1. Introduction to the pb Experiment

The Pion Beta Decay Experiment:

Calibrations and Developments

INAUGURAL-DISSERTATION

ZUR

ERLANGUNG DER PHILOSOPHISCHEN DOKTORWÜRDE

VORGELEGT DER

PHILOSOPHISCHEN FAKULTÄT II

DER

UNIVERSITÄT ZÜRICH

VON

CHRISTIAN BRÖNNIMANN

AUS ZIMMERWALD

BEGUTACHTET VON

Prof. Dr. Roland E. Engfer

ZÜRICH 1996

Die vorliegende Arbeit wurde von der Philosophischen Fakultät II der Universität Zürich auf Antrag von Prof. Dr. Roland E. Engfer als Inaugural-Dissertation angenommen.

Für Barbara, David, Tabea und Julian

Abstract

The pion beta decay

is one of the fundamental semileptonic weak-interacting processes. A precise determination of the pion beta decay rate provides a stringent test of the unitarity of the Cabbibo-Kobayashi-Maskava (CKM) mixing matrix. A failure of the test could signal extensions to the standard model of the electro-weak interactions. The existing discrepancy between superallowed Fermi decay and neutron beta decay, as well as the level of accuracy of the previous experiments call for a re-measurement of the pion beta-decay rate. The experimental difficulty in determining the beta-decay rate of the charged pion originates from the very small branching ratio of 10-8.

A new precision experiment is in progress at the Paul Scherrer Institute (PSI) in Switzerland. The essential part of the detector is a calorimeter consisting of crystals made of pure Cesium Iodide (CsI). The CsI-crystals have good energy resolution and high rate capability.

Special test methods were developed to measure the properties of the pure CsI-crystals. The response of the crystals to 70MeV positrons and photons was measured and a difference in energy resolution for the two particle types was observed. The resulting low energy tail of the response agrees with Monte Carlo simulations of the electromagnetic showers in the crystals.

In order to perform the experiment at the desired beam rate, efficient background suppression is essential. Therefore, a waveform digitizing system is being developed, based on a fast analog memory fabricated in CMOS technology, the Domino Sampling Chip DSC. It allows waveform digitizing of the signals from the pure CsI crystals with a frequency of 800MHz. A comparison of the waveform digitizing system to commercial electronic modules proves the distinct advantages for the pion beta experiment by implementing the DSC.

Zusammenfassung

Der Pion-Beta-Zerfall

ist einer der fundamentalen semi-leptonischen Prozesse der schwachen Wechselwirkung. Die präzise Bestimmung der Pion-Beta-Zerfallsrate erlaubt einen genauen Test der Unitarität der Cabbibo-Kobayashi-Maskawa (CKM) Matrix. Eine mögliche Abweichung von der Unitarität würde Erweiterungen des Standard-Modells der elektro-schwachen Wechselwirkung signalisieren. Die Diskrepanz zwischen übererlaubten Fermi-Zerfällen und dem Zerfall des Neutrons, sowie die Präzision der bisherigen Messungen erfordern eine Neumessung der Pion-Beta-Zerfallsrate. Die experimentelle Schwierigkeit in der präzisen Bestimmung der Zerfallsrate liegt im sehr kleinen Verzweigungsverhältnis von 10-8 des Beta-Zerfalls des geladenen Pions begründet.

Ein neues Experiment wird am Paul-Scherrer-Institut PSI durchgeführt. Das Herzstück des Detektors ist ein Kalorimeter, welches aus Kristallen reinen Cäsium-Iodids (CsI) besteht. Die CsI-Kristalle produzieren sehr schnelles Szintillations-Licht und besitzen eine gute Energieauflösung.

Spezielle Methoden sind entwickelt worden, um die Eigenschaften der CsI-Kristalle zu messen. Die Energieauflösung der Kristalle für 70MeV Positronen und Photonen wurde gemessen und eine Differenz wurde für diese beiden Teilchensorten beobachtet. Das experimentelle Resultat für den nieder-energetischen Anteil der Linienform stimmt mit der Monte-Carlo-Simulation der elektromagnetischen Schauer in den Kristallen überein.

Um das Experiment mit der gewünschten Strahlrate durchführen zu können, sind effiziente Untergrund-Unterdrückungsmethoden notwendig. Zu diesem Zweck wurde ein System zur Digitalisierung von analogen Signalen entwickelt, welches auf dem Domino Sampling Chip (DSC) basiert, einem in CMOS-Technologie hergestellten schnellen analogen Speicher. Es erlaubt die Digitalisierung der analogen Signale der CsI-Kristalle mit einer Frequenz von 800MHz. Ein Vergleich des Systems mit kommerziellen Elektronikmodulen beweist die Vorteile, die dem Pion-Beta-Experiment bei der Verwendung der DSCs erwachsen.

Table of Contents

1

1. Introduction

2. Motivation3

3. Rare Pion-Decay Experiments9

3.1 Pion Beta Decay Experiments10

3.1.1 Pion Beta Decay at Rest11

3.1.2 Decay in Flight15

3.2 Pion Decay into Positron and Neutrino16

4. The Pion Beta Experiment at PSI21

4.1 Experimental Technique21

4.2 Apparatus22

4.3 Pion Beam and Beam Monitoring Detectors25

4.3.1 Beam Line25

4.3.2 Beam Studies with the Active Target29

4.4 Shower Calorimeter32

4.5 Trigger and Electronics34

5. Properties and Performance of the Pure CsI Crystals39

5.1 General Properties40

5.2 Determination of the Fast/Total Ratio40

5.3 Distance Measurements44

5.4 Photoelectron Statistics49

5.5 Light Collection Non-Uniformity52

5.6 CsI-Crystal Data Base58

5.7 Simulated Photon and Positron Response of the CsI-Crystals59

6. Calibration with Photons67

6.1 Method of the Calibration67

6.2 Experimental Apparatus70

6.3 Analysis of the Data74

6.3.1 Neutron TDC Spectrum74

6.3.2 Normalization75

6.3.3 Pedestal and Noise Calculation76

6.3.4 Temperature Correction and Gain Matching78

6.4 Results and Discussion81

6.4.1 Experimental Result81

6.4.2 Comparison of Data and Simulation83

6.4.3 Outlook86

7. The Domino Sampling Chip DSC89

7.1 Introduction89

7.2 System Description90

7.2.1 Operation of the Domino Sampling Chip90

7.2.2 Zero Suppression92

7.2.3 The Motherboard DSM10093

7.3 Performance of the DSCs95

7.3.1 Test Set-Up95

7.3.2 Pedestal Subtraction96

7.3.3 Sampling Speed Calibration98

7.3.4 Timing Linearity and Resolution101

7.3.5 Amplitude Linearity104

7.3.6 Sampling of CsI-Pulses106

7.4 Summary and Discussion106

7.5 Outlook109

8. Conclusion111

Bibliography109

List of Figures111

List of Tables115

Acknowledgements117

1. Introduction

The aim of this work is to present the new precision experiment to determine the pion beta decay rate taking place at the Paul Scherrer Institute (PSI). As the experiment is still in its early stage the motivation for the experiment, the description of calibration measurements and new developments are the main subjects of this thesis, which is thus divided into 3 parts.

The subject of part I (chapters 2-4) is the proposed pion beta decay experiment (pibeta experiment) at PSI. The theoretical motivation for a new precision measurement is given chapter 2.

Chapter 3 discusses related rare pion‑decay experiments in order to understand the expected experimental difficulties. These experiments used the stopped pion technique, where the decay products were detected by inorganic scintillators. The scintillators had excellent energy resolution but a relatively slow light output. In order to avoid background from pile-up events, pions were stopped at low rates (~104 /s). It will be shown, that the low energy tail corrections of the scintillator response dominated the systematic uncertainties of these experiments.

In chapter 4 the experimental technique, the design of the detector and its components are presented. Due to the very small branching ratio of the pion beta decay, the new experiment needs to be performed at high beam-stopping rates. The essential part of the detector is an electromagnetic shower calorimeter, consisting of pure CsI crystals. It detects the two photons from the decay of the 0 and the positron from the decay (ee; the photons and the positron from these decays have both an energy of about 70 MeV. The calorimeter requires the detection of these particles with good energy resolution and the capability of handling high event rates. Experimental tests with a particle beam show that the proposed beam rates and contaminations can be handled.

In part II (chapter 5 and 6) the performance of the pure CsI crystals are discussed. The crystals need to meet very stringent requirements. In chapter 5 special methods are described, which serve to determine the properties of the crystals. The obtained results are used as parameters in a Monte-Carlo-Simulation for the calorimeter response to 70 MeV positrons and photons.

A calibration measurement with 70 MeV photons from the reaction ‑p(0n was performed with about 10% of the calorimeter modules. The method and the obtained results are presented in chapter 6.

New developments for the pion beta experiment are the subject of part III (chapter 7). A fast analog memory, the Domino Sampling Chip (DSC), has been tested and improved in the last two years. The DSC is capable of digitizing analog signals with frequencies from 100 to 800 MHz. In order to use the DSC for the pion beta experiment, an electronic module hosting several DSCs needs to be designed. The performance of the prototype module, hosting 6 DSCs, is compared to commercial ADCs and TDCs.

2. Motivation

In the last 50 years of the history of particle physics, the decays of the pion have been the subject of intense theoretical and experimental research activities. For example the decay

(2.1)

was first discovered in 1958 and provided a confirmation of the V-A theory of weak interactions. Pion decays are weak processes which are theoretically calculable with high precision. In order to provide experimental information about pions three pion production facilities have been built worldwide, LAMPF (Los Alamos Meson Production Facility), TRIUMF (Tri-University Meson Facility), and one facility at PSI (Paul Scherrer Insitute), which produce pion beams of high intensities at low momenta.

Pions are spin zero bosons with negative parity; they form an isospin one multiplet with

,

(2.2)

where I3 is the third component of the isospin I. The charged pion has an average lifetime of ( 26.03 ns; its most probable decay mode is

,(2.3)

with an average decay rate of

.

The process called pion beta decay is the decay

,(2.4)

with a -meson and two leptons in the final state, thus a so called semileptonic decay. Since the pion beta decay is a transition between two members of an isospin triplet (2.2) it is analogous to super-allowed Fermi transitions in nuclear beta decay with

,(2.5)

J denoting spin J and parity . At present, there are nine precise measurements of nuclear beta decay (a compilation is given in [Tow 95a]); one of them is the decay 14O to the first excited state of 14N [Cla 73]. The total decay energy of 14O is EF = 2.32 MeV and the decay rate is F=0.00971/s. A rough estimation on the pion beta decay rate is obtained from the fifth-power law for beta decays

.(2.6)

With

one gets ( 0.3/s, which leads to the very small branching ratio

.(2.7)

Super-allowed Fermi transitions are pure vector interactions, since the axial vector contributions to the matrix elements of the transitions vanish due to spin and parity of initial and final states (Eq. 2.5). Experimental measurements of different super-allowed Fermi transitions show, that the product ft of the Fermi integral function f and the decay half life t is constant. This is explained by the CVC-Hypothesis, which postulates the conservation of the weak vector current. Following the CVC-Hypothesis, the ft values for super-allowed Fermi transitions are given by

,(2.8)

where K is a product of fundamental constants (K = 8.1201(10-7). The uncorrected matrix element MF for transitions which fulfill (2.5) is

(2.9)

and the vector coupling constant GV can be expressed by

.(2.10)

The Fermi coupling constant G of pure leptonic decays like

is known with high precision from + mean life measurements. Vud is an element of the Cabbibo-Kobayashi-Maskava (CKM) mixing matrix V

,(2.11)

where (d, s, b) are the mass eigenstates and (d’, s’, b’) are the weak eigenstates of the quarks with charge -1/3. The unitarity of the CKM matrix V is tested most stringently in the top row

.(2.12)

The unitarity, which must be satisfied if the Standard Model with 3 leptonic generations is correct, is dominated by

(0.975. The term

is determined by analysis of semileptonic hyperon decays such as e.g.

; its present value [PDG 94] is

(0.220. The third term contributes only weakly to the sum in (2.12),

(0.004.

In order to determine Vud from the nine accurately measured super-allowed Fermi transitions Eq. (2.8) has to be modified:

(2.13)

Radiative corrections R are composed of dominating, Z-independent parts and of Z-dependent terms of the order Z2 and Z23, where Z is the atomic number of the nucleus and is the fine-structure constant ((. They are calculated for each of the nine mentioned transitions and amount to ~3.5( at most. The nuclear mismatch c corrects the fact that isospin symmetry along the isomultiplet is violated by the coulomb and the nuclear force. The estimates on c for the different nuclei are of the order of some tenth of a percent but have model dependent divergences [Wil 94]. A recent re-analysis [Tow 95b] , based on the newest Ft-values, leads to an unitarity test of

.(2.14)

This result indicates a violation of the unitarity condition for the three generations by 2.1 standard deviations. Thus, the present determination of Vud from super-allowed Fermi transitions is not limited by the experimental accuracy with which the relevant ft-values are determined nor by the confidence on the various radiative corrections, but rather by the uncertainty of the nuclear mismatch c.

Another independent determination of Vud comes from the decay of the neutron which does not require the c correction but has the disadvantage of being a mixed vector-axial transition:

. (2.15)

The extraction of Vud requires therefore the knowledge of the neutron lifetime n as well as the knowledge of GA/GV, determined by the asymmetry in the emission of electrons from polarized neutrons; both of these measurements are very delicate.

From the mean lifetime of the neutron n=887.0(2.0 s together with the weighted average of the ratio GA/GV (the results are compiled in [Tow 95a]) individual values for the coupling constants can be deduced.

Again, the value of GV obtained from neutron decay is used to test the unitarity of the CKM-matrix and leads to [Tow 95b]

,

which differs from unitarity in the opposite sense to the result from nuclear beta decay (eq. 2.14).

Figure 2.1: From [Tow 95a]. Allowed regions from the analysis of super-allowed Fermi transitions, neutron decay and CKM unitarity. The results are expressed in values for the corrected coupling constants G’V=GV(1+

) and G’A=GA(1+

), where

are the nucleus independent radiative corrections.

The present situation in determining the unitarity sum of the CKM-matrix can be summarized as follows:

· An analysis of the super-allowed Fermi transitions including the nuclear mismatch c violates the unitarity of the CKM-matrix by 2.1 standard deviations.

· Neutron beta decay has contributions from axial currents, the experimental data lead to a result 2 standard deviations above CKM-unitarity.

The present status of the analysis from super-allowed Fermi transitions and neutron decay is displayed in Fig. 2.1.

Due to its similarity to super-allowed Fermi transitions and the absence of nuclear and screening corrections, the pion beta decay presents another independent determination of Vud. However, the small branching ratio of the decay (Eq. (2.7)) makes it a very difficult process to study with a precision below 1(. The present determination of the pion beta decay rate has a precision of 4( (McFa 85(. A measurement below 1( would be a substantial improvement of the experimental tests of the CVC-Hypothesis and the radiative corrections. At a level of 0.5( it provides important information for determining Vud.

3. Rare Pion-Decay Experiments

The intention of the proposed pion beta decay experiment is a precise determination of the decay rate (ee relative to the rate for the decay (ee as will be discussed in section 4.1. In order to deal with the occurring experimental difficulties, a precise knowledge of the experimental technique and the calibration methods of previous experiments on both of the two pion decay modes is required. The presentation of previous experiments includes thus a discussion of their calibration methods (see 3.1.1) and low energy tail corrections (see 3.2), since some of these calibration methods are a central subject of the present work.

An overview of the decay channels of pions, muons and ’s is given in tables 3.1 and 3.2.

Process

R =

/

(

(99.98770(0.00004)(

(

(1.24(0.25)(10-4

(ee

(1.230(0.004)(10-4

(ee

(1.61(0.23)(10-7

(ee

(1.025(0.034)(10-8

Table 3.1: Pion decay modes [PDG 94]

Process

R =

/

Process

R =

/

+(e+e

(98.6(0.4)(

(

(98.798(0.032)(

+(e+e

(1.4(0.4)(

(e+e-

(1.198(0.032)(

(e+e

e+e-

(3.4(0.4)(10-5

Table 3.2: Muon and decay modes [PDG 94]

Figure 3.1: Michel spectrum of positrons from muon decays at rest.

The main decay of the pion (() produces a monoenergetic + which decays with a lifetime of ( 2.2s mainly into +(e+e

(e chain). For stopped pion decay experiments where the pion is assumed to be at rest before decaying, the muon has a kinetic energy of T ( 4.12 MeV. Since the range of the + is very small ( about 1mm in scintillator material) the + is also stopped in the target and the muon decay occurs at rest too. The energy spectrum of the e+ from the decay

is the Michel spectrum, shown in Fig. 3.1, with a maximum energy of 52.83 MeV. Positrons from the e chain are the main background for all stopped pion decay experiments.

3.1 Pion Beta Decay Experiments

The pion beta decay has been observed for the first time in 1962 at CERN [Dep 62]. In the years from 1962-1965 several experiments on this decay were published and lead to results with errors of 20-30%. Since then, two experiments have been carried out with errors below 10%. The first of these was an experiment using stopped pions (Dep 68(, whereas the second one (McFa 85( was a decay-in-flight measurement.

3.1.1 Pion Beta Decay at Rest

If the charged pion decays at rest, the kinetic energy for the decay products of 4.452 MeV is shared by the positron, the neutrino and the recoiling . The maximum kinetic energy of the is

(3.1)

i.e. the is almost at rest. The has a lifetime of 8.6(10-17 s, its decay modes are shown in table 3.2.

Figure 3.2: Kinematics of the pion beta decay: Calculated spectrum of the positron (top left) and of the (top right). Monte Carlo Generation of the deviation from collinearity (bottom left) and energy distribution (bottom right) of the two photons from the decay of the .

The energies of the two photons from the 0( decay are in the following range:

.(3.2)

The two photons are not exactly collinear (Fig. 3.2 bottom left).

An experiment using the decay-at-rest technique was carried out with a beam of 77 MeV pions, produced on the internal target of the CERN synchro-cyclotron (Dep 68(. The experimental setup is shown in Fig. 3.3. The pions were degraded and stopped in the center of the target counter; the stopping rate was ~3.5(104/s. The identification of the process was based on the summed energies and a prompt coincidence of the two photons and the positron. The pulses of the target counter and the summed pulses of the eight lead-glass counters have been displayed on an oscilloscope. A coincidence of two photons occurring 6 to 100 ns after a valid pion stop triggered the oscilloscope and its traces were photographed.

The -detector consisted of an array of eight lead-glass counters, with a thickness in radial direction of 17cm (6.8 radiation lengths X0) and a solid angle coverage of ca 60% of 4. For the -detection, a coincidence of any of the eight counters with an azimuthal separation of more than 90( and a total energy of more than 14 MeV was required.

Care was taken to determine the efficiency of the -detection

with good precision, using the reaction

.(3.3)

The from this reaction have a kinetic energy of 2.9 MeV, the two photons have a minimum angle of 157(, and their energies lie in a box spectrum between 55 and 83 MeV as opposed to Eq. (3.2). Due to this systematic difference, the efficiency measured by reaction (3.3) had to be corrected by the calculated ratio for the efficiency of the pion beta decay and reaction (3.3).

Figure 3.3: The experimental apparatus of the decay at rest experiment. 1,3: beam counters; 2: carbon degrader; 4: target counter; 5,6: veto counters for charged particles; A-H: lead-glass counters.

For the efficiency determination, the target counter was replaced by a hydrogen pressure bottle and the number of pions stopping in hydrogen was compared to the number of detected ’s. The overall efficiency for detecting ’s from pion beta decay was

(3.6%). The branching ratio of the pion beta decay was calculated according to

,(3.4)

where N=1.742(1011 was the number of triggers of which only a factor of f=0.85(0.01 were due to pions stopping in the target. The total number of N = 332(23 ((6.9%) pion beta events was found, which lead to a branching ratio of

.(3.5)

The main difference between the result above and earlier results was the improved precision in the detection efficiency.

3.1.2 Decay in Flight

In contrast to previous pion beta experiments, the experiment of McFarlane et al. (McFa 85( at LAMPF used decays in flight of a pion beam. The beam momentum was 522 MeV/c and its intensity was 2(108 /s. This technique has the advantage of not having to accept all the muons from pion decay. The -detectors, consisting of a converter array and an array of lead glass blocks (15 X0) were located outside the 5( cone filled by the intense flux of the muons (Fig. 3.4).

Figure 3.4: Experimental arrangement for the decay in flight experiment. 1: Beam defining collimator; 2: Magnetized collimator; 3: Vacuum tank and decay region; 4: Removable CH2 target; 5: Veto counter; 6: Converter array, 7: Lead-glass detectors; 8: Beam monitors.

The pion beta decay rate R was determined by using

,(3.6)

where N was the number of beam pions entering the apparatus, Nthe number of pion beta decay events, P2 the joint photon conversion probability and T the effective proper time spent by a pion in the decay region. The calibration of the energy scale, the conversion efficiency and the absolute timing of the detectors was done by inserting a CH2 target and using - and + beams which produced ’s from reaction (3.3). The conversion efficiency P2 was found to be 0.5151(0.0062 (1.2(). The total number of pions N in the beam was determined by the counting rates of three different monitors which were averaged; the final value was N = (2.144(0.0218)(1019 (1.01%). The quantity T, i.e. the acceptance for the 2 photons to hit the detectors was calculated by a Monte Carlo program. The final value was T=(3.534(0.031)(10-11s (0.9(), where the error primarily was from the statistics of the Monte Carlo simulation.

From the total of 667000 recorded events, N=1223(36.2 events were identified as pion beta events (error 2.9(). Together with the systematic uncertainties the numbers above inserted in equation (3.6) lead to a branching ratio

.(3.7)

This value is the best experimental determination of the pion beta decay rate so far.

3.2 Pion Decay into Positron and Neutrino

According to the V-A theory, the decay

(e) is suppressed with respect to the normal pion decay by a factor of

,(3.8)

because the positron is emitted in the “wrong” helicity state. The kinetic energy of the positrons from this decay is

.(3.9)

Results of two experiments on this decay mode have been published recently, each of them reached an overall precision of ~0.4(. One experiment [Cza 93] was carried out at PSI the other at TRIUMPH [Bri 94]. In order to avoid pile-up, i.e. several decay products for one trigger event, low beam intensities were used (7(104/s for the TRIUMF experiment and 5(103/s for the PSI experiment). Due to the low rate, inorganic scintillators with excellent energy resolution but slow decay times d could be used (d ~ 300 ns for BGO and d ~250 ns for NaI(Tl) ).

The main systematic errors for both experiments came from tail corrections, i.e. from the estimation of the number of events from (e+e decay below the edge of the Michel spectrum. The tail can be seen in Figure 3.5, which shows the recorded total energy spectrum for (e+e events. In the PSI experiment this tail occurred because of photo-nuclear absorption with neutron emission and could be estimated only by a Monte Carlo Simulation. In case of the TRIUMF experiment the tail was due mostly to the response function of the NaI(Tl) crystal. The response function of the crystal was measured directly in a positron beam. The result was convoluted with the response function obtained from Monte Carlo calculations.

Figure 3.5: The total energy spectrum (after applying cuts) of the PSI experiment [Cza 93]. The peak at 90 MeV results from the decay (e+e . The two vertical lines mark the window used to calculate the branching ratio. The dashed line shows the contributions from the e background, the dotted line is the pion strong interaction background (SIB). To determine the final branching ratio, the number of (e+e events below the e background edge had to be estimated.

4. The Pion Beta Experiment at PSI

4.1 Experimental Technique

The proposed experiment at PSI, the pion beta decay experiment, is designed with the aim of making a precise determination of the pion beta decay rate. The experimental method is chosen such as to achieve an overall level of uncertainty in the range of 0.5( which would be a considerable improvement of the present experimental uncertainty of 4(. To reach this goal, a total systematic error of 0.3( and a statistical error of 0.4( must be achieved. As can be seen from the previous experiments (see section 3.1) the systematic error is composed of the errors for the efficiency of the event detection and for the normalization on the absolute number N of decaying pions. It seems very hard to determine these parameters with the quoted precision. A way around this problem of absolute normalization and efficiency determination is a measurement of the pion beta decay rate relative to the decay rate of (e+e, which is known with high precision (see Table 3.1). The positrons and photons from pion beta decay produce similar showers, therefore the differences in detection efficiency for the two processes are small and manageable. This allows a measurement of the pion beta decay rate without the absolute knowledge of acceptances and conversion efficiencies for both processes.

Experimentally, the branching ratio for the pion beta decay is given by

(4.1)

where Re and

are given in Tables 3.1 and 3.2, N and Ne are the numbers of and e events, respectively. The corrections are ratios, for the two processes, of the following quantities :

· Detection efficiencies

· Live time corrections

· Low energy tail corrections

· Instrumental inefficiencies

These correction factors differ from unity only by a few percent. By calculating and measuring the associated errors, the overall systematic uncertainty can be reduced to the proposed value of about 0.3(.

In order to achieve a statistical error of 0.4(, N = 6(104 events need to be accumulated, a factor of 60 more than detected in the previous experiment (McFa 85(. This requires a large solid angle detector capable of handling high event rates. Assuming a detection efficiency = 0.5, the number of stopped pions required is

.(4.2)

Assuming a + stopping rate of 106/s, eq. (4.2) corresponds to 1.2(107s of beam time. The availability of the PSI proton beam per week is about 75% of 152 hours which corresponds to about 4(105 s/week. Thus the total required beam time to achieve the attempted statistical precision is about 30 weeks.

4.2 Apparatus

The detector (Fig. 4.1) will be placed in the E1 area of PSI. The pion beam with a momentum of 116 MeV/c (see section 4.3) and an intensity of 106 /s passes the beam counter B1, enters the apparatus through a conical vacuum pipe, traverses the active degrader and stops inside the target. The length of the active degrader in beam direction is 4 cm. Its dimensions are chosen so that pions stop and decay in the central region of the active target. The size of the target perpendicular to the beam must be as small as possible in order to keep the conversion probability for photons (from 0-decay) and the energy loss for positrons from +(e+e low. The target has thus a cylindrical shape with a length of 5 cm in beam direction and a radius of 2 cm.

Figure 4.1: A cut through the pion beta detector. 1) Central beam trajectory; 2) vacuum pipe; 3) active degrader; 4) active target; 5) fiber optic light guides; 6) cylindrical MWPC’s; 7) segmented plastic veto detector; 8) 1’’ PMT’s; 9) CsI-shower veto’s; 10) CsI shower calorimeter; 11) 3’’ PMT’s

As described in section 3.2, the muons from ( stop within the target too and decay mostly into Michel positrons, most of which escape the target. The positrons from +(e+e are exiting the target, but loose some of their energy depending on the amount of target material traversed.

The active target is surrounded by two cylindrical multi-wire proportional chambers (MWPC’s) for charged particle tracking. A cylindrical scintillator hodoscope (plastic veto detector) surrounds the MWPC’s in order to provide timing information for events induced by charged particles and to distinguish charged from neutral particles. The amount of material in the MWPC’s and the plastic veto detector must be as low as possible again in order to minimize the conversion probability for photons and the energy loss for positrons .

The two photons from pion beta decay leave the target and pass the MWPC’s and the scintillator hodoscope without any energy loss. To detect them, a calorimeter made of pure Cesium Iodide (CsI), an inorganic scintillating crystal material with large stopping power and fast light output. The light output and the good energy resolution makes pure CsI suitable for the detection of not only photons but also positrons and electrons. The photons from pion beta decay of about 70 MeV initiate showers in the calorimeter via pair production, whereas the positrons from (e+e initiate positron-photon showers via bremsstrahlung or suffer energy loss from ionization.

The detector and its supporting structure are surrounded by a thermal house to control temperature and humidity since the CsI crystals are slightly hygroscopic and their light output is temperature dependent. In order to avoid background from cosmic muons, the detector is enclosed by a “cosmic house”. It consists of plastic scintillator plates which detect cosmic muons with high efficiency.

The scintillator plates are shielded from the inside with 5cm of lead to avoid self vetoing in the cosmic veto counters due to shower leakage through the back of the calorimeter and to shield the detector from beam related background.

Pion Beam and Beam Monitoring Detectors

4.2.1 Beam Line

The E1 beam line (Fig 4.2) supplies high intensity pion and muon beams with momenta ranging from 10 to 500 MeV/c. The particles from target E are extracted at an angle of 10( with respect to the proton beam direction. The desired momentum of the channel is depending on the setting of the first dipole magnet ASZ51. For the pibeta experiment, the beam momentum of 116 MeV/c is chosen as a compromise between pion rate, positron contamination of the beam and separation of the beam particles due to time-of-flight (TOF) . At this momentum the beam is highly contaminated with positrons (e+/+ ( 8, [Poc 89]) which induces inordinate dead time and background counts in the detector. Proton, positron and muon contamination of the beam is suppressed by moving the graphite degrader plate DSC51 (4 mm) into the beam trajectory. Protons are stopping in the degrader. For 116 MeV/c the pion and positron momenta are reduced by 25 MeV/c and 1.7 MeV/c respectively. This results in different deflection angles in the dipole magnets ASY51 and ASL51 and thus in a positional displacement at the lead collimator L for the different particle types. The lead collimator L with a circular opening of 10 mm diameter thus reduces the positron contamination of the beam by about 2 orders of magnitude. The scintillator B1 (1 mm thick) is located right after the lead collimator and counts the remaining beam particles.

The additional beam line elements in the E1-area are the quadrupole magnets (quadrupole triplet) QSK51, QSL55 and QSK52 and a vertical (SSL51) and a horizontal (SSK51) steering magnet. The momentum bite of the beam is 2%.

Figure 4.2: The E1 beam line. The location of the detector platform is indicated. In the first part of the 1994 beam time, the beam line was set up with an active degrader B2 in front of the active target at the focal point F. The numbers after the names indicate distances in mm.

The beam envelope for the E1 channel calculated by the program Transport [Bro 73] is shown in Fig. 4.3. The solid curves correspond to the horizontal and vertical envelopes of the beam. The main features of the beam tune are as follows:

a) Maximum momentum dispersion and a double waist in the dipole magnet ASY51.

b) Narrow waist in both horizontal and vertical direction in the lead collimator L.

c) The waist in L is imaged onto the focal point F by the quadrupole triplet QSK51, QSL55, QSK52.

d) Beam spot size of about 1 cm diameter in both vertical and horizontal direction. This ensures that the beam is almost fully contained in the target.

Figure 4.3: Graphical ouput of a transport calculation for the E1 beam line with elements as shown in Fig 4.2. The upper part shows the vertical envelope y, the horizontal envelope x is shown in the lower part. The dashed line is the dispersion trajectory i.e. the horizontal trajectory of a particle with a deviation from the nominal momentum of 1( .

Beam Studies with the Active Target

In order to experimentally determine the beam parameters and the settings of the magnets, beam line studies were performed in several test runs in 1992 - 1994. In 1994 the beam line was set up in the final geometry.

Figure 4.4: Pulse height (ADC value) in the active degrader B2 versus time (TDC start: B2; TDC stop: RF-signal). A clear separation of the three different types of particles is visible. The contaminations have been determined using box cuts on these variables.

The active degrader B2 (40 mm thick scintillator) was put in front of the active target, located at the focal point F at a distance of 1250 mm from the mirror plate of the quadrupole magnet QSK52. The beam momentum was set to 116 MeV/c and optimized for pion stopping rate in the target. For each incoming particle, the pulse height in B2 as well as the timing relative to the accelerator frequency RF (50.63 MHz) was recorded. This allows further elimination of beam muons and positrons. Fig. 4.4 shows how the different particle types can be identified; the resulting values for the beam contamination with positrons and muons are listed in Table 4.1.

Figure 4.5: Cut through the active target used during the 1994 test run to measure the horizontal and vertical beam profiles.

The active target is used to monitor the transverse stopping distribution. The beam stopping distributions are needed for an accurate Monte Carlo simulation of the experiment and acceptance corrections for pion beta and (e+e decays. The present version of the target consists of 69 plastic scintillator fibers surrounded by 8 guard ring elements of the same material. It has a cylindrical shape of 4 cm diameter and a length of 5 cm. Each of the fibers has a square cross section of 2.76(2.76 cm2, and is covered with an acrylic cladding of 0.12 mm thickness for optical insulation. A cut through the active target is shown in Fig 4.5. Each of the scintillator fibers is connected to a one inch photomultiplier tube via a fiber optic light guide.

A measurement of the beam stopping distribution is shown in Fig 4.6. Table 4.1 contains the main parameters of the beam measured with the active degrader and the active target.

Figure 4.6: Two-dimensional beam stopping distribution measured with the active target. The beam spot size given in Table 4.1 is determined by fitting the x and y projections with a gaussian distribution.

Beam momentum

116 MeV/c

Momentum acceptance

2( (fwhm)

Rate B1(B2

5.5(105/s

Pions

4.3(105/s (78.3()

Muons

5.6(104/s (10.2()

Positrons

6.3(104/s (11.5()

Horizontal beam size

1.3 cm (fwhm)

Vertical beam size

1.0 cm (fwhm)

Table 4.1: Beam parameters at the focal point F located 1250 mm from the mirror plate of QSK54. The rates are obtained at a proton current of 0.8 mA.

4.3 Shower Calorimeter

The shower calorimeter, consisting of 240 crystals made of pure CsI, is the heart of the pion beta detector. Its geometry is spherical with two openings for beam entry and readout of the inner detectors as displayed in Fig. 4.7. The inner radius is 260 mm, the outer radius is 480 mm, the solid angle coverage of the calorimeter is ~77% of 4; the total weight is ~1600 kg. The thickness of the calorimeter in radial direction is 12 radiation lengths (X0); it was chosen as a compromise between energy resolution and the volume, i.e. the costs for the CsI. The modularity of the calorimeter is obtained from a class II geodesic subdivision of an icosahedron. As a result of the geodesic breakdown, there are nine distinct modular shapes which make up the 240 CsI crystal detectors (see Table 4.2).

Module Type

Name

Number

Volume [cm3]

Weight [kg]

Pentagon

PENT

10

1002

4.54

Hexagon A

HEXA

50

1444

6.54

Hexagon B

HEXB

50

1576

7.14

Hexagon C

HEXC

50

1721

7.80

Hexagon D

HEXD

40

1633

7.40

Half Hexagon D1

HEXD1

10

799

3.62

Half Hexagon D2

HEXD2

10

799

3.62

Veto 1

VETO1

10

1174

5.32

Veto 2

VETO2

10

1174

5.32

Table 4.2: The 9 module types which make up the shower calorimeter.

The dimensions of the nine different shapes were calculated in such a way as to leave a gap of 200 m between adjacent modules, in order to account for the wrapping of the modules.

1

0

c

m

H

E

X

A

H

E

X

B

H

E

X

C

H

E

X

D

H

E

X

D

1

V

E

T

O

1

V

E

T

O

2

H

E

X

D

2

P

E

N

T

Figure 4.7: The pion beta shower calorimeter and its segmentation as a result of a class II geodesic subdivision of an icosahedron. The nine different module types listed in Table 4.2 are indicated.

Each of the crystals is read out by a 3-inch photomultiplier tube (PMT) with quartz window except for the modules of type HEXD1, HEXD2, and VETO1, VETO2, which are read out by 2-inch PMT’s with quartz windows.

The mechanical support of the calorimeter with the requirement of easy access to inner detectors (the target, the MWPC's and the plastic veto) and upstream detector readouts was designed by Mr. H. Obermeier. All the parts are currently under construction.

4.4 Trigger and Electronics

In order to design the trigger with high efficiency, showers initiated by 70 MeV photons and positrons in the calorimeter have been simulated by use of the detector simulation package Geant [Gea 94]. The particles were tracked through the sensitive detector, recording the location of the energy deposition at each step. It was found, that clusters of seven CsI-crystals constitute excellent trigger elements since almost all of the shower energy is contained within the conical volumes of seven modules. A clustering scheme must be chosen such that each vertex point of the calorimeter (the edges of each crystal) is contained in at least one cluster.

The energy deposition of 70 MeV photons and positrons in various clustering schemes were studied1. The efficiency in detecting these particles is defined as the ratio of events with energies above 55 MeV in at least one cluster of events with energies above 55 MeV in the whole calorimeter. The resulting clustering scheme consists of 60 overlapping clusters, each containing six to nine modules. Each module belongs to at most three different clusters. Six clusters around a pentagon and the associated HEXB’s form a so called “supercluster”. Some of the clusters and one supercluster are visualized in Fig. 4.8 .

The clustering scheme is implemented in the pion beta trigger with the dedicated analog adder and discriminator UVA 125 (Adder), which is capable of analog adding nine PMT signals; 60 clusters require 12 Adder modules. The following description refers to the diagram of the trigger electronics in Fig. 4.9. A valid pion stop signal obtained from a coincidence of B1, the active degrader and RF opens the delayed pion gate DPG. The pion gate is delayed by 10 ns in order to avoid prompt interaction processes such as elastic scattering or pion charge exchange reactions. The trigger requires the coincidence of two showers exceeding the Michel endpoint (high treshold, ht=55 MeV) within 20 ns inside a valid DPG. Following the delayed pion gate another time window is opened (DPG’). Due to the pion lifetime the DPG’ is mostly sensitive to pile-up from Michel events and is used to study background from these events. The crystal PMT’s provide two identical signals: One of them is supplied to the trigger branch, where it is split three times and supplied to the Adders according to the clustering scheme. The other signal is delayed by 350 ns, split up and then distributed to the Analog-to-Digital-Converters (ADC’s), Time-to-Digital-Converters (TDC’s) and Domino Sampling Chip modules (DSC’s, see chapter 7), which reside in Fastbus- and NIM-crates, respectively.

The logic output from the Adders is supplied to LRS 4564 FAN-IN modules, where the logic OR’s for the supercluster signals are generated.

The Memory Look Up unit (MLU) is the central trigger generating unit. It is capable of making Boolean operations on the input signals which include the 10 supercluster signals, the DPG, etc. The trigger requires a combination of two superclusters in opposite hemispheres within a valid DPG. On the other hand, the (e+e trigger requires the presence of a single shower, also within a DPG, occurring in at least one supercluster. As a result, the (e+e trigger is more sensitive to accidental coincidences of Michel events. In addition to the two triggers described above, there will be a prompt trigger, a cosmic ray trigger, and a more delayed pion gate (DPG’) trigger. As outputs, the MLU produces the desired triggers which are stored in pattern registers. The event trigger is the logic OR of the various event triggers. It creates a LAM signal for the computer and supplies the ADC gate and the TDC start signal. A latch mechanism ensures that the event coincidence is closed until the analog- and time-to-digital-conversion processes and the read out phase is completed.

The readout of the fastbus and camac crates as well as the control of the scalers, the high voltage system and the temperature probes was done with the data acquisition system HIX (Heterogeneous Information Exchange). It allows the control of several “frontend” PC’s, which are connected over the Ethernet-network as well as the online analysis of the acquired data and their storage on disk or magnetic tape. The system has been developed by St. Ritt (UVA) and is described in [Rit 93].

Figure 4.8: Visualization of four of the 60 overlapping cluster types and of one of the 10 superclusters.

Figure 4.9: Block diagram of the pibeta trigger electronics.

5. Properties and Performance of the Pure CsI Crystals

In the preceding chapters, the proposed pibeta experiment at PSI was described. The experimental technique was presented as a relative measurement between the decay rates for +(0e+e and +(e+e. In order to achieve the attempted goals with this method the detector needs to meet specific requirements. The calorimeter, being the essential part of the detector, is requested to

· consist of a very fast scintillating material, capable of handling high event rates, and

· detect positrons and photons of 70 MeV with good energy resolution.

As mentioned in 4.2, the scintillator material of the pibeta calorimeter was chosen to be pure Cesium Iodide (CsI). The requests mentioned above condition a very careful examination of the delivered crystals.

The aim of this chapter is threefold:

1. The presentation of the properties of pure CsI.

2. Technical specifications of the crystals which have to be fulfilled by the manufacturers. This requires precise measurements of the specified quantities with dedicated methods. The quality control of the delivered crystals is of major importance since the success of the experiment strongly depends on the quality of the scintillator material.

3. It is shown how the properties of the individual crystals are defined in the MC simulation and what the resulting energy resolutions for the processes of interest are. A realistic simulation of the calorimeter response is essential for the calculation of the low energy tail and for the correction for background in the final experimental analysis.

5.1 General Properties

As one of the fast scintillators, pure CsI is an attractive material for use in particle physics experiments. Its main property is the exhibition of fast scintillating light. Due to high density and high atomic number Z pure CsI has a great stopping power and a good light output. The attenuation length for its own radiation is of the order of ~1m which enables a single-ended readout for crystals of a length of 22 cm. Pure CsI is reported to sustain radiation doses up to 10kRad. The temperature dependence of the light output is about -1.5%/(C [Woo 90]. The properties of pure CsI are summarized in table 5.1.

Density

4.53 g/cm3

Radiation length

1.85 cm

dE/dx (per MIP)

5.6 MeV/cm

Nuclear interaction length

36.5 cm

Refractive index

1.8

Fast component decay time

20 ns

Slow component decay time

1 s

Fast component peak emission

300 nm

Slow component peak emission

480 nm

Table 5.1: Some properties of pure CsI.

5.2 Determination of the Fast/Total Ratio

One of the characteristics of pure CsI is the scintillation emission at wavelengths of 305nm. The time response of this fast component can be characterized by two decay times of 10 ns and 36 ns respectively [Kub 87]. In addition to the fast component, there is a slow component with a decay time of about one microsecond, which forms a continuous emission spectrum in the wavelength region of 380-600nm (Fig 5.1).

The ratio of the intensity of the fast component to that of the slow component depends upon the quality of the raw material used and the conditions during the growth of the crystals. It is very important to know the portion of the slow component for each individual crystal, since it affects the rate capability and the energy resolution of the entire calorimeter.

Figure 5.1 [Ham 95] Emission spectrum of a pure CsI crystal.

For the PIBETA experiment, the “fast to total ratio” (F/T) is defined as the ratio of the fast integral (100 ns) to the total integral (1s) of the raw CsI-pulse. A crystal is accepted, if the following condition is fulfilled:

F/T>70%.(5.1)

A typical CsI-pulse and the definition of the integration limits are shown in Fig. 5.2. The F/T-value is measured for each CsI-crystal when it is delivered at PSI.

Figure 5.2: CsI-pulse of a cosmic muon penetrating a pure CsI-crystal. The PMT signal has been digitized with a digital scope TDS740. The software gates corresponding to the fast and the total integral are indicated.

Since the F/T measurements are very sensitive to various parameters like electronic noise, integration starting points etc., care has been taken to develop a measuring method which allows the comparison of F/T-values from measurements performed over several years: The unwrapped crystal is coupled to a dedicated PMT (EMI 9822QB) by air gap coupling. The PMT signals are recorded with a digital scope TDS740, which is read out by a PC. Cosmic muons penetrating the CsI-crystal produce CsI-pulses for each of which the fast and the total integral is calculated as shown in Fig. 5.2. The software gates start 15 ns before the peak, the gate lengths are 100 ns and 1 s for the fast and the total gate, respectively. The fast and the total integral are histogrammed for 1000 events. A typical result is shown in Fig 5.3 (top).

One source of background which could falsify the result for the F/T value are cosmic muons penetrating the quartz glass of the PMT producing Cerenkov light. These events can be seen by recording PMT signals without any scintillator connected. Cerenkov signals and CsI-pulses can be identified by their decay time, which is about 3 to 5 ns for the former.

Figure 5.3: Result of a F/T measurement on a HEXC type CsI-crystal. Top left: Fast vs. total integral with the slope corresponding to the F/T value. Top right: the ratio F/T for each event; the indicated mean value of 80.1% is defined as the F/T-value of the crystal. Bottom left (right): Rise-time (fall-time) of the pulses as defined in Eq.5.2 (5.3).

In order to clean the CsI-signal from background, its rise-time tr

(5.2)

and fall-time tf

(5.3)

are calculated, where t0 is the time at the maximal amplitude A0 in Fig. 5.2. The values for tf and tr are filled into the appropriate histogram (Fig 5.3 bottom); a cut is set on the fall time (tf>40 ns) for CsI-pulses. The resulting F/T-value of each CsI-crystal is entered into the pibeta crystal database (see 5.6).

5.3 Distance Measurements

Dimensions of 9 different crystal types are calculated to leave a 200 m gap between adjacent modules to accommodate the module wrapping. However, there is no additional “dead” material foreseen to support individual CsI-crystals; they are built up in a self‑supporting geometry. This design requires a very precise fabrication of the crystals, which is complicated by the irregular shapes of the 9 different modules. Tolerances for linear tl and angular (tn, to) deviations from the theoretical shapes are calculated to achieve a precision of

tl = (0.3 mm.(5.4)

In order to check the specified tolerances, each crystal is examined by a computer-controlled measuring machine, capable of recording the coordinates of any point inside a volume of 3 m3 with a precision of 7 m. The machine is programmed to automatically scan the surface of a CsI-crystal. For each side 6 points are recorded and a plane is fitted through these points with a least-square method. The planes are represented in the form

,

is the unit vector perpendicular to the surface of the plane and d is the distance from the origin of the coordinate system. The angle between two planes with normal vectors

is thus

.

Figure 5.4: Definition of the sides of the module type HEXA. Angular tolerances between neighboring sides (P/A,A/B,B/C,…) are 0.24(. For angles between opposite sides (opening angles P/C, A/B and B/A) the tolerance is 0.08( to achieve the required tolerance of (0.3 mm.

For angles between planes two categories are distinguished:

· Angular deviations between neighboring sides (Fig. 5.4). The resulting tolerance from (5.4) for the deviations is tn=0.24(.

· Angular deviations between opposite sides (Fig. 5.4), which are the opening angles of the module and thus the most critical quantities. The tolerance for the deviations is to=0.08(.

In addition, the vertices of the module are calculated and compared to the theoretical values. The vertices of the module allow the calculation of linear deviations for the front face and the back face as shown in Fig 5.5. The tolerance for the deviations is 0.3 mm as defined in (5.4). For each module the deviations are calculated and recorded in a data sheet. For a HEXA crystal, the data sheet is displayed in table 5.2.

Figure 5.5: Comparison of the shape obtained from distance measurements (solid lines), exaggerated for better visibility, to ideal shape (dashed lines). For each side, the deviations D1 and D2 are calculated, which are positive (negative) if the measured vertex lies outside (inside) the dashed shape. The tolerance for the deviations D1, D2 is (0.3mm. In addition, the angle is calculated for each side.

A summary data base of the 4 categories of deviations of each crystal is produced to overview the results from all the modules. For each category of deviation (e.g. angles between neighboring sides,), the mean value m, the number of values n exceeding the specified tolerance and the maximum value x is calculated. In order to provide an entry to the pibeta crystal data base, which classifies the geometrical precision a crystal, the quantity DIM is defined as

,(5.5)

where xo is the maximum value and to=0.08( the maximum allowed deviation of angles between opposite sides. The values for m, n and x of the different categories and the value DIM of measurements on 25 crystals delivered by Bicron Corporation is shown in Table 5.3 .

Angles btw. Neighboring sides [deg]

Angles btw. opposite sides [deg]

side

th

exp

diff

side

th

exp

diff

B\A

66.17

66.13

-0.04

A\B

14.28

14.32

0.04

A\P

54.17

54.06

-0.11

P\C

12.42

12.46

0.04

P\A

54.17

54.15

-0.02

A\B

14.28

14.32

0.04

A\B

66.17

66.19

0.02

B\C

58.34

58.38

0.04

C\B

58.34

58.45

0.11

Linear deviations back side

Linear deviations front side

side

D1 [mm]

D2 [mm]

[deg]

side

D1 [mm]

D2 [mm]

[deg]

A

-0.11

-0.22

0.11

A

-0.09

-0.13

0.08

P

-0.19

-0.17

0.02

P

-0.23

-0.20

0.05

A

-0.09

-0.04

0.05

A

0.02

0.05

0.07

B

-0.12

-0.09

0.03

B

-0.10

-0.10

0.00

C

-0.11

-0.11

0.00

C

-0.13

-0.16

0.04

B

-0.07

-0.19

0.12

B

-0.01

-0.09

0.13

Table 5.2 Data sheet from distance measurements of a HEXA type CsI-crystal showing the four categories of deviations.

Front sides

Back sides

Neighb. sides

Opposite sides

Serial

m

n

x

m

n

x

m

n

x

m

n

x

DIM

S001

0.21

0.00

-0.25

0.22

0.00

-0.28

0.07

0.00

-0.11

0.13

2.00

0.13

0.62

S002

0.17

0.00

-0.23

0.17

0.00

-0.20

0.05

0.00

0.06

0.05

0.00

0.06

0.00

S011

0.13

0.00

-0.23

0.14

0.00

-0.22

0.07

0.00

-0.12

0.04

0.00

0.04

0.00

S012

0.05

0.00

0.09

0.05

0.00

-0.10

0.08

0.00

-0.14

0.02

0.00

0.03

0.00

S013

0.23

2.00

-0.39

0.07

0.00

-0.10

0.07

0.00

0.11

0.12

2.00

0.15

0.97

S014

0.13

0.00

-0.21

0.06

0.00

-0.12

0.03

0.00

0.04

0.05

0.00

0.08

0.00

S061

0.10

0.00

-0.14

0.11

0.00

-0.15

0.03

0.00

-0.04

0.01

0.00

0.01

0.00

S062

0.12

0.00

0.20

0.20

2.00

0.37

0.07

0.00

-0.11

0.08

1.00

0.12

0.55

S111

0.21

0.00

0.29

0.14

0.00

0.25

0.06

0.00

-0.12

0.04

0.00

0.04

0.00

S112

0.18

0.00

-0.26

0.12

0.00

0.23

0.10

0.00

0.18

0.12

2.00

0.15

0.87

S113

0.17

0.00

0.23

0.09

0.00

0.16

0.03

0.00

-0.04

0.05

0.00

0.08

0.00

S114

0.16

0.00

0.25

0.14

0.00

0.27

0.03

0.00

0.05

0.04

0.00

0.07

0.00

S115

0.18

0.00

0.27

0.11

0.00

0.20

0.03

0.00

-0.05

0.04

0.00

0.06

0.00

S116

0.25

2.00

0.38

0.14

0.00

0.23

0.05

0.00

-0.07

0.06

0.00

-0.08

0.00

S117

0.23

1.00

0.35

0.12

0.00

0.21

0.03

0.00

0.05

0.05

0.00

0.07

0.00

S118

0.55

5.00

0.87

0.13

0.00

-0.20

0.19

2.00

0.36

0.16

2.00

-0.20

0.00

S161

0.12

0.00

-0.23

0.09

0.00

-0.19

0.14

0.00

0.22

0.07

1.00

0.09

0.09

S162

0.09

0.00

-0.13

0.08

0.00

0.15

0.13

0.00

0.22

0.06

0.00

0.07

0.00

S163

0.09

0.00

0.17

0.11

0.00

0.24

0.22

2.00

0.34

0.05

1.00

0.09

0.10

S164

0.07

0.00

-0.12

0.06

0.00

-0.15

0.14

0.00

0.22

0.05

0.00

0.07

0.00

S165

0.05

0.00

0.10

0.08

0.00

0.18

0.14

0.00

0.22

0.05

0.00

0.06

0.00

S166

0.10

0.00

0.17

0.11

0.00

0.17

0.12

0.00

0.22

0.02

0.00

0.03

0.00

S201

0.20

0.00

-0.28

0.12

0.00

-0.20

0.20

2.00

-0.31

0.24

1.00

0.33

3.23

S202

0.07

0.00

-0.14

0.14

0.00

-0.21

0.16

0.00

-0.21

0.19

1.00

0.27

2.42

S221

0.08

0.00

0.16

0.18

0.00

-0.27

0.09

0.00

-0.13

0.08

1.00

0.09

0.18

Table 5.3 Compilation of Distance Measurements of the 25 crystals delivered by Bicron Corporation. The quantities m, n, x and DIM are defined on page 44.

5.4 Photoelectron Statistics

In a crystal which contains nearly all of the energy deposited by an incident particle, the energy resolution is determined largely by the light output. The intrinsic light output of CsI is about 4000 photons per MeV of energy deposit [PDG 94]. The detected signal is quoted by the number of photoelectrons per MeV (np) produced by the PMT. The relation between photons/MeV produced and np involves factors like light collection efficiency (depending on the geometry of the crystal) and quantum efficiency of the PMT (15-20%). Values for np between 130 and 300 photoelectrons per MeV of large pure CsI-crystals were reported [Woo 90].

A determination of np can be based on the fact that the photoelectron statistics follows a Poisson distribution, with

,(5.6)

where N is the mean value, N the standard deviation and R the associated resolution of the distribution. N can be interpreted as the average number of photoelectrons produced by a particle depositing the energy E,

.(5.7)

The measurement of the standard deviation E for energy distributions with varying mean energies E leads to a determination of the number np:

.(5.8)

For every crystal the number np is measured with the tomography apparatus (see. section 5.5). A light emitting diode (LED) is connected to the open back face of each of the 6 crystals in the apparatus. The LED’s are pulsed with signals of various amplitudes (between 3 and 30V), a fixed width of 20 ns and a frequency of 10Hz. The variation of the amplitude from the LED driver (type LP100) is about 1%.

Figure 5.6: ADC spectrum of a HEXA crystal obtained from recording data with six different intensities of the LED (top). Each peak is fitted with a gaussian, the sigma2 of which is plotted against the associated mean value (bottom). The parameter P2 of the linear fit is the inverse of the number of photoelectrons per ADC channel (Eq. 5.8).

The amplitude of the LED pulses is varied and leads to a spectrum as shown in Fig. 5.6 (top). One “LED-Run” includes data of LED pulses and simultaneously data of cosmic muons penetrating the crystals. The data of cosmic muons are needed for two reasons:

1. The recorded cosmic ray spectrum for a crystal of a certain type is compared to a simulation of cosmic rays penetrating a crystal of the same type which leads to an absolute energy calibration.

2. A cosmic ray trigger in one of the six crystal produces an ADC pedestal value for the remaining five crystal, which delivers the “zero energy” point.

A cosmic ray spectrum is shown in Fig. 5.7.

Figure 5.7: Cosmic ray spectrum from a “LED-run” of HEXA crystal. For a conversion of ADC-channel to MeV scale the spectrum is compared to the result of a Geant simulation (Table 5.4).

The np-values obtained for the pibeta crystals (

(80) are a factor of about two lower than expected. One reason seems to be the partial coverage of the back face area of the crystals by using 3’’ PMT’s. The back face of a pentagonal crystal is covered to 61%; for the hexagonal crystals only about 40% is covered. A clear relation is observed between the area covered by the PMT, i.e. the crystal type, and the measured number of photoelectrons per MeV. A linear extrapolation to 1 (i.e. a total coverage of the crystal back face by the PMT) leads to np(130.

Crystal type

Cosmic muon peak

PENT

39 MeV

HEXA

48 MeV

HEXB

50 MeV

HEXC

52 MeV

HEXD

51 MeV

Table 5.4: Peak values of crystal spectra from a geant [Gea 94] simulation for cosmic muons penetrating CsI-crystals.

According to equations 5.6 and 5.7 np(80 would lead to an energy resolution of 1.3( (3.1( fwhm ). At 70 MeV this would correspond to 2.2 MeV (fwhm) which would be sufficient for the pion beta decay experiment. It should be mentioned that not only the number of photoelectrons per MeV contributes to the energy resolution of the crystals, but also the effect of light collection non-uniformity must be added, when detecting 70 MeV photons or positrons.

5.5 Light Collection Non-Uniformity

The light collection non-uniformity is strongly connected to the geometry of the detector. It can be determined by simultaneously recording tracks of particles penetrating the crystal and the resulting light output. This can be achieved by probing the crystal, positioned between MWPC’s, with a particle beam or cosmic muons. From the MWPC-information a track through the crystal is reconstructed and the pathlength is calculated. For rectangular crystals the light over pathlength is constant along the crystal axis [Woo 90] but for the tapered pyramidal crystals the shape of the function depends on the actual geometry.

The optical properties of a crystal can be influenced by wrapping the side faces and covering the front face. Different wrapping materials were tested for maximal light output and minimal optical non-uniformity. Best results were obtained by wrapping the crystal with three layers of teflon-foil (total (60m thick) and one layer of aluminized Mylar ((20 m) for optical insulation. Additional beam studies were performed to check the influence of the front face coverage on the light collection non-uniformity. Covering the crystal front-face with black paper turned out to be the optimal solution.

Figure 5.8: Six CsI-crystals as they are positioned in the tomography box. One of the chambers is mounted on the lid of the box, two chambers are below the box.

The optical properties of each CsI-crystal are systematically studied in the tomography apparatus (Fig. 5.8) before the module is selected for the assembly into the calorimeter. Parameters like the attenuation length of CsI, the temperature dependence of the light output, and the F/T ratio for the wrapped crystal (see footnote on page 125) are determined. Of major importance is the determination of the non-uniformity caused by the generation and collection of the scintillation light.

NO PICTURE AVAILABLE

Figure 5.9: The light non-uniformity obtained from the 2D-reconstruction procedure for one CsI-crystal of type HEXA. The vertical axis is the light output per unit pathlength. The horizontal axis are the mean values of the calculated entry (x1, z1) and exit point (x2, z2) of the muon at the surface of the crystal. The offset in the z-coordinate of about 29 cm is artificial. The PMT is located at (z1 + z2)/2 =52 cm.

The tomography apparatus consists of a light-tight box enclosing the modules, three drift chambers for tracking of cosmic muons and two scintillator paddles below the bottom chamber used as triggers. The crystals are positioned in the box with an accuracy of about 1 mm. Each of the drift chambers has two orthogonal x, y-wire planes surrounded by three ground planes.

For a cosmic muon penetrating the apparatus, the hits in the 3 chambers allow a precise determination of the track. The segments of the cosmic ray paths in the CsI-crystals can be calculated and compared to the actual crystal signal. Only muons penetrating the crystals in almost vertical direction (polar angle (85() are accepted. This allows the determination of the light per unit pathlength along the crystal axis (axial, z-coordinate) and perpendicular (transversal, x-coordinate) to the crystal axis. The resulting light non-uniformity from this 2-dimensional reconstruction procedure for one CsI-crystal is shown in Fig 5.9.

The cosmic ray tomography is a delicate project. It needs very careful tuning and calibration of the experimental apparatus as well as an elaborated analysis of the data. The quality of the data and their analysis are currently improved. The aim of the analysis is the quantification of the light non-uniformity for each crystal. Since the final data for each crystal was not available as the writing of this work was ongoing, only common features of the optical response as they are visible in Fig 5.9 can be given:

· bright spot at the front face (z = 0-5 cm) of the crystal.

· a “hole” in the response at z ( 15-18 cm, where the light output is ~10-15% lower.

· bright zone at the back face in front of the PMT (z = 22 cm)

· dark zones at the edges of the crystal.

In order to incorporate the optical response in the simulation of the electromagnetic shower, it is parametrized by an analytic function flnu(r,z) which approximates the features listed above. The light non-uniformity function flnu(r,z) (Fig. 5.10) is calculated for each space point x, y, z in the body coordinate system of the volume of a crystal, with

:

(5.9)

The length of the crystal is l=22 cm, the “hole” in the response is assumed to be at zd=15 cm. The parameter lnu corresponds to the difference between the light output at z=0 and zd of the crystal. The parameters PF and PB account for the transverse non-uniformity at the front and back of the crystal, which is assumed to be parabolic. Best correspondence with the experimental data available was obtained with PF=0.002, PB=0.02 and lnu=0.12.

Figure 5.10. Parametrization of the optical light non-uniformity for a HEXA type CsI-crystal by the function flnu(r,z), given in Eq. 5.9. The 3’’ PMT is located at z=22 cm.

The z-dependent function fz in (5.9)

(5.10)

is constrained as follows:

fz (z=0) = 1; fz (z=zd) = 0; fz (z=l) =-1.(5.11)

The resulting parameters are:

.(5.12)

It should be mentioned that (5.9) represents a first approach to parametrize the optical non-uniformity of the crystal. The function flnu(r,z) is likely to change with the improved analysis of the tomography data. The aim of the tomography project is the parametrization of the optical response of each crystal in the pibeta calorimeter.

5.6 CsI-Crystal Data Base

The parameters of 26 crystals, which were assembled for the 1994 test measurements are displayed in table 5.5. The column named crystal position refers to the position of the crystal in the array (Fig. 5.11). The numbers for Fast/Total are obtained as described in section 5.2. The entry DIM reflects the mechanical property of the crystal and is defined in equation 5.5. The N.PE./MeV (numbers of photoelectrons per MeV) are the result of the method explained in section 5.4. The italic numbers in this column are assumed since these modules were returned to the manufacturer because of low F/T-value or unacceptable mechanical dimensions. Once finally determined, the parameters on light non-uniformity of the individual crystals will be included in the database.

PSI Serial

Crystal Position

Type

Manufact.

Fast / Total

Dim

N.PE./ MeV

Accept.

S002

C16

PENT

Bicron

0.919

0.00

116

YES

S011

C14

HEXA

Bicron

0.827

0.00

94

YES

S012

C9

HEXA

Bicron

0.796

0.00

72

YES

S013

C22

HEXA

Bicron

0.826

0.97

63

YES

S014

C17

HEXA

Bicron

0.808

0.00

87

YES

S015

C15

HEXA

Charkov

<0.6

5.05

40

NO

S016

C24

HEXA

Charkov

<0.6

1.20

40

NO

S018

C23

HEXA

Charkov

<0.6

0.00

40

NO

S061

C8

HEXB

Bicron

0.900

0.00

84

YES

S062

C10

HEXB

Bicron

0.803

0.55

83

YES

S063

C18

HEXB

Charkov

<0.6

0.00

40

NO

S111

C25

HEXC

Bicron

0.812

0.00

104

YES

S112

C6

HEXC

Bicron

0.769

0.87

69

YES

S113

C7

HEXC

Bicron

0.684

0.00

57

YES

S114

C3

HEXC

Bicron

0.802

0.00

81

YES

S115

C12

HEXC

Bicron

0.810

0.00

68

YES

S116

C11

HEXC

Bicron

0.851

0.00

43

YES

S117

C21

HEXC

Bicron

0.814

0.00

74

YES

S161

C1

HEXD

Bicron

0.836

0.09

68

YES

S162

C13

HEXD

Bicron

0.847

0.00

61

YES

S163

C26

HEXD

Bicron

0.877

0.10

77

YES

S164

C5

HEXD

Bicron

0.872

0.00

82

YES

S165

C20

HEXD

Bicron

0.881

0.00

89

YES

S166

C19

HEXD

Bicron

0.863

0.00

79

YES

S202

C4

HD1

Bicron

0.902

2.42

67

YES

S211

C2

HD2

Charkov

<0.6

0.00

40

NO

Table 5.5: Parameters for the 26 crystals used during the 1994 test beam time.

5.7 Simulated Photon and Positron Response of the CsI-Crystals

It was reported, that it is very important to understand the calorimeter response to 70 MeV positrons and photons, since the number of - and (e+e-events below the e background needs to be estimated (see e.g. Fig 3.5). The response was simulated by use of the simulation package Geant [Gea 94]. Monoenergetic positrons and photons of 70 MeV are directed into an array of 26 crystals of the calorimeter (Fig. 5.11).

Figure 5.11: The array of 26 crystals of the calorimeter as it is defined and positioned in Geant. Monoenergetic photons and positrons of 70 MeV are directed from the origin into the crystals, uniformly distributed over their surface. The properties and the types of the crystals are listed in Table 5.5.

The resulting energy spectrum of the calorimeter is displayed in Fig. 5.12; one can see, that the two processes produce similar showers. The tails are due to shower leakage at the front and the back side of the detectors. The distributions are artificial, since they include only the effect of electromagnetic showering.

Figure 5.12: Simulated energy spectrum of the electromagnetic showers produced by 70 MeV photons (solid line) and positrons (dashed line) in the array of 26 crystals. The two distributions have almost identical shapes since a perfect detector response is assumed.

In order to compare the simulated spectra to experimental data, properties of the individual modules which affect the energy resolution of the calorimeter are taken into account in the simulation: The resolution depends on the photo-electron statistics and the light collection efficiency of the individual crystals. The effect of light collection efficiency is incorporated in the Geant code in a subroutine (gustep) which is called after each tracking step of the electromagnetic shower. In this routine the deposited energy (destep) and the current position (x,y,z) inside the crystal volume of any particle of the electromagnetic shower is recorded. The variable destep is multiplied by the current value of the function flnu(z,r) (Eq. 5.9), which depends on the current position of the secondary particle inside the crystal volume. After processing one event, the energies dE(j) (j=1‑26 denotes the crystal number) deposited in each of the crystals, smeared by the optical uniformity function flnu(z,r) are known. The parameters of the function flnu(z,r) are the same for all crystals. The energies dE(j) are then folded by a Gaussian function whose standard deviation (j) accounts for the effect of photoelectron statistics:

(5.13)

.(5.14)

The number of photoelectrons per MeV, np(j), are the numbers in Table 5.5 for each crystal, and G is a function that randomly generates a Gaussian distribution of mean zero and standard deviation one. For each event, the total energy Etot is calculated by summing the energies deposited in the individual crystals:

.(5.15)

The resulting energy-spectra are displayed in Fig. 5.13. A difference between showers initiated by photons and positrons occurs. It originates from the fact that positrons interact close to the front face of the crystals, whereas photons have a mean free path of about 3 cm in CsI; their showers thus are shifted slightly along the crystal axis. As a result, the two types of showers are weighted with different parts of the optical non-uniformity function flnu(z,r).

The energy resolutions E are obtained by fitting the distribution with a gaussian function with exponential tail as defined in eq (6.16) in section 6.4.1. They are Ee=4.8 MeV (fwhm) for positrons and E=6.0 MeV (fwhm) for photons, respectively.

Figure 5.13: Simulated energy spectrum of the array of 26 crystals including the effects of photoelectron statistics and optical non-uniformity. A difference between showers initiated by 70 MeV photons (solid line) and 70 MeV positrons (dashed line) can be observed caused by the light non-uniformity.

The simulated resolution for 70 MeV positrons and photons (Ee and E) are depending on the parameters of the light non-uniformity function flnu(z,r). The values of the parameters were chosen to explain the differences found in the test experiments in 1994:

· The energy resolution for a 70 MeV positron beam directed into the array of 26 CsI presented in [Ass 95] is 4.2 MeV for the best crystal and between 4.9 and 5.6 MeV for typical crystals.

· A measurement of the calorimeter response to 70 MeV photons (see chapter 6) leads to energy resolutions between 6 and 7 MeV for typical crystals.

For the final Monte-Carlo-Simulations it is desirable to extract the parameters for flnu(z,r) from the tomography data itself, which makes the simulation results even more reliable.

The numbers given for the energy resolution are mean values of the crystal material available in 1994. With higher quality of the modules (better F/T values, improved optical non-uniformity) the values will further improve.

6. Calibration with Photons

In order to experimentally test the performance of the pure CsI-crystals, an array of 26 crystals was assembled as displayed in Fig. 5.11 of the previous section. The main goals of the beam time in 1994 were:

1. Set up the electronics for a simultaneous operation of 26 CsI-crystal array and the active target with 76 channels.

2. Study the response of the CsI-array to a beam of 70 MeV positrons.

3. Make the trigger and perform a measurement of the decay (e+e.

4. Measure the response of the CsI-array to 70 MeV photons.

The data analysis for items 2 and 3 above is described in [Ass 95]. The description of the method for measuring the lineshape of 70 MeV photons and the corresponding data-analysis is the subject of this chapter.

6.1 Method of the Calibration

In the energy range of about 70 MeV, photons can be produced by stopping negative pions in a liquid hydrogen target. A fraction

of the -p atoms, where Rp is the Panofski Ratio, undergo the charge exchange reaction

,(6.1)

whereas almost all of the remaining 40( of the -p atoms undergo radiative capture:

,(6.2)

Due to the kinetic energy of the from reaction (6.1), the energies of the two photons from the decay range from 56 MeV to 84 MeV. Showers in the crystals initiated by such photons are used to calibrate the array of 26 CsI-crystals.

If the -p atoms are at rest before reaction (6.1), energy and momentum conservation lead to the following equation for the energy

:

.(6.3)

Here,

are the masses of the charged pion, the proton, the neutron and the neutral pion, respectively.

is the mean binding energy of the -p atoms just before reaction (6.1) and is

[Cra 91]. From Eq. 6.3, energy, momentum and velocity of the are

,(6.4)

whereas the velocity of the neutron from reaction (6.1) is

which corresponds to vn=0.894 cm/ns [Cra 91].

Figure 6.1: Schematic diagram of the charge exchange reaction and the terms used in the text.

The decays with a probability of 0.988 into two photons. In the rest-frame of the , the photons are emitted with an opening angle (12=180( isotropically in all directions with energies

. In the laboratory system, the energy E2 and the opening angle 12 are calculated using a Lorenz transformation and are

Figure 6.2: E2 and 12 as a function of the angle 10 as given in eqs. 6.5 and 6.6. The marked area indicates the acceptance of the experimental apparatus (Fig. 6.4).

, and (6.5)

,(6.6)

where

=28.04 MeV/c (6.4) and

. The uncertainty E2 is mainly depending on the uncertainty 10 and is

,(6.7)

with a maximum value at 10(70( of

.(6.8)

The aim of the calibration measurement is to detect all the decay products of the charge exchange reaction (6.1). According to (6.5), the energy E2 can be calculated from the angle 1n between the 1 and the neutron, with 10=(180(-1n). The second photon initiates a shower in the CsI-array. Based on equation 6.5 the energy E2(10) is calculated and compared to the energy deposited in the CsI-array.

In the following subsections the expression “good event” is used for events with the two photons and the neutron detected, i.e. events for which all the kinematical variables can be determined.

6.2 Experimental Apparatus

The beam line was set to negative pions with a momentum of 116 MeV/c. The pions passed a degrader consisting of a thick scintillator and aluminum plates, the thickness of which was optimized for maximum - stop rate in the liquid hydrogen (LH2). The LH2 was contained in a cylindrical cell of stainless steel with a length of 10cm in beam direction and a width of 1.6cm. The LH2 target cell was operated at a pressure of 1060mbar and a temperature of 20K.

Incoming pions were detected by the plastic scintillators B1 and the counter B2 (thickness 5cm) located right in front of the Al degrader. The counter B3, placed behind the target cell, served as a veto-counter.

Figure 6.3: Box with the 26 CsI-crystal array, which was assembled in 1994.

The 26 CsI-crystals in the crystal box are assembled as shown in Fig 6.3. The front faces of the CsI-crystals in the CsI-box were at a distance of 26cm from the center of the LH2-target. A special air-conditioning system was connected to the CsI-box to control the temperature and the humidity; it consisted of a modified air-conditioner and a heat exchanger box, with a long term temperature stability of 15(2(C and a relative humidity of less than 40% in the box. Seven temperature sensors and one humidity sensor were installed inside and outside the enclosure and were read out periodically.

The experimental arrangement (Fig. 6.4) of the detectors fulfilled the following requirements:

1. The photon energies in the CsI-array should be 70 MeV, which sets the following constraints on the setup: between the center of the neutron counter array and the tag counter array the angle is about 80(, whereas the angle between the tag counters and the center of the CsI-box is about 160(.

2. The cylinder axis of the target cell should coincide with the neutron flight direction.

3. None of the arrays should stand in the elongation of the pion beam axis.

Figure 6.4: Experimental arrangement for the energy calibration of the CsI-crystals with 70 MeV photons. The distance of the 30 neutron counters and the 12 tag counters from the center of the target is about 80 cm. The front faces of the CsI-crystals in the CsI-box have a distance of 28 cm from the center of the LH2-target.

The above conditions could not be fulfilled completely in the sense that only a portion of the CsI-array has been illuminated by photons from “good events”, mainly the cluster of crystals around C15 (C7, C9,C14-C16,C22, see Fig 5.11). The energies of photons from these events are between 68 and 75 MeV (see Fig. 6.2).

The array of 30 neutron counters and the tag detectors, 12 pure CsI-crystals of type HEXD1 and HEXD2, were located at a distance of 80 cm from the target. The total uncertainty from the positions of the detectors for 1n is about 2( = 0.035 rad. The corresponding energy uncertainty E from equation (6.8) is

.

The horizontal-plane opening angle between one neutron and one tag counter is about (5(. This results in a broadening of the distribution of E2, originating from the finite size of the neutron and the tag counter being hit. The fit of the energy spectrum with a gaussian leads to a FWHM of 0.7 MeV.

Each of the 30 neutron counters is a cylindrical PILOT U organic scintillator, 15 mm thick, with a diameter of 45 mm, attached to a XP2020 photomultiplier. The neutrons from the charge exchange reaction (6.1) have a kinetic energy of Tn (0.4 MeV; the dominant process is elastic scattering on the nuclei of the target material. In the scintillator material neutrons are scattered off protons, which loose their energy through ionization and excitation.

The scintillator was preceded by a 9 mm thick Pb plate, which served to convert photons. For photon energies above ca. 20 MeV, the efficiency of the photon detection is improved by a factor of ca. 3-4 to about 60%. For less energetic photons (1-20 MeV), the detection probability for the counter arrangement is ca. 10-20%.

The signal from a 0.4 MeV neutron produced 1 to 8 photo-electrons in the cathode of a photomultiplier. Each channel was transmitted trough a LeCroy 612 PMT Amplifier and amplified by a factor of 10. The high voltages of the PMT’s were matched such as to get a one electron signal of 30 mV at the input of the PS 7106 CAMAC discriminator; the neutron pulses extended up to about 250 mV.

The signals from the tag counters were set up similarly to those of the CsI-crystals (Fig. 4.9). After a signal splitter the analog signals are fed into the UVA 125 summing discriminator, the output of which goes into the event coincidence. The requirements for a valid trigger were:

1. A valid pion stop signal in the LH2 target, (

).

2. An event in the CsI-array.

3. An event in one of the 12 tag counters.

The stopping rate in the LH2 target, defined by the coincidence

was 1.3(105/s at 0.9 mA of proton current, which lead to a trigger rate of about 200/s.

In order to determine the background, data were taken with empty target and with the described trigger configuration. The resulting event rate was only 1/30 s-1, more than a factor of 5000 lower than with the filled target, thus showing that the trigger was very restrictive.

6.3 Analysis of the Data

6.3.1 Neutron TDC Spectrum

Since the neutron counters were not part of the trigger only a fraction of about 10-3 of the recorded events have a neutron counter signal. The neutron TDC spectrum for such events is shown in Fig. 6.5. The events above TDC channel 115 are neutrons from reaction 6.1, which have a velocity of 0.894 cm/ns. The prompt peak in the TDC channels 20‑40 are photons from shower backsplash in the CsI-array and in the tag counters, which was identified as following: About 20 cm of lead placed in the flight path of the neutrons between target and neutron counter enhanced the prompt peak over the neutron peak. Since the probability of penetrating 20 cm of lead is very low for photons, they must come from a source other than the degrader or the target. Photons below 20 MeV can be detected by the neutron counter with a probability of ca 10-20% . The time difference between the prompt peak and the neutron peak agrees with the TOF difference for neutrons and photons at a distance of 0.8 m from the target. The remaining events in Fig. 6.5 have a flat time distribution and are accidental. In order to determine the energy of the photon detected in the CsI-box, events which fulfill

119( tn (127,(6.9)

where tn denotes the tdc channel of the neutron, were used for the analysis.

Figure 6.5: TDC spectrum