
linear
-0.28-0.37
constant
-0.27
-0.40

χ2 /ndf
562.4/244
562.5/245
563.2/246

Fitting Range
The changes in the upper limit only strengthen the constraint on the background parameters and did not aﬀect the energy deviations. However, thechanges in the lower limit had non-negligible eﬀect to the energy deviation
since the lower limits lay in the structure of titanium peaks.
Table 4.8: Diﬀerence in the energy deviation by the fitting range.

lower limit
1000
1000
1000
1000
900
1200

upper limit
3200
2800
3000
3400
3200
3200

∆EM nKα1 (eV)
0 degree 60 degrees
-0.18
-0.35
-0.20
-0.32
-0.21
-0.35
-0.17
-0.36
-0.28
-0.49
-0.33
-0.45

χ2 /ndf
562.4/244
477.0/194
534.7/219
597.3/269
605.6/256
526.6/219

Eﬀect of Incident Angle and Linearity of the System
The diﬀerence in ∆EM nKα1 between two incident angles was -0.17 ± 0.2(stat.) eV in the best fit condition. Other fittings also coincided with thisvalue within the statistical error. Note that the eﬀect of the incident angle
for the peak position can be evaluated almost independently from the othereﬀects.
However, since the ∆EM nKα1 appears as a mixed eﬀect of all the factor
mentioned in the beginning of this section, it’s diﬃcult to discuss the linearity

CHAPTER 4. RESPONSE FUNCTION OF SDDS

66

of the system alone. What we can say from this study is over all systematic
uncertainty of the energy scale at 6 keV can be controlled conservatively
below 1 eV in our system.
Further studies to check the validity of the energy scale should be donein the final setup.
Energy dependent resolution
From the obtained resolutions of three Kα lines, we checked the energy dependence of the energy resolution described by eq. (4.6) . ω is fixed to 3.81
eV, which is the known experimental value at 77 K although the SDD temperature was at ∼130 K in our measurements. The diﬀerence of ω value dueto the temperature was absorbed to the Fano factor and the white noise.
Three resolutions were well fitted with eq. 4.6 and the obtained parameters are written in Table 4.9. The parameters of two diﬀerent incident-angle
coincided well and the obtained Fano factors were consistent to other experimental values ( F ∼0.12 )Table 4.9: Obtained white noises and Fano factors.
spectrum55
Fe 0 degree55
Fe 60 degree

White Noise
Fano Factor
9.15 ± 0.13 0.1280 ± 0.0016
9.18 ± 0.13 0.1251 ± 0.0016

1

0

Ti Kα

Mn K αResolution in FWHM (eV)Energy Deviation (eV)

CHAPTER 4. RESPONSE FUNCTION OF SDDS

Ni Kα

-1

-2

Ti Kα

Mn K α

-3

170
165

Ni Kα

160
155

Mn Kα

150
145

Ni Kα

0 deg
60 deg

-4

-5
4

67

4.5

5

5.5

0 deg
60 deg

140

Ti Kα

135
6

6.5

7

7.5

8

8.5

9

Energy (keV)

Figure 4.18: Energy deviations of the
x-ray peaks.

130
4

4.5

5

5.5

6

6.5

7

7.5

8

Energy (keV)

Figure 4.19: Energy dependent energy resolution.

Chapter 5
SDD Commissioning with the
Beam
From November 8th midnight to November 11th morning in 2011, we used
about 30-hour beam time for an SDD commissioning at the K1.8BR beamline in the J-PARC hadron experimental facility. The purpose of the beamcommissioning was• To confirm the SDD operation in the real beam condition.
• To investigate yields of characteristic x-rays and signal-to-noise ratio
in the diﬀerent beam intensity.
We observed characteristic x-rays from titanium, iron and nickel foils inducedby the beam.

5.1

J-PARC

5.1.1

J-PARC

J-PARC consists of three proton accelerators, Linac as an injector, 3 GeV
Rapid Cyclotron (RC), and 50 GeV Main Ring (MR). The concept of theaccelerator complex is to utilize secondary particle produced by intense primary proton beam of 1 MW class. RC acts as a booster for MR whileproviding the beam to the Material and Life science Facility (MLF) where
secondary muons and neutrons are used. MR, now operating at 30 GeV,
provides a fast extraction (FX) beam to produce neutrino beam to Kamioka
68CHAPTER 5. SDD COMMISSIONING WITH THE BEAM

69

or a slow extraction (SX) beam to the hadron experimental facility, where
mainly secondary kaons are used for the experiments.
Unfortunately, the accelerators still being in the commissioning stage,available beam intensity is limited especially for the SX beam.

5.1.2

K1.8BR Beamline in the Hadron Experimental
Facility

The K1.8BR beam line, where our experiment is going to be performed, islocated at the north side of the hadron experimental hall. As the nameimplies, we need to share beam with K1.8 beam line. The configuration of
K1.8BR beam line is shown in Fig. 5.1 and its parameters are summarizedin Table. 5.1.
K1.8BR has a rather long length of 31 m from the production target(T1) to the final focus point (FF), where the experimental target will beset. However, a 6-m-long Electrostatic Separator (ESS1), together with Correction Magnets (CM) and vertical slits (IF-V, MS1), has excellent particle
separation power.
Since this beamline is a brand-new one, we are putting many eﬀorts on
beamline tuning. Especially for a stopped -K− experiment, the tuning shouldbe performed carefully, otherwise few kaons stop in the target.
Hardware online triggers for the particles (k, e, π, p) had been establishedand beamline study is well under way on the optics, acceptance of beamline
ESS1 and slits, particle yields against momentum, central momentum of thebeamline and so on. Now we are almost ready to stop kaons for the E17
physics run. A typical in-flight negative kaon yield at 0.9 GeV/c, which will
be adopted momentum for E17, is 8 k/ spill with a primary proton beam
intensity of 1 kW (1.2 × 1012 protons per pulse with a repetition cycle of
6 seconds) using the Pt production target. The stopped kaon number is
expected to be more than two order of magnitude smaller.

CHAPTER 5. SDD COMMISSIONING WITH THE BEAM

70

Figure 5.1: Schematic drawing of K1.8BR beam line in the J-PARC hadronexperimental facility.

Table 5.1: Parameters of K1.8BR beam line as of November, 2010.
Primary beam
Repetition cycle
Flat Top
Spill Length
Production target
Beam Length (T1-FF)
Momentum range
Acceptance
Momentum bite

30 GeV/c proton
6 sec
2.93 sec
2.1 secPt(50% loss)/Ni(30% loss)
31.1 m
1.1 GeV/c max.
2.6 msr · %±3%

CHAPTER 5. SDD COMMISSIONING WITH THE BEAM

5.2

Setup

5.2.1

Beamline Detectors

71

At the down stream of the D5 magnet, a beam was detected by the T0 counterand Defining counter (Define) together with tracking information provided by
the beamline drift chambers (BLC1 and BLC2). Although Lucite Cherenkov
counters (LC2) are set for an online particle identification, they were notused for the present commissioning.

Figure 5.2: Side view of the detector alignment downstream the D5 magnet.

T0 counter
The T0 counter consists of 5 segmented scintillator hodoscopes. Each segment has 16 cm (vertical) × 3.2 cm (horizontal) eﬀective area with a thicknessof 1 cm. Two PMTs, HAMAMATSU 6612B, with three-stage boosters aremounted on the both ends of the each scintillator. The T0 counter was used
to determine the timings of beam triggers.

CHAPTER 5. SDD COMMISSIONING WITH THE BEAM

72

Figure 5.3: T0 counter.

Defining CounterTo suppress the trigger rate, we prepared an additional beam defining counterjust in front of the target chamber. The plastic scintillator (BC420) is 1 cm
thick and has the size of 12 cm (vertical) × 12 cm (horizontal), which just covered the foil positions inside the target chamber. One PMT, HAMAMATSU
6612B with three-stage boosters is attached on it.

CHAPTER 5. SDD COMMISSIONING WITH THE BEAM

73

Figure 5.4: Defining Counter.

Beam Line Drift Chamber
BLC1 and BLC2 are planner drift chambers consisted of 8 layers (xx’yy’xx’yy’).
The detailed description of BLCs is omitted here since their information is
not used for the present analysis.

5.2.2

SDD & Liquid-3 He Target System

8 SDDs and corresponding 8 preamplifiers were installed to the target chamber as illustrated in Fig. 5.5. They were cooled by liquid nitrogen andtemperatures were controlled with the similar method described in Chapter
3.
The liquid-3 He target was not installed and an iron foil was set instead,in addition to titanium and nickel foils which were located the same position
as in the physics run.

CHAPTER 5. SDD COMMISSIONING WITH THE BEAM

74

Figure 5.5: Front and side views of the SDD & liquid-3 He target system.

5.2.3

Trigger Scheme & Data Acquisition

An SDD trigger was defined as (Fig. 3.4 (c))
SDD = LowT h ⊗ Reset ⊗ HighT h
and a BEAM trigger as
BEAM = Def ine ⊗ T 0retiming
whose timing was determined by the T0 counter.
Then the master trigger was defined as
SDDOR ⊗ BEAM + SDDself (SDDOR)
As is the case of the measurement in the test cryostat, we constructed
TKO based data acquisition system including two major upgrades. One was
the introduction of a second level trigger scheme and the other one was anadditional DAQ system to use VME modules.

CHAPTER 5. SDD COMMISSIONING WITH THE BEAM

75

Second Level Trigger Scheme
Since SDD responses are very slow ( 1 µs), they are not in time to make gates
for the signals of the fast detecters in the beam line (scintillation counters,
drift chambers). Therefore, we need to make gates for the beam line detectors
by BEAM triggers. Then, if SDDOR comes (doesn’t come) within a certain
time, the event is accepted (rejected) by using the VME-SMP functionality.
The second level trigger circuit is shown in Fig. 5.6 and the settings for thegate and delay generators are listed in Table 5.2. Typical dead times of DAQ
system for an accepted event and a rejected event were 690 µs and 5 µs,
respectively.

BEAM

SDDOR

Gate&Delay 1

SMP busy

VME busy

Gate for beam-line counters

Gate for
Drift Chambers

TDC start (T0 timing)

Gate&
Delay 2

retiming

Gate&Delay 9

Gate&Delay 10

Figure 5.6: Second level trigger circuit

Gate&Delay 4

Gate&Delay 3

Gate&Delay 5

30 ns

Gate&
Delay 7

Gate&Delay 12

Gate&Delay 6

Gate&Delay 8

Gate&
Delay 11

SMP Reject

SMP Accept

VME DAQ trigger

TDC start(SDD timing)

Gate for XOUT

Gate for
OUT&FOUT

CHAPTER 5. SDD COMMISSIONING WITH THE BEAM76

CHAPTER 5. SDD COMMISSIONING WITH THE BEAM

77

Table 5.2: Settings for the gate and delay generators in the second level
trigger circuit.
Number
1
2
3
4
5
6
7
8
9
10
11
12
13

Delay
Width Description
Through 3.3 µs wait for second level decision
Through 2.0 µs timing gate for second level decision
440 ns 1.52 µs gete for beam line chambers
220 ns 1.45 µs gate for beam line chambers
510 ns
30 ns delay
390µs
80 ns wait for conversion
Through 430 µs conversion veto
Through 130 ns TDC start
2.18 µs
40 ns rejectThrough 2.2 µs reject veto
Through 5.3 µs ADC gate for SDD OUT&FOUT
Through 2.1 µs ADC gate for SDD XOUT
1.2 µs390 ns delay

Table 5.3: Thresholds of the discriminators and veto widths for the SDD
trigger circuit.

SDD #
1
2
3
4
5
6
7
8

Discriminator Vth (mV) Veto Width (µs)
LowTh
HighThReset HighTh
150.5
810
600
200
150.4
807
500
220
148.8
806
480
210
149.7
796
400
200
150.2
802
400
420
151.0
805
500
200
149.8
805
500
220
149.4
797
800
200

CHAPTER 5. SDD COMMISSIONING WITH THE BEAM

78

VME DAQ System
A VME DAQ system was prepared for a Flash ADC module and a Peak Hold
ADC module which has a better linearity than the TKO PHADC module.
These data were recorded in a separated file from the TKO data. Both TKO
and VME data contained a spill number and an event ID distributed bya Master Trigger Module, which made it possible to synchronize two data
oﬄine.
The whole scheme of the data acquisition system is shown in Fig 5.7.
Beam-line & SDD signals

Spill Number
event IDTKO

Master Trigger Module(NIM module)

Scaler Signals

SDD Signals

VME
VME

PC

TKO DAQPC

VME DAQ

Figure 5.7: DAQ scheme in the SDD beam commissioning.

CHAPTER 5. SDD COMMISSIONING WITH THE BEAM

5.2.4

79

Experimental Condition

SDD Temperatures
All 8 SDDs showed similar behavior during the 3 days (Figure 5.8 (a)). They
were kept at 132 ∼ 137 K with stabilities below 2 K. The gain diﬀerence dueto these temperature changes were expected to be ∼ 1 eV (Sec. 3.4), whichwere compensated by the in-situ calibration anyway.
Preamplifier Temperatures
As for preamplifiers, some of them showed strange behavior (Figure 5.8 (b)).
Temperatures of preamplifier #2 and #3 dropped when accelerator accidentally stopped. These phenomena implied that the ramped output from thepreamplifier disappeared due to the low detection rate. We don’t know, however, why these phenomena happened only to specific modules. Anyway, weobserved no eﬀect to the resolutions and the gain stabilities. The temperature sensor for preamplifier #7 was not available due to a problem in theread-out line.
However the temperatures of 7 preamplifiers ranged as large as 30 K,
all of them were in the optimal region. The stabilities of each preamplifier
temperature were satisfactory ( ∼ 1 K ).

SDD Rod Temperature [K]CHAPTER 5. SDD COMMISSIONING WITH THE BEAM

80

140
139
138

SDD 1
SDD 2
SDD 3
SDD 4

SDD 5
SDD 6
SDD 7
SDD 8

137
136
135
134
133
132
131
130

08th/00

08th/1209th/00

09th/12

10th/00

10th/12Preamp Temperature [K]Time (Day/Hour)
330

320

Preamp 1
Preamp 2
Preamp 3
Preamp 4

Preamp 5
Preamp 6
Preamp 8

310

300

290

280
08th/00

08th/1209th/00

09th/12

10th/00

10th/12

Time (Day/Hour)

Figure 5.8: (a) SDD temperatures and (b) preamplifier temperatures during
the beam time. Hatched areas indicate that the beam was oﬀ in those periods,
when We put 90 Sr source instead.

CHAPTER 5. SDD COMMISSIONING WITH THE BEAM

5.3

81

Data Summary

We used -0.9 GeV/c kaon-tuned beam ( ESS1 voltage = ± 200 kV ). Various
conditions in terms of the hit rates on the Defining counter were realized bychanging the IF-V slit width. We obtained the data with hit rates from 40
kilo to 1.4 mega hits per spill.
In addition to the beam rate study, we narrowed the HighT h veto widths
for the study of pileup with FADC data in the condition #9, 12, 13, andchanged beam direction on purpose to directly hit on the SDD for the study ofthe background origin in the condition #6, 7. These data were not analyzed
in this thesis.
The recorded data for each event are listed in Table 5.4 and a data summary for each condition is described in Table 5.5. Scaler values of each SDD
discriminator for each condition are plotted in Fig 5.9.
Table 5.4: Obtained data in the beam commissioning.

moduleremarkTKO PHADC Signal Hight
OUT (3.0 µs)
VME PHADC Signal HightVME FADC
Wave form analysis
FOUT
TKO PHADC Correlation cut with OUT
XOUT
TKO PHADC Baseline information
OUT (0.2 µs)
TKO TDCSDDOR start
TKO TDCT0 start
Reset Timing
TKO TDCSDDOR start
HighTh Timing
TKO TDCSDDOR start
Define Timing
TKO TDCSDDOR startT0 Timing
TKO TDCSDDOR startFirst level Timing TKO TDC
SDDOR start, identify SDDself trigger
beamline counters TKO
PID by TOF etc...
beamline chambers TKO
track information
Scaler counts
VME
LowTh, HighTh, Reset, DAQ info etc...

Nov.
9∼10

Date
Nov.
8
Nov.
8∼9

1434
1434

0.4
0.4

Duration Define rate
Beam
( k/spill )intencity (hours)
2.9 kW
2.9
443
2.9
100
3.15 kW
2.1
399
2.8
106
0.7
1006
0.6
495
0.6
303
3.55 kW
1.2
427
1.0
423
1.8
47
2.9
431

3.5

3.9
7.0

7.3

Yield (k counts)
Ti Kα Ni Kα
13.5
21.1
2.6
3.6
7.8
11.3
2.1
4.5
5.3
9.5
3.5
2.3
2.2
2.0
4.6
6.7
3.9
5.8
0.9
1.2
11.8
16.8
SDDself only
HighT h width 1/10
SDDself only
HighT h width 1/100

HighT h width 1/10

SDDself only
D5 +45 (direct hit)D5 -60 (direct hit)

remarkTable 5.5: Data summary of the SDD beam commissioning.

13

12

condition
#
1
2
3
4
5
6
7
8
9
10
11

CHAPTER 5. SDD COMMISSIONING WITH THE BEAM
82

LowTh / spill

CHAPTER 5. SDD COMMISSIONING WITH THE BEAM

83

3500
SDD 1
SDD 2
SDD 3
SDD 4

3000
2500

SDD 5
SDD 6
SDD 7
SDD 8

2000
1500
1000
500
0

0

2

4

6

8

10

12

14

HighTh / spill

Condition Number

SDD 1
SDD 2
SDD 3
SDD 4

1400
1200

SDD 5
SDD 6
SDD 7
SDD 8

1000
800
600
400
200
0

0

2

4

6

8

10

12

14

Reset / spill

Condition Number
1200
SDD 1
SDD 2
SDD 3
SDD 4

1000

SDD 5
SDD 6
SDD 7
SDD 8

800

600

400

200

0

0

2

4

6

8

10

12

14

Condition Number

Figure 5.9: Scaler counts of each discriminator for each SDD.

CHAPTER 5. SDD COMMISSIONING WITH THE BEAM

5.4

Analysis

5.4.1

Cut Condition84

To reduce the pileup events, cross-talk events and other irregular signals, weapplied following cuts for all the data.
• Single hit event selection• Baseline cut by 3 Gaussian σ• OUT-FOUT correlation cut• Reset-followed event cut• HighTh-followed event cut

± 5 ch103

85

CountsCountsCHAPTER 5. SDD COMMISSIONING WITH THE BEAM

3σ cut

102
102

10
10

1

1
500 1000 1500 2000 2500 3000 3500 4000
SDD TDC (SDD start) [ch]0

SDD FOUT Correration Function

SDD FOUT ADC[ch]

0

250

200

150

100

500 1000 1500 2000 2500 3000 3500 4000
SDD Delayed XOUT (baseline) [ch]

100

50
± 10
0

-50

50
-100
0
0

500 1000 1500 2000 2500 3000 3500 4000
SDD OUT ADC[ch]0500 1000 1500 2000 2500 3000 3500 4000
SDD OUT ADC[ch]Figure 5.10: Common cut conditions. (a) select the events which madethe triggers, (b) baseline cut, (c) OUT-FOUT correlation, (d) OUT-FOUT
correlation cut.

5.4.2

Spectral Fitting

After applying the common cut conditions, gains of 8 SDDs were roughly
adjusted. Then summed up spectra of 8 SDDs were studied.
First, we checked the typical energy resolution in the beam commissioning. A summed spectrum of condition #3 was fitted by response functionsfor 6 x-ray lines and a second order polynomial background. As for response
functions, only Gauss and T ail components were included.

CHAPTER 5. SDD COMMISSIONING WITH THE BEAM

86

Counts / 25 eV

The spectrum and the result of the fitting is shown in Fig. 5.11 and Fig.
5.12. The resolution at Kaonic 3 He Lα energy was estimated to be better
than 150 eV from the obtained resolutions of 3 Kα peaks. Thus, a successful
operation of all 8 SDDs in a realistic beam condition was confirmed. However,the peak position of the Fe Kα could not be correctly reproduced from thetitanium and nickel peaks so far.

1400
1200

Ni Kα
Ti Kα

1000
Fe Kα

800
600
400

Fe Kβ

Ni Kβ

7000

8000
9000
Energy (eV)200
Residual

0
100
50
0
-50
-100
4000

5000

6000

Figure 5.11: Typical spectrum in the beam commissioning (condition #3).
χ2 /ndf = 161.2/176.

165
160
155

Noise: 10.09 ± 1.14
Fano: 0.103 ± 0.014
Ni Kα

150
Fe Kα

145

Peak position deviation(eV)Resolution FWHM (eV)

CHAPTER 5. SDD COMMISSIONING WITH THE BEAM

5
0

-10

135

-15

130

Ti Kα

125
4

4.5

Fe Kα
Ti Kα

-5

140

87

Ni Kα

Ti Kβ
Ni Kβ

Fe Kβ

-20
5

5.5

6

6.5

7

7.5

8 8.5 9Energy(keV)

4.5

5

5.5

6

6.5

7

7.5 8 8.5
Energy(keV)

Figure 5.12: (a) Energy resolutions obtained in the fitting. (b) Energy deviations from the energy scale calibrated by Ti and Ni Kα1 peaks.

5.4.3

Characteristic X-ray Yields

Then we tried fittings for each condition to see the diﬀerence of the characteristic x-ray yields and the signal-to-noise ratio. In these fittings we used
only Gauss for the response functions.
The yields were defined by the Gaussian area. Figure 5.13 shows theyields dependence on the beam rate. Condition # 1, 2, 3, 4, 5, 8, 10 and 11
were plotted here since the conditions of these runs diﬀer only in the hit rateon the Defining counter controlled by the opening width of IF-V slit.
We can see linear dependences of the x-ray yields on the beam rate as
naively expected. From the linear fitting of these points, the yields are evaluated to be• ∼900 Ti Kα / hour / 100 k beam on the Defining counter• ∼1400 Ni Kα / hour / 100 k beam on the Defining counterX-ray yield / hour /8 SDDs

CHAPTER 5. SDD COMMISSIONING WITH THE BEAM

88

20000
18000
16000
14000

Ti Kα Yield / hour
Ni Kα Yield / hour

12000
10000
8000
6000
4000
2000
0
0

200

400

600

800

1000

Hit rate on Defining Counter (k hits/spill)

Figure 5.13: Characteristic x-ray yields at the diﬀerent beam rates.

5.4.4

Signal to Noise Ratio

Without a calculation, we could see the improvement of the signal-to-noise
ratio in calibration spectrum compared to E570 (Figure 5.14). It may due
to the improvement of the K/π ratio of the beam or the detector geometry.
However, we can not directly compare to the E570 result since we had notinstalled the degrader and the target in the commissioning. In-flight reactions
with them are expected to increase high-energy γ-ray background.
As for the rate dependency, we only observed a small diﬀerence for thewide range of the beam rate (Figure 5.15). Here we defined the signal-to-noise
ratio asTiKα Gauss Gain
SN = ∫ TiKmean +TiKFWHMαα
pol1(E) dE
TiKmean−TiKFWHM
α
α

(5.1)

But it does not mean the same holds for the “kaonic x-ray spectrum”, whose
signal-to-noise ratio is expected to have strong dependence on the stoppedK− /other particles ratio of the beam.

CHAPTER 5. SDD COMMISSIONING WITH THE BEAMCounts (Arbitrary)

Summed energy spectrum of 8 SDDs

KEK E570 [16]400k beam/spill
100k beam/spill

Ni-Kα

Ti-Kα
Fe-Kα

Ti-Kβ

2000

3000

4000

5000

Fe-Kβ

6000

7000

Ni-Kβ

8000

9000 10000
Energy (eV)

Signal to Noise ratio at Ti KαFigure 5.14: Comparison with the E570 calibration spectrum.

7
6.5
6
5.5
5
4.5
4
3.5
3
0

200

400

600

800

1000

Hit rate on Defining Counter (k hits/spill)

Figure 5.15: Signal-to-noise ratio at the diﬀerent beam rates.

89

Chapter 6
Conclusion
First, we searched the optimal operational condition within the experimental
requirements; SDDs at low temperatures and their preamplifiers also in thevacuum. After optimizing the bias voltages, the temperature behaviors were
investigated in terms of the energy resolution, time resolution, and the deadtime. We found 130 K and over 270 K were optimal for the SDDs andpreamplifiers, respectively, in which condition the energy resolution at 6 keV
was ∼ 150 eV in FWHM and the time resolution was ∼ 500 ns in FWHM.
Next, we succeeded in rejecting pileup events caused by the charged particle hits, which will significantly contribute to reduce the systematic errorin E17 and enabled us to study further systematic eﬀect on the response
function of the SDD. Although we found no dependence of the response
function on the detection rate, there was a significant dependence on the incident angle. It should be properly considered in E17 since the incident-angle
distributions are completely diﬀerent for the kaonic helium x-rays and thecharacteristic x-rays for the energy calibration.
Then, the validity of the energy scale calibrated by the characteristic xrays of titanium and nickel was studied. The Mn Kα energy was reproducedwith a deviation below 1 eV from the reference value including the incidentangle eﬀect.
Finally, we performed the commissioning with the beam. All 8 SDDs
were worked properly with a good energy resolution ( < 150 eV in FWHM
at 6 keV ). The beam commissioning also revealed that the background level
was smaller than KEK E570. However it may partly due to the absence ofthe degrader and the target.
Toward the physics data taking, which is expected to be performed in JFY
90

CHAPTER 6. CONCLUSION

91

2011, we need further studies in the final setup especially on the linearity ofthe energy scale and the longterm stability.

Acknowledgement
First of all, I would like to express my sincere gratitude to my supervisor,
Prof. R. S. Hayano, who introduced me this interesting field of physics. He
gave me continuous support and valuable advice throughout my work andlearning in these two years.
I am grateful to Dr. H. Outa and Dr. T. Suzuki, under whom I started
my experimental carrier with beamline works. Their great knowledge about
the experimental techniques always impressed me and I learned a lot fromthem.
I would like to thank Dr. M. Sato and Dr. M. Iio with sincere respect.
We have always worked together at Tsukuba and Tokai. Dr. M. Sato taught
me how to deal the x-ray detectors, and also the researching attitude andprocedure with deeds as well as words. This work owes so much to them.
Dr. M. Iio taught me many things about the cryogenic physics and often
encouraged me with the warmest words.
I am grateful to Dr. S. Ishimoto, who helped us as a cryogenic specialist.
He also kindly took us to lunch so many times at Tsukuba.
I also acknowledge Prof. E. Widmann, Dr. J. Zmeskal, Dr. T. Ishiwatariand Ms. B. K. Wunschek, who arranged the x-ray detectors and sometimes
joined the work at Japan.
I would like to express my best regards to all the other collaborators of JPARC E17 experiment for their helps and advices. I hope that our powerfulcollaboration will end up with a great success of the experiment.
Lastly, I would like to express my gratitude to all the people who supported and encouraged me, including the members of the nuclear experimentgroup at Hongo, my friends and my family.

92

Appendix

93Appendix A
Asymmetry in Characteristic
X-ray Lines
Since we calibrate the energy scale by using Ni and Ti Kα lines, the eﬀect of
the natural line shapes of them to the resulting peak positions in the fitting
is of great interest.
Asymmetry due to the satellite lines
Kα x-rays are emitted when a K shell vacancy is filled with a L shell electron( 2p → 1s ), and the fine structure due to the spin-obit coupling separates
them to two lines ( Kα1 : 2p 3 → 1s, Kα2 : 2p 1 → 1s ). Furthermore, the real22
spectra have much more satellite multiplets due to the additional vacancies
in the outer shell, which make the peak shape asymmetric. As for the Kαlines of 3d transition metals, the peak shapes can be approximated by using
5 or 6 Lorentzian peaks as shown in Fig. A.1 and Fig. A.2 [28, 29].
In our measurements, Ti and Ni Kα lines were considered to be suﬀeredfrom such eﬀect since they were induced by the electrons which could create
additional vacancies in the outer shell. On the other hand, Mn Kα line whichcame from the 55 Fe source were considered to be simply represented by thesummation of two symmetric lines.

94

APPENDIX A. ASYMMETRY IN CHARACTERISTIC X-RAY LINES 95

Ti

Kα1
Kα2

Figure A.1: Measured Ti Kα line
shape [28].

Figure A.2: Measured Ni Kα line
shape [29].

Eﬀect to the fitting result [30]We generated Kα lines with satellite lines like Fig. A.3 and smeared it with
the SDD energy resolution as shown in Fig. A.4. The parameters used togenerate the original line shape are listed in Table A.1. Then the smeared
spectra were fitted with asymmetric and symmetric Gaussians, where thesymmetric Gaussian was the summation of the two Gaussians with the meanvalue of Kα1 and Kα2 , and the asymmetric one was the summation of 5 or 6
Gaussians with the mean values given in Table A.1. Intensity ratios for theeach Gaussian were fixed.
The resulting energy deviations are plotted in Fig. A.5, where the energy
deviation ∆E is defined by∆E = Ef it − Eorg .
Ef it and Eorg are the values obtained in the fitting and the energy originallyused to generate the spectrum.
Considering that the Mn Kα can be represented by the asymmetric Gaussian, our study indicates Mn Kα energy become ∼ 0.3 eV larger when wecalibrated the energy scale by using asymmetric Gaussian for Ti and Ni
peaks. Thus, the asymmetric Gaussians should be used for the Ti and Ni
fluorescence x-ray peaks.

APPENDIX A. ASYMMETRY IN CHARACTERISTIC X-RAY LINES 96

Ni

Kα1

Kα2

Figure A.3: Generated line shape ofNi Kα with satellite peaks.

Ti

Figure A.4: The generated spectrum
was smeared by the detector resolution.

Mn

Niasymmetricsymmetric

Figure A.5: Energy deviations between the fitting results and the values used
to generate the spectra.

APPENDIX A. ASYMMETRY IN CHARACTERISTIC X-RAY LINES 97

Table A.1: Parameters used to generate the spectrum with satellite lines.
Element peak
Ti
α11
α12
α13
α15
α21
α21
Ni
α11
α12
α21
α22
α23

mean(eV)4510.901
4509.940
4507.757
4513.975
4504.911
4503.092
7478.281
7476.529
7461.131
7459.874
7458.029

width (eV)
1.36
2.21
3.74
1.70
1.88
4.48
2.013
4.711
2.674
3.039
4.476

Intensity (a.u)
236480
51208
31099
8831
143370
8073
0.487
0.171
0.250
0.064
0.028

Reference
[28]

[29]

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