Measurement of the charged pion photoproduction cross ... 11 detecting photons energy range was set from 167:675 MeV to 179:636 MeV [2]. The target selected was the hydrogen contained

UNIVERSITÀ DEGLI STUDI DI PAVIA

FACOLTÀ DI SCIENZE MATEMATICHE, FISICHE ENATURALI

CORSO DI LAUREA IN FISICA

Measurement of the charged pionphotoproduction cross section close to

thresholdMisura della sezione d’urto della

fotoproduzione di pioni carichi vicino alla soglia

Relazione per la laurea magistrale diFederico Cividini

RelatoreProf. Paolo Pedroni

Dipartimento di Fisica Nucleare e TeoricaCorrelatore

Prof. Lennart IsakssonMAX-Lab, Lund

Anno Accademico 2010/2011

2

Contents

1 INTRODUCTION 9

2 THEORETICAL BACKGROUND 132.1 Pion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Quark Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3 Partial waves expansion . . . . . . . . . . . . . . . . . . . . . 18

3 EXPERIMENTAL SET-UP 233.1 Electron beam . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2 Photon beam . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.3 Targets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.4 Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.4.1 Focal Plane . . . . . . . . . . . . . . . . . . . . . . . . 303.4.2 Telescope CsI/SSD . . . . . . . . . . . . . . . . . . . . 323.4.3 Lead glass . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.5 Data taking electronic . . . . . . . . . . . . . . . . . . . . . . 383.5.1 Events trigger . . . . . . . . . . . . . . . . . . . . . . . 39

4 DATA ANALYSIS 414.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 414.2 Preliminary analysis . . . . . . . . . . . . . . . . . . . . . . . 424.3 Pions selection . . . . . . . . . . . . . . . . . . . . . . . . . . 434.4 Background removal (using the TDC plot) . . . . . . . . . . . 48

3

4 CONTENTS

4.5 Tagging efficiency . . . . . . . . . . . . . . . . . . . . . . . . 514.6 Cross section calculation . . . . . . . . . . . . . . . . . . . . . 534.7 Error analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.7.1 Statistical uncertainties . . . . . . . . . . . . . . . . . 554.7.2 Systematic errors . . . . . . . . . . . . . . . . . . . . . 56

4.8 Energy dependent analysis . . . . . . . . . . . . . . . . . . . . 584.9 Further analyses . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5 RESULTS AND CONCLUSIONS 635.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.1.1 Energy range between 167.7 and 179.6 MeV . . . . . . 635.1.2 Energy range between 170.7 and 179.6 MeV . . . . . . 655.1.3 Energy range between 177.0 and 179.6 MeV . . . . . . 66

5.2 Comparison with similar experiments and models . . . . . . . 685.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

List of Figures

1.1 Positively charged pion photoprodution cross section data forEγ below 200 MeV; colored points represent the data analyzedin this thesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.1 Quark rearrangement in γ + p −→ π + n reaction. . . . . . . 17

3.1 MAX-Lab rings. . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2 Injector at MAX-Lab. It is possible to see the electron gun,

the Linac and the exit. . . . . . . . . . . . . . . . . . . . . . 253.3 Radiator and focal plane system. . . . . . . . . . . . . . . . . 273.4 Example of plot provided by the focal plane TDC. The second

peak from the left is the “prompt” peak, and it contains trueand random coincidences. . . . . . . . . . . . . . . . . . . . . 28

3.5 Layout of the channel in the focal plane detectors. During theexperiment the overlapping of even and odd scintillators wassmaller than in the picture. . . . . . . . . . . . . . . . . . . . 31

3.6 Number of electrons in the focal plane coincidence channels. . 323.7 The SSD/CsI telescope at 90° to the photon beam. . . . . . . 333.8 Plot ∆E/E provided by telescope. The upper “banana” is

formed by protons, the lower ridge is formed by electrons; thepions are just a little above the electrons. . . . . . . . . . . . 37

3.9 Trigger and electronic used for the experiment. . . . . . . . . 38

4.1 Focal plane TDC for even channels without any cut. . . . . . . 44

5

6 LIST OF FIGURES

4.2 Double-peaked signal in the Flash ADC. . . . . . . . . . . . . 444.3 Upper plot: ∆E/E ADC plot after the conditions for the sec-

ond peak have been applied. Lower plot: zone of the pionselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.4 Focal plane TDC for even channels after cut 34. . . . . . . . . 474.5 Double gaussian fit for the “prompt” peak, cut 34. The yellow

line represents the random coincidences, the blue the promptones and the red one is their sum. . . . . . . . . . . . . . . . 48

4.6 Separation time between the two CsI Flash ADC peaks. Leftplot: “prompt” zone (between channel 670 and 690 in the FPTDC); right plot: “random” zone (between channel 1230 and3760). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.7 Peaks time separation in Flash ADC for “prompt” zone with-out random with Rebin (10) after cut 34. . . . . . . . . . . . 50

4.8 Focal plane TDC for the Carbon, cut 34. On the right re-bin(10) has been used. . . . . . . . . . . . . . . . . . . . . . . 51

4.9 Fits around the peak in the TDC plots divided from the lowestenergy of the photons (0 energy), to the highest (3 energy);it is possible to notice that the best peak is with the highestenergy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

4.10 Fit around the prompt peak in the analysis with the eventsfrom the the focal plane channels 16-60, for the CH2 1mm at90° . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4.11 Fit around the prompt peak in the analysis with the eventsfrom the the focal plane channels 48-60, for the CH2 1 mm at90° . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.1 The obtained differential cross section points obtained in thisthesis are compared to the pion photoproduction SAID pre-dictions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

List of Tables

2.1 Quarks. [5] . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2 The s-wave amplitude E0+ at threshold. . . . . . . . . . . . . 21

3.1 Targets values. . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.1 Summary of recorded data. . . . . . . . . . . . . . . . . . . . 414.2 Correction on each channel. . . . . . . . . . . . . . . . . . . . 434.4 Selection for the second ADC peak. . . . . . . . . . . . . . . . 474.5 Tagging efficiency for each focal plane channel. . . . . . . . . 534.6 Percent systematic errors for the differential cross sections il-

lustrate in Sec. 5.1 . . . . . . . . . . . . . . . . . . . . . . . . 58

5.1 Number of events selected during the work for each target. . 635.2 Number of electrons and photons for each target for the data

analysis in the energy range . . . . . . . . . . . . . . . . . . . 645.3 Number of electrons, photons and pions of the analysis in the

energy range between 170.7 and 179.6 MeV. . . . . . . . . . . 655.4 Number of electrons, photons and pions of the analysis in the

energy range between 177.0 and 179.6 MeV. . . . . . . . . . . 675.5 Pions energy range for the photon beam energies. . . . . . . . 685.6 Values for the differential cross section . . . . . . . . . . . . . 68

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8 LIST OF TABLES

Chapter 1

INTRODUCTION

Nowadays one of the challenges of nuclear physics is to confirm and test out,with laboratory experiments, the theoretical framework provided by Quan-tum Chromodynamics (QCD). Specifically QCD provides a theory about thestrong nuclear force and the interaction between quarks and gluons.

Pion photoproduction from the nucleon is a crucial process which is to testthe predictions of chiral effective-field theories, dispersion-theory approachesand other quark-based models of the nucleon. An accurate description ofthis process and nuclear Compton scattering is essential to understand theproprieties of the strong nuclear force.

The photon is an ideal probe for studying the interaction in the nuclearenvironment, whereas strongly interacting particles do not penetrate to theinterior. Further the electromagnetic interaction is well understood and weak,so the nucleus is only mildly perturbed.

In the simplest case of the nucleon there are four reaction channels whichinvolve pion photoproduction:

γ + p→ p+ π0

γ + p→ n+ π+

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10 CHAPTER 1. INTRODUCTION

γ + n→ p+ π−

γ + n→ n+ π0

however, only the channel which involves neutral pion from the protonγ + p → π0 + p has been extensively examined close to threshold, a regionwhere predictions from several approaches can be compared. In fact, forthis channel, there are more than 1200 data points covering all energies fromthreshold to Eγ = 200MeV. The two charged pion channels have much lessdata available and only a few energy values and angular ranges have beeninvestigated [1].

Figure 1.1: Positively charged pion photoprodution cross section data for Eγbelow 200 MeV; colored points represent the data analyzed in this thesis.

For this reason in 2010 at the MAX-Lab photon-tagging facility a series ofmeasurements of the channel γ+p→ π+ +n have been started. This channelwas chosen because detecting π+ is relatively easier than detective π−. The

11

detecting photons energy range was set from 167.675 MeV to 179.636 MeV[2]. The target selected was the hydrogen contained in the CH2, also a Ctarget was used to subtract the carbon background. The use of a standardliquid hydrogen, which would be the best choice for this experiment, requiresdifferent containers that would absorb most of the low-energy pions emittedin this energy region. The use of a solid target partially avoid this problem,but requires a careful study of the Carbon response.

This thesis work contains all the analysis data from the experimental datato the value of the differential cross section of pion photo-production fromthe proton.

Outline of the thesis

The thesis is organized as follows: in Chapter 2 there is an overview of thetheoretical physics processes involved during the experiment. Especially thequark model description used by Quantum Chromodynamics is presentedand the pion-photoproduction from the nucleon.

In Chapter 3 there is a brief description of the MAX-Lab in Lund, wherethe data of this work were collected, and a presentation of the experimentalset-up, from the beam production to the data taking electronic.

In Chapter 4 the framework of logic order used to data analysis in thisthesis is provided, the main steps are explained in detail.

In Chapter 5 the results of the analysis data are listed and compared withthe results and reports from other similar experiments. A comparison withthe theoretical expectations is also shown.

12 CHAPTER 1. INTRODUCTION

Chapter 2

THEORETICALBACKGROUND

The development of modern descriptions of the strong interaction based onQuantum Chromodynamics (QCD) can now provide detailed predictions inthe nuclear regime, in particular about the nuclear strong force and theinternal structure of the nucleon. Comparisons between these theoreticalpredictions and experimental measurements serve as a stringent test of theseQCD-based models, and form an important check on our understanding ofthe underlying dynamics in the nucleon system.

The pion is fundamental in the structure of the nucleon, because throughthe exchange of virtual pions between the nucleons, the nucleus can be stable.Pion photoproduction is a process with many theoretical calculations previ-sions and it is experimental accessible, for this reasons is a very interestingreaction to study.

2.1 Pion

In 1935 Yukawa had predicted with a theoretical work the existence of mesonsas the carrier particles of the strong nuclear force. Initially he called this par-ticle mesotron, this name was due to the hypothesis that its mass was between

13

14 CHAPTER 2. THEORETICAL BACKGROUND

that of the light known particle, as electrons, and the nucleons. He tried alsoto explain why the strong nuclear force has a short range limited around at1 fm, on the contrary than the electromagnetic and the gravitational forceswhich have an infinite range. Yukawa thought that, using the Heisenberguncertainty principle x = ct = ~c/mc2 and the assuming that the range of thestrong force would be k−1 = ~/mc, it was possible to calculate the mass of thisparticle and he obtained a value of about 100MeV/c2.

The particle accelerators technology of the 1930’s did not allow to gene-rate the predicted particle. Many test had been done at high altitudes withphotographic emulsions because it was believed that high energy cosmic rayscould produce these mesons through collisions with nucleons. Anderson andNeddermeyer observed a meson with a mass around 100MeV/c2, and theybelieved it was the exchange meson predicted by Yukawa. Later studiesshowed that this particle had a range much larger than the predicted valuefor the exchange particle for the nuclear strong force. This particle wascalled µ−meson, and it was the muon. Only some years later it was discove-red that the muon was a lepton and not a meson. Anyway this particle wasconnected to the strong force and Bethe and Marshak hypothesized that itwas a consequence of the decay result of the Yukawa exchange meson.

In the end of the 1940’s the pion was observed, two different particles wereseen in emulsion tracks. One had mass of about 150MeV/c2, the second ofabout 100MeV/c2. The heavier particle was the exchange meson predictedby Yukawa and it was called π−meson or pion, while the lighter was themuon. Further studies determined that there were two different pions, apositive (π+) and a negative (π−) one. Current understanding of chargedpions is that they decay with a probability more than 99% into muons aftera lifetime of about 26 ns. The hypothesis of Bethe and Marshak had beenconfirmed.

In the following years modern technologies allowed new experiments andthe production of pions in laboratory become possible using cyclotrons andin 1950 the neutral pion π0 was detected at the University of Berkley.

2.2. QUARK MODEL 15

With the new synchro-cyclotron accelerators the production of pionsbeams became possible and it was used to study the interactions of pionswith the matter and with different nuclear targets [3].

2.2 Quark Model

The strong nuclear force has a fundamental role in the nature, it is the forcethat binds nucleon together in the nucleus and, because it has a very shortrange, it is difficult to study. The particles that interact through the strongforce are called hadrons. The hadrons are further divided in two groups:half-integer spin hadrons are called meson and they include pions, eta meson,kaon and others; integer spin hadrons are called baryons and they includeneutrons, protons and other heavy particles.

With the new experimental results obtained in the 1960’s it was evidentthat hadrons are composite particles made up of quarks.

Quarks were first theoretically introduced by Gell-Mann and Zweig in1964 [4]. The current quark model has six quark flavors with different massesshown in Tab. 2.1

Quark Symbol Charge (e) Mass (MeV/c2) Isospin (I3)up u +2/3 1.5− 3.3 +1/2

down d −1/3 3.5− 6.0 −1/2strange s −1/3 104 0charm c +2/3 1270 0bottom b −1/3 4190 0top t +2/3 171200 0

Table 2.1: Quarks. [5]

Nowadays both the nucleus and the nucleons structure is described withthe quark model.

All baryons are made up of three quarks qqq. In particular the proton ismade up of two up quarks, each of which carries a charge of +2/3 , and one


down quark with charge −1/3. In this way the total charge of the proton is+1 and it is denoted with uud. Neutron has two down quarks and one upquark, so it results having neutral charge and it is denoted with udd.

The mesons are formed from a quark anti-quark pair qq. In particularpion can be created with a collision between energetic particles, in order tothe energy is enough high to create a quark anti-quark pair. From this quarkanti-quark pair, along with the three quarks of the nucleon, a pion is formed.

The positive charged pion, π+, is made up of an up quark with charge+2/3 and an anti-down quark with charge +1/3 and it is written ud . Thetotal charge of positive pion results +1.

The negative charge pion, π−, is made up of an down quark with charge−2/3 and an anti-up quark with charge −1/3 and is written du. The totalcharge of this particle results −1.

The charged pions have a mass of 139.6MeV/c2 and positive and negativepions are considered a particle and anti-particle pair. The mean lifetime ofthe charged pion is 26.0 ns and it decays as follows:

π+ → µ+(4.12 MeV) + νµ (2.1)

with a probability 99.99%.

Negative charged pion has the same decay but the respective anti-particlesare involved.

The neutral pion, π0, has two possibility: it can be formed from an up

quark and the anti-up quark, uu, or from a down quark and the anti-downquark. The total charge of π0 is zero and it is written as the combination ofboth the configuration, uu+ dd/

√2. The value of the mass is lower than the

charged pions and it is around 135MeV/c2. The neutral pion is consideredto be its own anti-particle. Its mean lifetime is very short, 8.4 · 10−17 s andit decays as follows with probability 98.8%:

π0 −→ γγ

2.2. QUARK MODEL 17

and with probability 1% it decays into a photon and an electron-positronpair:

π0 −→ γ + e− + e+

Because its very short lifetime, π0 is impossible to detect, but it is identifiedby its double photon decay.

The pion photoproduction is an important process because during theinteraction there is a rearrangement of the quarks in the nucleons. For thecase useful for this thesis of γ+ p −→ π+ +n , shown in Fig. 2.1, the protonis formed from three quarks in the uud configuration, while the photon canbe seen as a dd pair.

Figure 2.1: Quark rearrangement in γ + p −→ π + n reaction.

The resulting neutron is formed from three quark in the udd configuration,and the positive charged pion is ud pair. It is possible to see that in thisreaction there is an exchange of quarks: the proton “gives” an up quark andit keeps one down quark and in this way it becomes a neutron, the photon“loses” the down quark and with the acquisition of one up quark it becomesthe π+.


Quantum Chromodynamics is the current theory that describes the strongforce (also called color force) between the quarks and gluons which make uphadrons and it is an important part of the Standard Model.

Low-energy events of QCD are studied using a new effective field theory,called Chiral Perturbation Theory, that solves QCD equations of nuclearprocesses when the kinetic energies of the interacting hadrons are very low.

This rearrangement of the of quarks into the nucleon during the pion pho-toproduction can provide many information in order to check the theoreticalpredictions.

2.3 Partial waves expansion

Near-threshold pion photoproduction from the nucleon (151.44MeV) is oneof the few low-energy phenomena for which several theories can be formulatedand experimental measurements can than provide an important consistentlycheck test.

This analysis requires an angular momentum decomposition in both ini-tial and final states. In the initial state the proton carries spin 1 and has anorbital momentum lγ relative to the target nucleon [6].

The wave function can be characterized by vector spherical harmonics [7]:

YlγLM =∑

C(1λ, lγν|LM)eλYlγν(r)

where:

• L = lγ ± 1 is the total photon angular momentum;

• λ = ±1 is the transverse polarization leading to electric and magneticmultipole;

• ν = 0, ...,±lγ;

• M = 0, ...,±L.

2.3. PARTIAL WAVES EXPANSION 19

The final state is described by an orbital momentum l of the pion relative tothe recoiling nucleon, with parity (−1)l+1 due to the intrinsic π parity.

The total spin of the final state J has to be equal to the total spin of theinitial state:

J = |l ± 1

2| = |L± 1

2|

Parity and angular momentum conservation allow to possibilities:

• EL : (−)L = (−)l+1 → |L− l| = 1;

• ML : (−)L+1 = (−)l+1 → L = l

The corresponding photoproduction partial wave amplitudes (multipoles) aredenoted as El± andMl±, where the ”+” and the ”−” signs indicate whetherthe nucleon spin and l are parallel or anti-parallel [6].

In the region close to threshold, only l = 0 (s-wave) and l = 1 (p-wave)multipoles are relevant. The total cross section σtotal can be expressed as [8]:

σtotal = 4π(q

k)|E0+|2 + |p− wave|2 (2.2)

where q is the momentum of the pion and k is the momentum of thephoton, and it can be parametrized as:

k

q

dσ

dΩ= [A+B cos θ + C cos2 θ]

where θ is the angle of the pion and the coefficients A, B and C arecombinations of magnetic and electric multipole amplitudes:

A = |E0+ |2 + |P23|2

B = 2Re(E0 + P ∗1 )


C = |P1|2 − |P23|2

and

P1 = 3E1+ +M1+ −M1−

P2 = 3E1+ −M1+ +M1−

P3 = 2M1+ +M1−

|P23|2 =1

2(|P2|2 + |P3|2)

.Within 1−2 MeV above threshold the contribution, of the s-wave (l = 0)

is predominant and the contribution of the p-wave (l = 1) is very smallcompared to the s-wave and it becomes zero at threshold. Neglecting thecontribution of the s-wave eq. 2.2 becomes:

k

q

dσ

dΩ= |E0+|2

implying a flat angular distributions in the center of mass system.The measurement of the pion photoproduction cross section allows to

measure the contribution of the s-wave, and to obtain a value for the funda-mental E0+ multipole amplitude.

This value, for the charged pion photoproduction at threshold, is well de-scribed by the so-called Kroll-Ruderman term (pion photoproduction with-out internal nucleon excitation) which is non-vanishing in perturbation chirallimit and has a value of [9]:

2.3. PARTIAL WAVES EXPANSION 21

Ethr0+ =

egπN

4π√

2m(1 + µ)3/2= 27.6 · 10−3/Mπ

with µ = Mπ/m and using g2πN/4π = 14.28, e2/4π = 1/137.036 . In the

limit Mπ = 0 used by low energy theorem, the value µ becomes zero and theEthr

0+ = 34 · 10−3/Mπ .

LET (10−3m−1π ) ChPT (10−3m−1

π ) Experimental valuesγp→ π+n +27.6± 0.2 +28.2± 0.6 +28.1± 0.5γn→ π−p −31.7± 0.2 −32.7± 0.6 −31.5± 0.8γp→ π0p −2.3 −1.16 −1.32± 0.08γn→ π0n −0.5 +2.6 −

Table 2.2: The s-wave amplitude E0+ at threshold.

The values of the correction for E0+ provided by low-energy theorems andchiral perturbation theory are shown in Tab. 2.2.

In particular chiral perturbation theory (ChPT) provides new correctionsto the more traditional low-energy theorems (LET) based on current algebraand the partially conserved-axial-current hypothesis. Early experimental de-terminations of the new corrections from ChPT have now been confirmed byexperiment for the γ + p −→ π0 + n [10]; in this thesis the focus is on thecorrections for the positive charged pion reaction.


Chapter 3

EXPERIMENTAL SET-UP

The experiment described in this thesis was made at Nuclear-Physics Beam-line at MAX-Lab in Lund, Sweden. The data were collected during the RunPeriod 27, between 7th June and 5th July 2010. This run period was devotedto π+ production data tacking [2].

MAX-Lab

The MAX-Lab is a national laboratory in Lund, Sweden which performsresearches in three different areas: accelerator physics, nuclear physics andsynchrotron radiation applications [11]. There are three storage rings, Fig.3.1: MAX-I (opened 1986, 32.4 m circumference, 550 MeV), MAX-II (opened1997, 90 m circumference, 1.5 GeV) and MAX-III (opened 2008, 36 m circum-ference, 700 MeV) and one electron pre-accelerator (MAX injector). All thesestorage rings produce synchrotron light used in a wide range of experimentsin different disciplines and technologies (like macromolecular crystallography,electron spectroscopy, nanolithography). In this mode the injector fills therings, the electron energies are ramped up in the rings to suitable energiesafter which the electrons are stored in the rings for several hours. MAX Iworks at 550 MeV and it provides synchrotron radiation from the infraredregion to the ultraviolet. Also MAX-III works in this range, but its energy

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24 CHAPTER 3. EXPERIMENTAL SET-UP

resolution is higher. MAX-II is operated at 1.5 GeV providing synchrotronradiation in the ultraviolet and soft x-ray regions.

Figure 3.1: MAX-Lab rings.

The MAX I ring is also used as an electrons source for experiments innuclear physics. For these experiments MAX-I ring stretches the electronbunches to provide a nearly continuous electron beam which is transportedto a basement experimental area which contains the photon tagging spec-trometer and detector systems associated with the various experiments.

The Nuclear Physics involves studies of photonuclear reactions using thehigh-energy electron beam produced by the accelerator to produce high en-ergy photons.

3.1 Electron beam

Electrons are emitted at the Rutherford gun by the cathode which is eitheroperated in the thermal or photo-electric effect mode. The thermal mode isused for storage ring injection, while a short pulse laser is used to generatephoto-electrons used for the FEL experiments (in MAX-II). In the thermalmode the electron gun generates electrons with a 3 GHz radio frequency

3.1. ELECTRON BEAM 25

Figure 3.2: Injector at MAX-Lab. It is possible to see the electron gun, theLinac and the exit.

thermionic by heating a BaO cathode to 900° C and accelerates them to 1.8

MeV.After the gun the electrons are accelerated by two linear accelerator

(linacs), each having an energy gain of 100 MeV, since from the entrancethe electrons are relativistic and their speed is very close to light one. Thisallows to have the linac with equidistant cavities situated. This system ismade by two 5.2 m long sections, each operated by a 35 MW klystron andboosted with a SLED cavity, Fig. 3.2. Without the SLED cavity, each linacsection would provide up to 75 MeV. With the SLED cavity, which producesa more powerful but shorter pulse, the linac energy can be boosted to 125

MeV.For nuclear physics experiments the electron beam is then brought up-

wards to the MAX-I storage ring, but for other experiments it can then eitherbe brought recirculated by two 180° bending magnet structures for anotheracceleration in the linacs up to 400 MeV and then injected into the MAXII or MAX III. The electron pulse from the injector is 200 ns long and therate is 10 Hz. The electron density in each bunch is very high around 109

electrons. So it is essential to stretch the electron beam because the pulse


is too short and intense. This high intensity would overload the detectorsand the electronic devices and there would be an available electron beam foronly 200 ns every 100 ms. Moreover too many electrons in a very short pulsewould generate too many random coincidences.

MAX-I radius is 32.4 m, the electrons lap in 108 ns. The electrons areextracted from the ring a few for each lap and directed towards the nuclearphysics facility. It follows that each bunch is stretched by a factor 500000,becoming 100 ms long. In this way the beam becomes nearly continuouswhile the total flux remain as high as possible. The lap time is affecting thebackground in the focal plane TDC plots. The background is not flat but ithas a “wave” form with around 100 ns between two adjacent “waves”, as itcan be seen in Fig. 3.4.

The MAX-I ring and the magnets in the path can be set-up to have awell-defined energy. For this run period the output beam energy from theMAX-I ring was set at 192.94 MeV.

3.2 Photon beam

The stretched electron beam from the MAX-I ring is directed onto a radi-ator, a 300 µm thin piece of aluminum, where bremsstrahlung photons areproduced. All accelerated charged particles radiate bremsstrahlung energyand the emission probability varies as the inverse square of the particle mass.Electrons and positrons are the only particles in which bremsstrahlung radia-tion is very active. For instance, radiation lost by muons (106 MeV), the nextlightest particle, is thus some 40000 times smaller than that for electrons.

After the radiator there is a magnetic spectrometer which can measurethe energy of electrons. The electrons, after the bremsstrahlung, having alower energy than the incident beam, are deflected by the magnetic fieldand hit the detector in the focal-plane. The focal-plane detector is dividedinto many channels, and from the position of the channel hit it is possibleto determinate the radius of the electron trajectory. From the radius, it is

3.2. PHOTON BEAM 27

therefore possible to calculate the energy using the Lorentz force formula[12]:

Ee− =RecB

β(3.1)

where:

• R is the radius of the trajectory;

• e is the charge of the electron;

• B is the intensity of the magnetic field;

• β = vc.

Figure 3.3: Radiator and focal plane system.

Equation 3.2 allows to determinate the energy of the post-bremsstrahlungphotons:

Eγ = Ebeam − Ee− (3.2)

where:


• Eγ is the output photon energy;

• Ebeam is the electron beam energy (during the experiment was 192.94

MeV);

• Ee− is the electron energy.

A coincidence between a signal from the focal plane array and a signal inthe experiment detector allows the determination of the photon energy as-sociated with an event detected in the experiment detectors. These signalsare collected by a time-to-digital converter (TDC) module and their timedistribution is measured. The result plot (Fig. 3.4) from the TDC showsa “prompt” peak which contains true coincidences between the experimentdetectors and the focal plane, and “randoms”, due to accidental correlationsbetween events in the tagger and experiment detector events. This accidentalbackground must be subtracted for when determining the total number ofpions for the data.

Figure 3.4: Example of plot provided by the focal plane TDC. The secondpeak from the left is the “prompt” peak, and it contains true and randomcoincidences.

The bremsstrahlung process produces photons with any energy from zero

3.3. TARGETS 29

to a maximum equal to the incident electron energy. With appropriatechoices for the electron beam energy, the location of the focal plane detectorsand the magnetic field setting, it is possible to select the energy range of thetagged photons.

The tagger magnet was used with a field of 0.12 T, which resulted in atagged-photon energy range from 167.675 MeV to 179.636 MeV.

The produced bremsstrahlung beam enters into the experimental cavethrough a 19 mm diameter collimator and then it hits the targets.

A photograph of the photon beam was taken at the location of the targets,and the resulting spot found was a little less than 5 cm in diameter.

It is important to emphasize that each post-bremsstrahlung electron tag-ged in the focal plane corresponds to a photon produced, but not everyphoton reaches the target. The photons have a conical angular distributionwith a characteristic opening angle. For this reason a relevant fraction ofthe photons is absorbed by the collimator and only a few of these get to thetarget. This determines a lower intensity of the photon flux.

The ratio of the number of photons surviving the collimator and thenumber of electrons in the focal plane detector is called tagging efficiencyεtagg(see Section 4.5). To measure this parameter a 100% efficient detectorPb-Glass is moved from time to time into the beam line and a dedicatedexperiment is performed.

3.3 Targets

The main target used was made of CH2. There were two different targets 1mm thickness, and one 2 mm. Two 0.5 mm thick Carbon targets were usedfor the subtraction of the Carbon background present in CH2 .

The targets were placed at around 5 m from the collimator with a 30°angle with respect to the photon beam. This doubles the photon beam paththrough the target. In this way also the photons interaction probability withthe target becomes twice. The value entering in the cross section calculation


is the surface density; the values of this density are shown in Tab. 3.1 for allthe different targets used in this experiment.

Target Thickness Volume density (g/cm3) Superficial density (g/cm2)CH2 1 mm 0.95 0.104CH2 2 mm 0.92 0.194C 0.5 mm 0.69 0.035

Table 3.1: Targets values.

Many tagging efficiency runs were made without any target and with andwithout beam to check the environment background of the laboratory.

3.4 Detectors

During the experiment three detectors were used: the focal plane detectorand the telescope CsI/SSD during the standard acquisition runs with thetargets; the focal plane detector and a lead-glass during the tagging efficiencyruns.

3.4.1 Focal Plane

The focal plane detector consists of 63 overlapping scintillators (3 mm thick,50 mm high and 25 mm wide) providing 62 coincidence channels arranged asshown by Figure 3.5.

The focal plane output is generated by a coincidence between the signalsfrom two overlapping detectors, and only simultaneous signals in the front-plane and back-plane scintillators result in a trigger. In this manner thebackground radiation is greatly suppressed and only charged particles suchas energetic recoiling electrons are selected. Each scintillator is coupled witha photomultiplier to produce an electron avalanche from the light emittedby the scintillator. The model of photomultiplier used is Hamamatsu R1450and it provides a gain factor of 1.7 · 106.

3.4. DETECTORS 31

Figure 3.5: Layout of the channel in the focal plane detectors. During theexperiment the overlapping of even and odd scintillators was smaller than inthe picture.

The overlapping is not symmetrical when viewed from the direction ofthe electron path. Consequentially even coincidence channels are larger andcover around 180 keV, while the odd ones are smaller and cover 20 keV andthey detect about 20 time less electrons than the evens (Fig. 3.6).

In this work only even channels events are considerate.As it can be seen in Fig. 3.6, channel number 32 had problems during

the runs and it did not provide any events, so the total number of channelsused is 30.

The energy calibration was performed on 2009. The range covered by theeven channels is between 25.265 to 13.304 MeV for the electron energy, thatcorrespond to a range from 167.675 MeV to 179.636 MeV for the photons.

An electron, hitting the focal plane detector, triggers the discriminatorwhich generates a τp =50 ns long logic pulse. During these 50 ns, and foran additional τr =15 ns the discriminator is blind, so any new electronsarriving will fail to be registered. These signals are then delayed and usedby the multichannel TDCs (each coincidence channel has its own TDC) as“stop” signals. The “start” signals come from the events occurring in the


Figure 3.6: Number of electrons in the focal plane coincidence channels.

telescope. The time interval between the events in the telescope detectorand the detection of scattered electrons should be constant. Due to the highelectron flux the TDC is also stopped by electrons not correlated with theevents, but there is a peak where it is possible locating more “prompt” thanrandoms events. This is discussed further in chapter.

3.4.2 Telescope CsI/SSD

The detector used in the detection of positively charged pions is a ∆E/E

telescope formed by a plastic scintillator (PS) placed in front of two thinsilicon strip detectors (SSD), which then followed by the cesium-iodide crystal(CsI) detector.

During the runs the telescope was located at two different angles, 90° and60° to the right of the beam.

3.4. DETECTORS 33

Figure 3.7: The SSD/CsI telescope at 90° to the photon beam.

Plastic scintillator

The plastic scintillator is 1 mm thick and its voltage supply was set at 1350

V. Its energy resolution is worse than the SSDs, so it is used only to triggerthe events for its fast response.

When a charged particle goes through this detector, a flash of light pro-portional to the energy of the incident particle is emitted. Then the flashreaches a photomultiplier where it is converted into an electrical signal suit-able for the acquisition electronic.


Silicon strip detector

Each SSD is 0.5 mm thick, 64 mm wide, octagonal in shape and divided in 64,1 mm wide strips. The strips are read out in groups of two due to limitationsin available electronics, so the number of the channel is 32 for each detector.The strips are located vertically in this way they provide information aboutthe horizontal position of the particles detected. The signal from the stripis very weak, so there is a pre-amplifier before bringing the signal to theacquisition room.

These detectors are very thin so that the particles release only a smallpart of their total energy.

The distance between the two SSD is 15 mm. The area of each SSD is3300 mm2.

Cesium-iodide crystal

The CsI crystal is a scintillator having a cylindrical shape. It is 4 inches (10.1

cm) long with a 5 inch (12.7 cm) diameter, and it is read out by a 5 inchphotomultiplier Hamamatsu R1512 attached at the end. The voltage supplywas set at 1400 V.

This detector is a stopping detector, it stops all the charged particlesemitted from the target in the measured photon energy range and measuresall their energy.

Moreover the π+ is not a stable particle, its mean lifetime is 26.0 ns andit decay into a muon as shown in eq. 2.1.

Also the µ+ is not a stable particle and it decays after a mean lifetime2.197 µs:

µ+ → e+(5-50 MeV) + νe + νµ

This energy is released inside the CsI, but only the µ+ decay can be usedto identify the positive pions since the decay constant of the light in the

3.4. DETECTORS 35

crystal is 1.1 µs long. So a 20 MHz Flash ADC1 is used to record the shapeof the signal from the CsI in order to check the presence of a delayed pulse.

The distance between the CsI crystal and the second SSD is 15 mm.

The component of the telescope which determines the total solid angle isthe second SSD. With the telescope at 90°, the second SSD was 10 cm fromthe photon beam, making the total solid angle of the telescope approxima-tively 300 msr, while at 60° the entire telescope was moved 4.2 cm fartherfrom the target, making the total solid angle to be approximately 165 msr.

The charged particles collected by the CsI/SSD telescope in this experi-ment are essentially protons, pions and electrons.

The quantity of energy loss per distance traveled by charged particlestraversing matter is described by the Bethe-Bloch formula [13]:

−dEdx

= 2πNar2emec

2ρZ

A

z2

β2

[ln

(2meγ

2v2Wmax

I2

)− 2β2 − δ − 2

C

Z

](3.3)

where:

• NA = Avogadro constant = 6.027 · 1023 mol−1;

• me = electron mass = 1.67 · 10−27 cm;

• re = classical electron radius = 2.917 · 10−13 cm;

• c = speed of light;

• ρ = density of the target;

• Z = atomic number of the target;

• A = mass number of the target;120 MHz is the nominal value for this element, during the data analysis, in particular

in the Fig. 4.7, this value has been used.


• z = charge of the incident particle;

• v = speed of the incident particle;

• β = vc;

• γ = 1√(1−β2)

;

• Wmax = maximum energy transfer in a single collision;

• I = mean excitation potential of the target;

• CZ= density correction at high energy;

• δ = shell correction.

For the telescope signal, a plot with the correlation value between the energydeposited in the SSD and in the CsI by each particle can be obtained. Everytype of particle has a characteristic ∆E/E graph based on the Bethe-Blochformula. In this way it is possible to identify which particles pass throughthe detector, as shown in Fig. 3.8.

In the output plot from the telescope the pions and the protons are locatedin two different banana-shaped zones; while electrons are in a pedestal in thelower part of the plot. Unfortunately, as shown in the Fig 3.8, the bordersof these three zones are not well defined, so only a crude selection is possible(for further details Sec. 4.3).

3.4.3 Lead glass

The nuclear group at MAX-Lab uses a lead-glass (Pb-glass) for dedicatedtagging efficiency runs, see Sec. 4.5. This is a Čerenkov detector and it usesthe mass-dependent threshold energy of Čerenkov radiation. This radiationis emitted only by charged particles when their speed in a material withan high refractive index (n) where they are passing throw is higher the lightspeed and it is emitted with an angle θ resultant from the following equation:

3.4. DETECTORS 37

Figure 3.8: Plot ∆E/E provided by telescope. The upper “banana” is formedby protons, the lower ridge is formed by electrons; the pions are just a littleabove the electrons.

cos θ =1

n

c

v

When the photons hit the detector an electromagnetic shower is started.In order for a photon to produce at least one secondary particle travelingfaster than light, and hence produce a signal in the detector, the energy ofthe incoming photon must be larger than approximately 500 keV. This givesan inherent discriminating level which removes some of the background. Thepositrons and the electrons are very energetic and their speed in the lead-glass is higher than the light speed. In this way the radiation Čerenkov isemitted and recorded by the detector and then transformed into an electricalsignal by a photomultiplier tube. The detector also has a very short responsetime, allowing rather high count rates to be used without causing any pile-up


problems when the beam intensity is not very high. The efficiency for thisdetector is practically 100%, and this value has been used during the dataanalysis.

3.5 Data taking electronic

The acquisition electronic used during the experiment includes many com-ponents; in this section only the main steps are presented with particularattention for the trigger. The main trigger is provided by the telescope andit is generated when there is a signal both in the CsI and in the plasticscintillator [2].

Figure 3.9: Trigger and electronic used for the experiment.

3.5. DATA TAKING ELECTRONIC 39

3.5.1 Events trigger

A fan-out module splits up the single signal from the CsI detector into four.One of these outputs is sent to a delay module and then into a coincidencemodule (first blue point in the Fig. 3.9) where also the signal from the plasticscintillator arrives. This is the main coincidence but also another signal isnecessary to start the trigger.

Another signal from CsI fan-out and one from the plastic scintillator arecombined in a fan-in module in order to obtain a single signal (red point inthe Fig. 3.9). Then this signal enters in a discriminator which cuts the signalunder its threshold and removes some of the background. Then it enters ina coincidence module (second blue point in the Fig. 3.9) with the signalcoming from the coincidence. This second coincidence module is the maintrigger, and it starts all the focal plane TDC, the Flash ADC attached atthe SSDs and the QDC at the

Another signal from the CsI fan-out is sent to a Flash ADC and latercombined with the signal from the Flash ADC matched with the SSDs. Inthis way it is possible to obtain the ∆E/E plot.


Chapter 4

DATA ANALYSIS

4.1 Introduction

The data were recorded during a run period four weeks long in July 2010.During this run different targets were used: the main were CH2, with twodifferent thicknesses (1 or 2 mm), and the Carbon, used to subtract theCarbon background present in the CH2.

About 200 hours of data were taken for Carbon and CH2, and almost 50hours for tagging efficiency runs (Tab. 4.1).

The data were recorded using the ROOT software package, an object-oriented framework developed at CERN. It is written in C++ and it wasoriginally designed for the data analysis of high-energy physics experiments.

Run type Time (hours) FilesCH2 2 mm 90° 48.1 26CH2 1 mm 90° 87.2 51CH2 2 mm 60° 45.3 31C 0.5 mm 90° 27.1 17C 0.5 mm 60° 13.1 7

Tagging Efficiency 47.5 84

Table 4.1: Summary of recorded data.

41

42 CHAPTER 4. DATA ANALYSIS

The offline analysis developed or this thesis work was also performedusing the ROOT framework. During the analysis many C++ codes wereused, some of them are part of the standard during the analysis package ofMAX-Lab data, others had been written by the author of the present thesiswork.

All the plots shown in this chapter are evaluated from the data collectedwith the CH2 1 mm thick at 90° (if not otherwise specified). This config-uration had the longest run time and then higher statistics available. Alsoduring the offline work this set-up was the preferentially used to develop thedifferent analysis the obtained results. In the following sections this workwill be explained, and the differences made with the other experimental con-figurations will be discussed.

4.2 Preliminary analysis

The raw output data from the electronics are difficult to manage and weredivided into many files. Therefore the first operation was to rewrite themin a format suitable for the off-line analysis. This code was developed bythe nuclear physics group at MAX-Lab and it reorganizes all the histogramsand plots, useful during the recording, into files where the different detectorsresponses are visible.

The second operation was to combine all files collected with the sameexperimental configuration. Since the collected statistics in each file waslow, this allowed an easier analysis development.

Then it was possible to start the real data analysis. The first step was toequalize the outputs from each focal plane TDC. Each coincidence channelwas read by a single TDC, and each TDC module has a different calibrationvalue and slightly different cable lengths. Therefore it is impossible to addtogether the output from different TDC channels. The second peak, whichwas the best defined, was used as a reference and arbitrarily centered on theTDCs’ channel 680. In Tab. 4.2 the value of these corrections are displayed.

4.3. PIONS SELECTION 43

Channel Correction value0 -202 +104 +106 +108 +1010 -812 +1014 -2516 +1318 +2520 +2022 +1324 +3426 +2928 -330 +12

Channel Correction value32 empty34 +2836 +1338 +1040 042 +3444 +646 +2548 +1650 +2452 +1154 +3956 +1658 +560 +10

Table 4.2: Correction on each channel.

After this all the 32 focal plane coincidence channels were combined to-gether as shown in Fig. 4.1.

In these plots two zones had been chosen: the “prompt” and the “random”ones. The first is around the second peak from the left, between TDC channelnumber 670 and channel 690, and it includes the prompt signal made by thepions and some random coincidences. The purely “random” ones are betweenTDC channels 1230 and 3760. These last events had been used to count howmany random events there are inside the prompt peak zone.

4.3 Pions selection

The main and longest task of data analysis was to identify the pions stoppedinside the telescope during the run period. The first step was to remove thoseevents recorded by the detector that definitely were not pions.


Figure 4.1: Focal plane TDC for even channels without any cut.

Time (50 ns/div)0 50 100 150 200 250

Pu

lse a

mp

litu

de (

a.u

.)

30

40

50

60

70

80

90

Flash ADC

Figure 4.2: Double-peaked signal in the Flash ADC.


Only the events with a double peak in the plot provided by the CsI FlashADC were selected. The second peak should suggest the presence of a π+

decay, but it could be also induced by another event recorded by the detector.A selection based on the height and the relative positions of the peaks wasperformed subsequently.

The ∆E/E plot obtained after this selection using the SSD and the CsIsignals, is shown in Fig. 4.3. The electrons and the pions zones are veryclose, and only a little part of the events located in the lower left cornerwas rejected. The separation between the proton and the π region is on thecontrary much more seizable. Many cuts were tested but is was difficult toimpose more restrictive selections without rejecting a relevant part of thepions.

In Fig. 4.3 the result of this first selection is shown and the number ofevents decreased approximately by a factor of twenty.

The second step was to set different conditions about the second peakrecorded by the Flash ADC, in order to select only the events π −→ µν

decay.

Unfortunately the muon decay is a three body process so the positronenergy can fluctuate between 5 and 50 MeV. For this reason it was impossibleto predefine a clear selection and different conditions were tried and carriedout simultaneously. The cut number 34, which appeared to be the best one,was chosen in the end of this first part. These conditions are shown in Tab.4.4 and they had been used for every target. The selected height value forthe first peak was based on the discriminator minimal electric threshold.

After this cut, the peak in the focal plane TDC plot is more marked, asit can be seen in Fig 4.4.

During this analysis some new plots were made to show the time differencebetween the two peaks in the Flash ADC. Three plots of this type had beenmade for each “cut”: one over all the value of TDC, one for the “prompt”zone and one for the “random” one. In particular the “prompt” plot shouldrepresent the time distribution of the muon decay and it should be a negative


Figure 4.3: Upper plot: ∆E/E ADC plot after the conditions for the secondpeak have been applied. Lower plot: zone of the pion selection


exponential distribution with a decay rate λ = 1τwhere τ = 2.2µs is the muon

mean lifetime. However, also in the selected zone, besides the charged pionsthere are many events due to random coincidences.

Cut 341stpeak height >30

1stpeak location 48<x<602ndpeak height >50

2ndpeak location 0<x<2502ndpeak rise over the first peak tail >12

Table 4.4: Selection for the second ADC peak.

Since no further pion selection procedures were possible using the ADCsignal the focal plane TDC detector response was used to perform the rejec-tion of the experimental background.

Figure 4.4: Focal plane TDC for even channels after cut 34.


Figure 4.5: Double gaussian fit for the “prompt” peak, cut 34. The yellowline represents the random coincidences, the blue the prompt ones and thered one is their sum.

4.4 Background removal (using the TDC plot)

The selections shown in the previous section were not sufficient to select onlysignals created by pions. There was still a relevant background in the focalplane TDC plots, as it can clearly seen in Fig 4.4.

The chosen was to fit the prompt peak distribution, in order to find howmany events were present in the random background. The known ADC sep-aration time distribution for the events in the “random” zone of the FP TDCplot can be subtracted from the separation time distribution for the eventsin the “prompt” zone of the FP TDC plot. The resulting plot should containonly the information about the pions’ peaks, with a negative exponentialdistribution due only to muon decay. In addition, the value of its integralshould give the total number of pions detected.

The first step was to select the “prompt” and the “random” areas fromthe TDC plot and to calculate the values of their integrals.

The “prompt” zone in the TDC plot was selected in order to find howmany random were present in the TDC peak. The prompt peak was fitted

4.4. BACKGROUND REMOVAL (USING THE TDC PLOT) 49

with a double gaussian function, one for the background and the other forthe prompt coincidences, as shown in Fig. 4.5.

An alternative way to fit the peak was also tested. Since the trend ofthe background in the TDC had an wavelike shape, a fit with a sine plus agaussian function was developed. However the fit using the double gaussianturn out to give the best results.

Afterwards the integral value of the lower gaussian (the dark one in theFig. 4.5) in the prompt zone was calculated. This value gives the number offalse coincidences in the “prompt” zone. The ratio between this number andthe number of events in the “random” zone was calculated. The resultingvalue was used as coefficient to make the difference between the “prompt”and “random” peaks present in the time separation plots. In this way theresultant plot should show only the time distribution of the muon decay, andits decay constant should be around 2.2 µs.

Figure 4.6: Separation time between the two CsI Flash ADC peaks. Leftplot: “prompt” zone (between channel 670 and 690 in the FP TDC); rightplot: “random” zone (between channel 1230 and 3760).

Because of the low statistic in the data the resulting plot was not sowell defined for a single TDC channel, it was necessary to group some X-axis(rebin) channels to clearly see the expected negative exponential distribution.Many tests had been made with different numbers of channels; the final choicewas to group at least 10 channels.


In Fig. 4.7 the results of this analysis is shown for the cut 34; this cuthas been chosen because it was the best and the conditions for this cut havebeen used for all the targets. Also the fit to the exponential function hadbeen done to check the value of the muon mean lifetime. For this set-up thedecay constant was also very close to the right value, but this was not theonly criterion used.

Finally the integral of this final plot was calculated and its value gives thenumber of pions detected by the CsI/SSD detector. This part constitutes themain part of the whole project; many different attempts, fits and comparisonsperformed are not showed in this thesis.

Figure 4.7: Peaks time separation in Flash ADC for “prompt” zone withoutrandom with Rebin (10) after cut 34.

The steps described had been done for every set-up. However for the Car-bon target data the analysis was very difficult due to the low statistics. In thecarbon TDC plots, (see Fig. 4.8), it was very difficult find a “prompt” peak,and so the number of pions for this target can not be precisely evaluated.

4.5. TAGGING EFFICIENCY 51

Figure 4.8: Focal plane TDC for the Carbon, cut 34. On the right rebin(10)has been used.

4.5 Tagging efficiency

The knowledge of the number of photons impacting on the target is an essen-tial ingredient to can calculate the cross section value, as already mentionedin Sec. 3.4.3. The tagging efficiency is the ration between the number ofelectrons detected in the focal plane, and the number of photons which passthrough the collimator and arrive to the target [14]:

εTag =Nγ

Ne−(4.1)

where:

• Nγ is the number of photons which arrive on the target area;

• Ne− is the number of post-bremsstrahlung electrons detected by thefocal plane detector.

During the bremsstrahlung process the photons are emitted at an angle givenby the following formula:

θ ∝ 1

γ=

1E0

mec2


and the photons with higher energy E0 emitted in a cone with a smallerangle.

The tagging efficiency measured during this experiment is not constantfor each focal plane channel, but, as it is possible to see in Tab. 4.5, it de-creases when the photon energy increases (and the electron energy decreases).Therefore the tagging efficiency shown in eq. 4.1 has been calculated for eachfocal plane channel.

During the run period many tagging efficiency runs have been made, withtwo different triggers. For this analysis the data with the focal plane triggerhave been used. For each tagging efficiency run two files have been collected,one with the beam on, and one with the beam off, in order to subtract fromthe eq. 4.1 the signals in the focal plane detector due to the environmentalbackground.

For this analysis a standard code developed by the nuclear physics groupat MAX-Lab was used and the output shows the tagging efficiency for eachfocal plane channel. After a quick check many files have been rejected becauseof problems during the data acquisition and only 16 couples of files have beenused.

Since the tagging efficiency value for each channel appeared almost con-stant through out the run period, an averaged tagging efficiency value wasevaluated for each channel, as shown in Tab. 4.5.

Afterwards a code has been developed to count the number of electronsin each target file for each focal plane channel, and the sum for each channelover the files with the same configuration has been made. Then these num-bers were multiplied for the corresponding values of the tagging efficiency, inorder to calculate the number of photons for each channel. Finally the to-tal number of photons has been derived summing the photons for each focalplane channel.

For the analysis shown in Sec. 4.8, the number of photons for the focalplane channels 0-14, 16-30, 34-46, 48-60 have been grouped.

4.6. CROSS SECTION CALCULATION 53

Channel Average Error0 0.2403 0.00072 0.2361 0.00084 0.2352 0.00076 0.2338 0.00078 0.2345 0.000710 0.2333 0.000712 0.2303 0.000714 0.2315 0.000716 0.2320 0.000818 0.2300 0.000720 0.2286 0.000722 0.2276 0.000724 0.2257 0.000726 0.2256 0.000728 0.2232 0.0007

Channel Average Error30 0.2230 0.000734 0.2193 0.000736 0.2197 0.000738 0.2170 0.000740 0.2164 0.000742 0.2162 0.000744 0.2089 0.000746 0.2054 0.000748 0.2059 0.000750 0.2036 0.000652 0.2021 0.000754 0.2017 0.000756 0.1954 0.000758 0.1972 0.000860 0.1963 0.0008

Table 4.5: Tagging efficiency for each focal plane channel.

4.6 Cross section calculation

The last part of the analysis, once every experimental parameter had beenevaluated, was the calculation of the differential cross section for the differenttargets and different positions of the CsI/SSD telescope. The equation usedfor this calculation is [15]:

dσ

dΩ(Eγ,θ) =

Nπ+(Eγ,θ)

∆Ω ·Nγ · επ+ · d · εdeadtime(4.2)

where:

• dσdΩ

(Eγ,θ) is the differential cross section, calculated at 90° and 60° ( cm2

sr);

• Nπ+(Eγ,θ) is the number of positive pions seen by the detector calcu-lated in the Sec. 4.4;

• ∆Ω is the detector acceptance (330 msr for 90° and 165 msr for 60°);


• Nγ is the number of photons on the target, calculated in the Sec. 4.5;

• επ+ is the telescope π+ detection efficiency1;

• εdeadtime is the correction of the electronic dead-time, unitary value hasbeen used because when the focal plane scalers are inhibited also theacquisition system is blocked;

• d is superficial density of the target interaction centers.

The density of the interaction centers in the target had been calculated usingthe following formula:

d =ρ ·NA · h

A(4.3)

where:

• ρ is the mass density of the target (g/cm3);

• NA is the Avogadro constant (6.022 · 1023 ·mol−1);

• h is the thickness of the target (cm);

• A is the molar mass of the target (14.0318 for the CH2 and 12.0107 forthe C).

Once the cross sections for all the targets were found, it was possible tocalculate the value of the differential cross section of pion photo-productionfrom the proton. This value was calculated subtracting from the cross sectionof the CH2 the value of the background due to the Carbon, then divided bytwo because there are two atoms of Hydrogen in each molecule of CH2; asillustrated by the following formula:

dσ

dΩH=

dσdΩCH2

− dσdΩC

2

1This value has been assumed to be 0.8, the error for this value and the reasons of thishypothesis are explained in Sec 4.7.2.

4.7. ERROR ANALYSIS 55

This equation should also guarantee the removal of the environmentalbackground. Nevertheless during the run period some files without targetand beam have been collected, three with the telescope for the 60° positionand four for the 90° one. No peak has been detected in their TDC plots, sono further operation has been made.

After the cross sections, for the 60° and 90° configuration, were calculated,the error analysis has been made.

4.7 Error analysis

The statistical uncertainties have been calculated for the number of photonsand for the number of pions. For the other terms in the eq. 4.2 the systematicerrors has been valuated.

4.7.1 Statistical uncertainties

The first step to calculate the statistical error for the number of photons wasto find the error for the electrons and the tagging efficiency in each focal planechannel. The tagging efficiency code provided the error for each channel andfor each file, afterwards the error for the tagging efficiency average for eachchannel has been calculated.

For the statistical error for the electrons in each channel the square roothas been used.

Subsequently the error for the photons for each focal plane channel hasbeen calculated using the following formula [17]:

s2f =

n∑i=1

(dfdxi

)2s2i (4.4)

Finally, using again eq. 4.4, the total error for the total number of photonsover all the channels has been calculated.

For the number of pions the statistical analysis was more difficult becausethe value of the fit parameter has been considered. The square root of the


detected event numbers has been used as error for the events in the promptregion.

The error for the random coincidences in the prompt zone has been calcu-lated using the height and the standard deviation of the “random” gaussianprovided by the ROOT fit. Since the fits parameters are correlated, eq. 4.4is not appropriate and the covariance among parameters has to be taken inaccount by using the following formula:

s2f =

n∑i=1

(dfdxi

)2s2i + 2

∑i 6=j

dfdxi

dfdxj

Cov(xi, xj)

For the evaluation of the error for the number of pions, eq. 4.4 has beenused to combine the error for the random coincidences with the errors of thetotal number of events in the “prompt” zone.

Finally the error for the cross section has been calculated combining theerror for the number of photons and the number of pions.

4.7.2 Systematic errors

For the other values involved in the Eq. 4.2 and 4.3 the systematic errorshave been considered, with attention at the instrumental accuracy.

For the value of the targets density the relative errors were calculated anda value of 2% has been used for all the targets due to the systematic errorduring the measurements of their masses and the areas.

For the position of the telescope a value of 1 mm has been assumed forthe uncertainty of its position. The total relative error assumed for the solidangle is 0.02.

The biggest source of systematic error comes from the evaluation of thedetection efficiency of the SSD/CsI telescope. A preliminary simulation forthe pions detection has been made and the value obtained was 9 MeV forperpendicular pions. A more comprehensive calculation is one of the ongoingprojects at the MAX-Lab photonuclear group. Anyway it is reasonable to

4.7. ERROR ANALYSIS 57

suppose that the average threshold for pions with different angles is higherthan 9 MeV.

This parameter is very critical since the energy range of the measuredpions is between 10 and 19 MeV for 90° set-up and between 15 and 26 MeVfor 60° set-up. In particular for the 90° set-up it is possible that many lowenergy pions were not detected by the CsI due to the crystal aging , asdiscussed in Sec. 5.4.

The pion energy values have also been used to calculate the amount ofpions which decay during the flight from the target to the CsI. The time offlight tF has been calculated using the following formula:

tF =d

c√

1− 1( Em

+1)2

where:

• d is the length of the path: 11.5 cm for the 90° configuration and 15.6

cm for 60°;

• c is the speed of light;

• m is the mass of pion;

• E is the energy of incoming pion.

Then is was possible to calculate the amount of pions which do not decayduring the flight using the following equation:

NCsI = e−tF /τ

where τ is the pion mean lifetime. The decay process causes pion loss of5%.

For these reasons it was not possible to assume an error smaller than the20%.


Also for the number of photons on the targets a systematic error waspresent, a value of 1% has been used.

All the systematic errors are shown in Tab 4.6.

Targets density 1%Solid angle 2%

Detection efficiency 20%Number of photons 1%

Table 4.6: Percent systematic errors for the differential cross sections illus-trate in Sec. 5.1

4.8 Energy dependent analysis

The analysis shown above has been made without any consideration to theenergy of the photon beam. This beam was considered monochromatic be-cause the statistics was very low and it was not possible working with dividingthe data for every channel in the focal plane.

Anyway, only for the CH2 1 mm thick, an attempt was made dividingthe focal plane channels, and therefore the events recorded, in four parts:

• group number 0, channels 0-14, energy range of the photons: 167.675

and 170.465 MeV;


and 173.655 MeV;


and 176.646 MeV;


and 179.636 MeV;

The statistics became very low and it was difficult working, in particular,for the first selection (with the lowest photons energy). Finding a peak in

4.9. FURTHER ANALYSES 59

Figure 4.9: Fits around the peak in the TDC plots divided from the lowestenergy of the photons (0 energy), to the highest (3 energy); it is possible tonotice that the best peak is with the highest energy.

the focal plane TDC was impossible and the analysis for the energy between167.675 and 170.465 MeV has not been carried out. In addition the sum ofnumber of the pions of all the four groups, due to the approximate fits, isnot equal to the number found in the main analysis. In Fig. 4.9 the peaksfor the cut number 34 are shown.

The results of this attempt are reported in the next chapter after theresults of the main work.

4.9 Further analyses

The plots obtained by dividing the focal plane channels in four groups (Fig.4.9) show that the signal peak is better defined when the photon beam energyis higher. So two further analysis has been carried out using only a selectionof the events in the focal plane. These analyses are exactly the same as theone previously explained.

The biggest problem for these analysis is that the statistic is very low for


the carbon targets.

Analysis without the lowest energy events

Figure 4.10: Fit around the prompt peak in the analysis with the events fromthe the focal plane channels 16-60, for the CH2 1mm at 90°

The first analysis has been performed rejecting all the events recorded bythe focal plane channels 0 − 14 and a complete analysis for all the targetshas been carried out in order to have a better signal above the randomcoincidences. In this analysis the photon beam energy range was between170.86 and 179.64 MeV.

It is possible to see that the peak in Fig. 4.10 is lower than the peak inFig. 4.4 than around 10%, while the total number of events recorded by theTDC is smaller than 25%.

Analysis with only the highest energy events

Because with the highest energy the signal peak is more evident, a newanalysis using only the events recorded by the focal plane channels 48 − 60

has been performed. With this configuration the photon beam energy was

4.9. FURTHER ANALYSES 61

Figure 4.11: Fit around the prompt peak in the analysis with the events fromthe the focal plane channels 48-60, for the CH2 1 mm at 90° .

between 177.04 and 179.64 MeV. The events plot recorded by the focal planeis shown in Fig. 4.11, the total number of events is a third of the eventsrecorded in the previous analysis, but the peak height is only one half.


Chapter 5

RESULTS AND CONCLUSIONS

In this chapter all the results obtained at the end of the different analysesprocedure are shown. Moreover the results are compared to the results ofother similar experiments and to some theoretical expectations.

5.1 Results

5.1.1 Energy range between 167.7 and 179.6 MeV

The main task of the work analysis was to evaluate the number of pionsrecorded by the detector set-up. In Tab. 5.1 the number of events selectedafter all applied cuts are shown for all the considered targets.

Target Starting Pion 2ndpeak Prompt Numbercondition conditions zone of pions

CH2 1mm 90° 1.5 · 107 4.5 · 106 8.1 · 104 1806± 54 569± 78CH2 2mm 90° 1.1 · 107 3.8 · 106 7.1 · 104 1642± 41 589± 67CH2 1mm 60° 2.0 · 107 2.9 · 106 5.9 · 104 1011± 32 236± 49C 0.5 mm 90° 1.8 · 106 2.9 · 105 2121 32± 8 7± 6C 0.5 mm 60° 4.6 · 105 1.8 · 105 8327 124± 15 21± 13

Table 5.1: Number of events selected during the work for each target.

63

64 CHAPTER 5. RESULTS AND CONCLUSIONS

The number of pions coming from the Carbon is very low, and it was verydifficult to find the correct values; small changes in the fit initial parameterscould significantly modify the final results.

The differential cross sections have been evaluated using the values shownin Tab 4.5 for the number of electrons in each focal plane channel and thevalues shown in Tab. 5.2 for the number of photons impacting on the targets.

Target Number of electrons Number of photonsCH2 1mm 90° 9.045 · 1011 1.9950 · 1011 ± 3.45 · 109

CH2 2mm 90° 4.261 · 1011 9.3957 · 1010 ± 1.63 · 109

CH2 1mm 60° 2.301 · 1011 5.0789 · 1010 ± 8.81 · 108

C 0.5 mm 90° 2.817 · 1011 6.2168 · 1010 ± 1.08 · 109

C 0.5 mm 60° 8.028 · 1010 1.7718 · 1010 ± 3.09 · 108

Table 5.2: Number of electrons and photons for each target for the dataanalysis in the energy range .

The resulting cross section values for all cases are:

• 5.30± 0.73µb/sr for the CH2 1 mm thick at 90°;



• 0.53± 0.45µb/sr for the C 0.5 mm thick at 90°;

• 10.66± 6.3µb/sr for the C 0.5 mm thick at 60°.

It is possible to see that the values for the cross section for CH2 1 and 2mm thick at 90° are compatible thus showing the consistency of the offlineanalysis.

The differential cross sections values for the proton result to be:

• 2.16± 0.52µb/sr for the 90° configuration with the CH2 1 mm thick.


5.1. RESULTS 65

• 2.55± 2.33µb/sr for the 60° configuration.

These results show the good agreement between the cross section valuesthe two different CH2 targets. However the values of the differential crosssections on the proton are smaller than the expected ones shown in Fig. 5.1.Because the energy detection threshold of the CsI detector is at least 9 MeV,it is possible that the lowest energy pions were not detected, as mentionedin Sec. 4.7.2.

The error for the Carbon is very large because of the poor statistics. Itwas difficult to fit the TDC peak and the errors for the fits parameters arelarge. This is partially due to the fact that medium and heavy nuclei are lessefficient in photoproducing pions than nucleons, due to the π+ re-absorptioninside the nuclear medium [19] [20].


The results obtained from the analysis of the events recorded by the focalplane channels 16−60, corresponding to the energy range between 170.7 and179.6 MeV, are shown in Tab. 5.3. It is possible to see that the number ofpions is larger than in the previous analysis. The most probable explanationis that the number of pions is around the same, but the back-ground is smallerand less random coincidences are in the random gaussian.

Target N. of electrons N. of photons N. of pionsCH2 1mm 90° 6.49 · 1011 1.3977 · 1011 ± 2.12 · 109 566± 58CH2 2mm 90° 3.06 · 1011 6.5856 · 1010 ± 9.98 · 108 562± 48CH2 1mm 60° 1.64 · 1011 3.5434 · 1010 ± 5.38 · 108 299± 70C 0.5 mm 90° 2.01 · 1011 4.3393 · 1010 ± 6.58 · 108 12± 6C 0.5 mm 60° 5.74 · 1010 1.2371 · 1010 ± 1.89 · 108 19± 13

Table 5.3: Number of electrons, photons and pions of the analysis in theenergy range between 170.7 and 179.6 MeV.

The cross sections values are:






• 13.45± 9.2µb/sr for the C 0.5 mm thick at 60°.

The differential cross sections for the proton result to be:



• 7.60± 4.78µb/sr for the 60° configuration.

It is possible to note that the results for CH2 1 and 2 mm are in agreement,and that the value of the cross section are bigger than in the previous analysis.In particular for the 60° configuration the value is close to expected valuesillustrated in the Sec. 5.2.


The results obtained after the analysis of the events recorded by the focalplane channels 48-60, corresponding to the energy range between 177.7 and179.6 MeV, are shown in Tab. 5.4.

The value for the cross sections are:



• 40± 10.3µb/sr for the CH2 1 mm thick at 60°;


5.1. RESULTS 67

Target N. of electrons N. of photons N. of pionsCH2 1mm 90° 1.92 · 1011 3.8564 · 1010 ± 3.54 · 108 232± 26CH2 2mm 90° 9.19 · 1010 1.8424 · 1010 ± 1.69 · 108 290± 24CH2 1mm 60° 4.78 · 1010 9.5950 · 109 ± 8.83 · 107 113± 29C 0.5 mm 90° 5.86 · 1010 1.1761 · 1010 ± 1.08 · 108 4.8± 4C 0.5 mm 60° 1.68 · 1010 3.3637 · 109 ± 3.12 · 107 5.5± 6

Table 5.4: Number of electrons, photons and pions of the analysis in theenergy range between 177.0 and 179.6 MeV.

• for the C 0.5 mm thick at 60° the statistic is too low and it is impossibleto see any peak over the background.

The differential cross section for the proton has been calculated only for the90° configurations and they result to be:



These are the best results for the CH2 at 90° and their average is: 5.16 ±0.60µb/sr .

From the results shown in the previous sections it is possible to observethat the cross sections increase selecting events with higher incoming photonsenergy. In particular the value of cross sections for the 90° configurationincrease more than the values for the 60° configuration. Even in Sec. thenumber of detected pions is higher than in Sec. 5.1.1. This is probablydue to a threshold effect in the CsI crystal and it is possible conclude thatits detecting threshold is higher than 9 MeV resulting from the preliminarysimulation. In Tab. 5.5 the energy ranges of pions are shown. Since fromthe results it is possible to see that only when the pion energy is higher than12− 14 MeV the cross section is close to the expected value it is very likelythat the detecting threshold of the CsI is included within this range.


Photon and pion energy (MeV) 90° 60°Eγ = [167.7− 179.6] Sec. 5.1.1 Eπ+ = [10− 19] Eπ+ = [15− 26]Eγ = [170.7− 179.6] Sec. 5.1.2 Eπ+ = [12.25− 19] Eπ+ = [17.75− 26]Eγ = [177.0− 179.6] Sec. 5.1.3 Eπ+ = [16.75− 19] Eπ+ = [23.25− 26]

Table 5.5: Pions energy range for the photon beam energies.

5.2 Comparison with similar experiments andmodels

As previously mentioned, there are not many data available for the chargedpion channel at threshold. One experiment with the same targets but withdifferent angles and energy a slightly higher energy had been performed at theSaskatchewan Accelerator Laboratory, in Canada and the values measuredare shown in Tab. 5.6 [21].

Eγ θc.m. dσ/dΩ (µb/sr)(MeV) (deg) Hydrogen Carbon213 51 10.0± 0.9 14.4± 0.7

81 10.3± 0.8 15.7± 0.8109 6.9± 0.7 10.7± 0.7141 5.2± 0.5 10.1± 0.7

204 51 7.7± 0.7 9.6± 0.681 10.0± 0.7 9.0± 0.6109 6.5± 0.6 7.8± 0.5141 5.0± 0.5 7.5± 0.5

194 51 8.6± 0.7 5.9± 0.581 7.9± 0.6 6.1± 0.5109 5.1± 0.5 4.7± 0.4141 3.8± 0.5 3.4± 0.4

184 51 7.8± 0.6 3.2± 0.481 6.9± 0.5 2.6± 0.3109 2.2± 0.3141 1.7± 0.3

Table 5.6: Values for the differential cross section

5.3. CONCLUSIONS 69

It is important to emphasize that the data are collected with differentangle (81° for the Saskatchewan data and 90° for MAX-Lab data), but thevalues from this work, in particular for the events with highest energy, seemto be in a good agreement with the trend of Saskatchewan points.

A partial-wave analysis procedure (SAID), which take into account theexisting π production data has been developed at the center for Nuclear Studyat George Washington University (USA) [22]. In Fig. 5.1 the differential crosssection curve predicted by this model is compared to the results obtained inthis thesis.

The relevant statistical errors and the limited angular range of the mea-sured points prevents a detailed comparison with the SAID model. However,the satisfactory agreement that is obtained shows that this feasibility testhas been successful and a more comprehensive data taking can be then beplanned.

5.3 Conclusions

The best values for the differential cross section on the proton at 60° is7.60 ± 4.78µb/sr, gotten with the photon beam energy between 170.7 and179.6 MeV. The statistic collected with the photon beam energy between177.0 and 179.6 MeV is too low and it is impossible to evaluate the crosssection from the Carbon at 60°.

For the configuration at 90° the best value is 5.16± 0.60µb/sr, obtainedwith the photon beam energy between 177.0 and 179.6 MeV, because only inthis range the pions energy is certainly higher then the threshold of the CsIcrystal.

This analysis has proven that measurements of charged pion photopro-duction cross section with solid targets as CH2 are possible, but some im-provements and new data taking are requested.

The next analysis step will be a simulation to obtain an accurate valueof the energy detection threshold and the corresponding efficiency for the


Figure 5.1: The obtained differential cross section points obtained in thisthesis are compared to the pion photoproduction SAID predictions.

CsI/SSD telescope. Then it will be need a new and longer data taking periodin order to have an higher statistic. Moreover it will be necessary to measurethe differential cross section at different angles in order to perform an accurateextraction of the multipole values and to make a sensible comparison withthe model expectations.e end it will be possible to say if this experiment willconfirm the value provided by the theory .

Bibliography

[1] G.V. O’Rielly et al., Charged Pion Photoproduction from Threshold upto the First Resonance Region, Proposal submitted to the MAX-lab,2004.

[2] W. Briscoe et al., Summary of the MAX-Lab Run Period 27, 2010.06.07-2010.07.05, MAX-Lab internal report.

[3] Kennet A. Magno, Pion photoproduction in the energy range betweenthreshold and the ∆− resonance region, thesis, 2008.

[4] K.S. Krane, Introductory Nuclear Physics. John Wiley and Sons, Inc.,New Jersey, 1988

[5] Particle data group, Particle Physics Booklet 2010, website:http://pdg.lbl.gov/

[6] H. Rollnik, Photoproduction, Lectures Cern Eastern School, 1965.

[7] D. Drechsel, L. Tiator, Threshold pion photoproduction on nucleons,Journal of Physics G18 (92), 449,

[8] E. Kormaz at al., Measurement of the γp→ π+n Reaction near Thresh-old, Physical Review Letters 83, 3609, 1999.

[9] V. Bernard et al., Chiral corrections to the Kroll-Ruderman theorem,Physic Letters B 383, 116-120, 1996.

71

72 BIBLIOGRAPHY

[10] M. Fuchs et al., Neutral pion photoproduction from the proton nearthreshold, Physic Letters B 368, 20-25, 1996.

[11] Information and pictures from the MAX-Lab website:http://www.maxlab.lu.se/maxlab/about/index.html.

[12] E. J. Burge, Atomic Nuclei and Their Particles, Oxford Science Publi-cations, 1988.

[13] W.R. Leo. Techniques for Nuclear and Particle Physics Experiments.Springer- Verlag, New York, 2nd edition, 1994.

[14] Jürgen Ahrens, Experiment with real photons, Internal report, Mainz,1993.

[15] J. Lilley, Nuclear Physics, principles and applications, Wiley & Sons,2006.

[16] Electromagnetic Interactions of Hadrons, Plenum Press, New York,1978.

[17] P. Pedroni, A. Rotondi, A. Pievatolo, Probabilità Statistica e Simu-lazione, Springer, Milano 2005.

[18] D. Drechsel, Hadron structure at low Q2, Reviews of Modern Physics,2008.

[19] P. Golubev, Pion emission in 2H, 12C, 27Al (γ, π+) reactions at thresh-old, Nuclear Physics A 806, 216, 2008.

[20] J. R. M. Annand et al., High Resolution Measurements of 12C and theImplication for the (γ, N) Reaction Mechanism at Intermediate Energy,Physical Review Letters 71, 2702, 1993.

[21] K. G. Fissum et al., Inclusive positive pion photoproduction, PhysicalReview C 53, 1278, 1996.

BIBLIOGRAPHY 73

[22] SAID interactive multipole analysis,http://gwdac.phys.gwu.edu/analysis/pr_analysis.html

[23] Andreas Fuhrer, Pion photoproduction in a non-relativistic theory, Nu-clear Physics b 692, 130, 2010.

74 BIBLIOGRAPHY

Acknowledgements

If I forget an equation or a picture it doesn’t get offended, but if I forgetsomebody he has all the rights to get offended...so this is really the mostdifficult part of this thesis!! And I am very sorry if I have forgotten somebody.

The first thank you is for Paolo Pedroni who helped me in Italy and inparticular for suggesting me the MAX-Lab as my Erasmus destination.

A big thank you to Lennart Isaksson and Jason Brudvik and to all theNuclear Physics group for their help and suggestions during my stay in Swe-den. I have to thank Jason for his patient, especially for my questions aboutC++ and ROOT!

Then I want to acknowledgement all the people living in the flat in SanktMånsgatan, 23 street. Thank you to all the Carlehed family, Mats, Hannaand all the sons and company (little Joshi, Sam, Simon, Alex, Marcus, An-dreas and everyone who walked that, even better, those doors), for havingme feel like I was at home during my period in Lund, and to Catherine forher help with my English the company and all the chat during the dinners.I want to see all of you soon in Italy!

Ci sono ancora tantissime persone che ho incontrato durante questi annidi università, ed è difficile anche solo incominciare, cerco di andare con unpo’ di ordine iniziando dalla gente di Pavia. Partendo dai primi come noncitare il nucleo storico di Fisica formato Smartuz, Giofanni, Michele, Aleffio,Polpi, la Ele, Dario, Paolo a cui poi si sono aggiunti Grigno (già presente acasa), Bonfus, Lucia (sì, lo so che facevi Fisica dal primo anno, ma non è dicerto colpa nostra se non ci parlavi!!). E tutta la gente che ho conosciuto a

75

76 BIBLIOGRAPHY

Pavia al di fuori del dipdip: i miei coinquilini, Giulia, Michela, i coinquilinie morosi/morose di amici/he e compagni di corso, gli amici del treno BG-MI-PV della domenica sera. Un pensiero anche agli amici della Ronda dellaSolidarietà del martedì sera, sia ai volontari ma anche ai tanti visi ed occhibisognosi incontrati in questi anni.

Grazie a tutti quelli che hanno sopportato con estrema pazienza le miedomande e dubbi di questi anni, soprattutto ai Micheli e a Pietro per lerisposte alle mie domande riguardanti ROOT e C++, e un grazie anche adAntonio per avermi permesso di impiantarmi a casa sua dopo il ritorno dallaSvezia, ed ai suoi coinquilini per avermi accolto e sfamato.

Un ringraziamento anche ai compagni della SISN: Andrea, James, An-napia, Mary a tutti gli altri, ma soprattutto a Swiffer.

Ringrazio poi tutte le persone incontrate durante gli anni di scout, chesono stati una presenza costante e parallela alla vita universitaria e civile.Grazie a coloro che sono stati in staff con me (la prima staff non si dimenticamai, Emmino, Chiara e la Sghè), ai miei esploratori, ai miei rover, alla genteincontrata agli incontri nazionali o lungo un sentiero.

Un grazie anche a Luca, pur avendo avuto poco tempo di stare insiemedurante i miei anni a Pavia, sapevo che era sempre presente in caso di bisogno.

Un ringraziamento particolare va ai miei genitori per avermi permessodi studiare quello che preferivo, sostenendo sempre ogni mia scelta anchequando io stesso non apparivo del tutto convinto.

Credo proprio di aver concluso...ah no! Mi stavo quasi dimenticando (no,non è assolutamente vero!) del ringraziamento, anzi dei ringraziamenti chedevo ad Elena, per tutto il tempo passato insieme, per le sue visite in Svezia,per avermi (o averti?) sopportato, per le risposte puntuali ai miei dubbi diinglese e per tante altre cose che per ovvi motivi di spazio non posso elencare.

Sicuramente mi sono dimenticato di inserire qualcuno, quindi, chiunquetu sia: Grazie anche a te!

Un abbraccio a tutti.

Federico

Documents

Measurement of the charged pion photoproduction cross ... 11 detecting photons energy range was set from 167:675 MeV to 179:636 MeV [2]. The target selected was the hydrogen contained