IL NUCLEARE

Direttore

Ettore GUniversità degli Studi di MilanoPiero Caldirola International Centre for the Promotion of Science

Comitato scientifico

Giuseppe VUniversità degli Studi di Padova

Elio SUniversità degli Studi di Milano–Bicocca

Comitato redazionale

Francesca BUniversità degli Studi di Pavia

Francesco CEuropean Organization for Nuclear Research CERN

Comitato editoriale

Giuseppe BIstituto Nazionale di Fisica Nucleare

Laszlo S BUniversidad Simón Bolívar

Elio SUniversità degli Studi di Milano–Bicocca

Giuseppe VUniversità degli Studi di Padova

IL NUCLEARE

La Fisica Nucleare ha portato a scoperte fondamentali ed è tuttora uncampo di indagine alle frontiere della ricerca che permette in modopeculiare ed esclusivo lo studio della materia elementare in condizioniestreme.

Non meno importante è il suo utilizzo in ricerche e applicazionitecnologiche di immediato interesse per la Società, tra cui oggi sonodi particolare importanza la produzione controllata e sicura di energiae le applicazioni mediche per la diagnosi e la terapia di tumori.

Conclusioni analoghe si raggiungono se si considerano le ricerchesulla radioattività: accanto a studi di carattere fondamentale, le appli-cazioni di tipo medico ed industriale, per il controllo ambientale, lasicurezza, la datazione di reperti sono innumerevoli.

Questa collana si propone la pubblicazione di testi volti a descriverequesta variegata moltitudine di argomenti e a rappresentare una fontedi informazioni obiettive e documentate.

Alessandro Rizzo

High Precision X–Ray SpectroscopicMeasurements of the K–P System

The SIDDHARTA Experiment at the DAΦNE Collider

Preface byAnnalisa D’Angelo

Copyright © MMXVARACNE editrice int.le S.r.l.

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via Quarto Negroni, Ariccia()

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I edition: May

A mio padre

Quelli che s’innamoranodi pratica senza scienza

son come il nocchiere,che entra in naviglio

senza timone o bussola,che mai ha certezza

dove si vada.

L V

4.3 Characterization of the SDD detectors: the response function andthe calibration analysis . . . . . . . . . . . . . . . . . . . . . . . . . 674.3.1 The structure of the response function . . . . . . . . . . . . 674.3.2 Calibration Analysis . . . . . . . . . . . . . . . . . . . . . . 734.3.3 The calibration results . . . . . . . . . . . . . . . . . . . . 794.3.4 Production spectra: the calibration strategy and the SDD

selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.4 The analysis cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

4.4.1 The Drift-Time cut and the Slewing Correction . . . . . . . 854.4.2 The Hit-rate variable definition and the related cut . . . . . 924.4.3 Kaon-Detector coincidence cut . . . . . . . . . . . . . . . . 944.4.4 The cut on DAΦNE currents . . . . . . . . . . . . . . . . . 96

4.5 The iterative simultaneous fit . . . . . . . . . . . . . . . . . . . . . 984.5.1 Characteristics of the SIDDHARTA hydrogen and deuterium

spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 984.5.2 The simultaneous fit - functions definition . . . . . . . . . . 98

Results5.1 The final result on � and Γ parameters . . . . . . . . . . . . . . . .

5.1.1 Discussion on the obtained results . . . . . . . . . . . . . .5.2 The analysis consistency study . . . . . . . . . . . . . . . . . . . .

5.2.1 The old KeK-like iterative simultaneous fit . . . . . . . . .5.2.2 The SIDDHARTA-like iterative fit . . . . . . . . . . . . . .5.2.3 The model-dependent simultaneous fit . . . . . . . . . . . .5.2.4 The direct subtraction methods . . . . . . . . . . . . . . . . 1135.2.5 The analysis consistency study result . . . . . . . . . . . . . 118

5.3 Evaluation of the systematic errors . . . . . . . . . . . . . . . . . . 1195.3.1 The instability of the last phase of the iterative fit . . . . . 1205.3.2 The calibrations systematic errors . . . . . . . . . . . . . . 1205.3.3 Evaluation of the KC5→4 as the reference peak for the CuKα1215.3.4 Correlation of the Pile-up and resolution sigma: the system-

atic error . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1215.3.5 Use of mean Fano and ENC parameters: the systematic error1245.3.6 Hit-rate cut on the hydrogen data: the systematic error . . 1255.3.7 The analysis systematic error . . . . . . . . . . . . . . . . . 1255.3.8 Rate-correction: the systematic error . . . . . . . . . . . . . 1265.3.9 Free ratio for the peaks overlapping the KH signal: the

systematic error . . . . . . . . . . . . . . . . . . . . . . . . 128

Conclusions 1296.1 The SIDDHARTA experimental technique . . . . . . . . . . . . . . 1296.2 The data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

List of Figures 132

105

List of Tables

105

111109

106106

106

135

Prefacennalisa D’Angelo

Observing matter under conditions very different from those weobserve everyday provides important information about the laws thatrule the universe, especially the microscopic world dominated bystrong interactions. The vast majority of the matter surroundingus is made of electrons and nuclei, the latter composed by protonsand neutrons. At the Laboratori Nazionali di Frascati of INFN theSIDDHARTA experiment has been devoted to the production andthe study of “exotic” atoms. These atoms are rare in nature as a Kaonreplaces an orbital electron. The Kaon contains a strange quark, itsmass is a thousand times larger than the electron one and its electricalcharge may be positive, negative or neutral. Negative Kaons mayform a bound system with a target proton known as the Kaonichydrogen. The study of X-ray spectra emitted by such atoms providesinformation about the properties of the strong interaction betweenordinary and strange matter.

The work by Alessandro Rizzo accurately describes the apparatusof the SIDDHARTA experiment and presents in a critical way all thedata analysis steps leading to the interpretation of the X-ray spectraemitted by the Kaonic hydrogen and the Kaonic deuterium atoms.

Special attention is given to the data quality control in terms of sta-bility and reliability of calibrated spectra; accurate iterative proceduresallowed the author to determine the physical parameters of X transi-tions (energy shift and width) with the highest precision, improvingover the published results. The author’s passion and expertise lead thereader towards the understanding of the most advanced results in thefield of exotic atoms.

11

by A

I

Contents

Introduction

The strong interaction in light kaonic atoms2.1 The kaonic hydrogen and the exotic atoms scenario . . . . . .

2.1.1 From the capture to the quantum cascade . . . . . . . . . .2.2 The quantum cascade in exotic hydrogen . . . . . . . . . . . . . .

2.2.1 Stark mixing . . . . . . . . . . . . . . . . . . . . . . . . . .2.2.2 Coulomb de-excitation . . . . . . . . . . . . . . . . . . . . .2.2.3 The external Auger effect . . . . . . . . . . . . . . . . . .2.2.4 Discussion on the experimental techniques for KH studies

2.3 The strong interaction effects in light kaonic atoms . . . . . . . . . 222.3.1 The Deser-type formulae . . . . . . . . . . . . . . . . . . . . 222.3.2 The optical Potential in Schrodinger-type theories . . . . . 252.3.3 The partial wave approach to the low energy scattering . . 26

The SIDDHARTA experiment3.1 The DAΦNE collider . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.1.1 The DAΦNE injection-cycle and the SIDDHARTAproduction run . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.1.2 The DAΦNE calorimeters for luminosity measurement . . 393.2 The SIDDHARTA experimental setup . . . . . . . . . . . . . . . . 40

3.2.1 The IP1 Beam-pipe . . . . . . . . . . . . . . . . . . . . . . 403.2.2 The Kaon-Detector . . . . . . . . . . . . . . . . . . . . . . . 403.2.3 The lead shielding . . . . . . . . . . . . . . . . . . . . . . . 413.2.4 The degrader . . . . . . . . . . . . . . . . . . . . . . . . . . 443.2.5 The target cell . . . . . . . . . . . . . . . . . . . . . . . . . 46

3.3 The Silicon Drift Detector . . . . . . . . . . . . . . . . . . . . . . . 503.3.1 The SDD working principles . . . . . . . . . . . . . . . . . . 503.3.2 The SIDDHARTA detectors, the front-end electronics and

the DAQ chain . . . . . . . . . . . . . . . . . . . . . . . . . 543.3.3 The SIDDHARTA file structure . . . . . . . . . . . . . . . . 59

Data analysis4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4.1.1 The dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.2 Data handling procedures . . . . . . . . . . . . . . . . . . . . . . . 6

4.2.1 Removal of the crosstalk events . . . . . . . . . . . . . . . . 64.2.2 ADC-fluctuations correction . . . . . . . . . . . . . . . . . . 6

9

13

12

4

2020

1919

17

115

35

61

5

20

3

3

11

Preface I

4.3 Characterization of the SDD detectors: the response function andthe calibration analysis . . . . . . . . . . . . . . . . . . . . . . . . . 674.3.1 The structure of the response function . . . . . . . . . . . . 674.3.2 Calibration Analysis . . . . . . . . . . . . . . . . . . . . . . 734.3.3 The calibration results . . . . . . . . . . . . . . . . . . . . 784.3.4 Production spectra: the calibration strategy and the SDD

selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.4 The analysis cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.4.1 The Drift-Time cut and the Slewing Correction . . . . . . . 844.4.2 The Hit-rate variable definition and the related cut . . . . . 914.4.3 Kaon-Detector coincidence cut . . . . . . . . . . . . . . . . 934.4.4 The cut on DAΦNE currents . . . . . . . . . . . . . . . . . 95

4.5 The iterative simultaneous fit . . . . . . . . . . . . . . . . . . . . . 974.5.1 Characteristics of the SIDDHARTA hydrogen and deuterium

spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 974.5.2 The simultaneous fit - functions definition . . . . . . . . . . 97

Results5.1 The final result on � and Γ parameters . . . . . . . . . . . . . . . .

5.1.1 Discussion on the obtained results . . . . . . . . . . . . . .5.2 The analysis consistency study . . . . . . . . . . . . . . . . . . . .

5.2.1 The old KeK-like iterative simultaneous fit . . . . . . . . .5.2.2 The SIDDHARTA-like iterative fit . . . . . . . . . . . . . .5.2.3 The model-dependent simultaneous fit . . . . . . . . . . . .5.2.4 The direct subtraction methods . . . . . . . . . . . . . . . . 1115.2.5 The analysis consistency study result . . . . . . . . . . . . . 116

5.3 Evaluation of the systematic errors . . . . . . . . . . . . . . . . . . 1175.3.1 The instability of the last phase of the iterative fit . . . . . 1185.3.2 The calibrations systematic errors . . . . . . . . . . . . . . 1185.3.3 Evaluation of the KC5→4 as the reference peak for the CuKα1195.3.4 Correlation of the Pile-up and resolution sigma: the system-

atic error . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1195.3.5 Use of mean Fano and ENC parameters: the systematic error1225.3.6 Hit-rate cut on the hydrogen data: the systematic error . . 1235.3.7 The analysis systematic error . . . . . . . . . . . . . . . . . 1235.3.8 Rate-correction: the systematic error . . . . . . . . . . . . . 1245.3.9 Free ratio for the peaks overlapping the KH signal: the

systematic error . . . . . . . . . . . . . . . . . . . . . . . . 126

Conclusions 1276.1 The SIDDHARTA experimental technique . . . . . . . . . . . . . . 1276.2 The data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

List of Figures 131

103

List of Tables

104

109107

104104

104

133

12 Contents

Introduction

Introduction

The study of the strong interaction at low energies is nowadays one of themain topics of the modern particle physics. The improvements reached so far inthe experimental techniques, both in accelerator and detector sectors, allowed toperform high precision measurements which led to a deeper understanding of thefield. In particular, a fundamental role has been played by the X-ray measurementsof hadronic exotic atoms, bound systems made of a negative charged hadron (X−)and a target atom. The X− particle, after being captured in an external atomicorbital replacing the electron, forms the hadronic atom bound system and starts aseries of electromagnetic (EM) transitions towards the low lying levels. The lasttransitions, when the hadron comes closer to the nucleus, are radiative in X-rayband and are dictated by both the electromagnetic and the strong interactions.The presence of strong interactions involves a shift of the emitted photon energy �and a broadening of the width Γ with respect to the pure EM case. By comparingthese transition energies (few keV) and the hadronic scale (about 1 GeV), it isstraightforward to understand why these systems offer the unique possibility toperform experiments equivalent to scattering at vanishing relative energy, allowingto study strong interactions in the non-perturbative regime without requiringdata-extrapolations.The subject of the present work is the experimental investigation of the KaonicHydrogen (KH) atom, the fundamental bound system among the Light KaonicAtoms (LKA). The presence of the K− particle in this bound system opens thelow-energy strangeness sector to the physical investigation, providing the accessto the fundamental low energy parameter aK−p, the complex s-wave kaon-protonscattering length. The aim of this thesis is to extract the most precise values ofthe � and Γ parameters from the KH X-ray data collected by the SIDDHARTA(SIlicon Drift Detector for Hadronic Atom Research with Timing Application)experiment. This result has been achieved thanks to a deep knowledge of theSIDDHARTA experimental techniques together with the development of specificanalysis techniques. The participation of the author of the present thesis to allthe phases of the SIDDHARTA experiment, starting from the first preliminarytests on the detectors to be used (subject of a first level degree thesis [1]), to theoptimization of the experimental apparatus (subject of a second level degree thesis[2]) and to the data-taking shifts, allowed a deep understanding of the SIDDHARTAexperimental technique. Moreover the author’s efforts during these years in thedata analysis allowed to develop specific analysis techniques, all used in this work.The application of different analysis techniques to the same analyzed data hasgranted to this thesis a secondary aim which is an analysis consistency study.The thesis is structured as follows. In the second chapter we introduce the basicconcepts of the exotic atoms physics, pointing out the processes which take placein KH system constraining the experimental techniques. The optical potentialapproach is then treated in order to show how the experimental X-ray measurement

13

Chapter I

13

High precision X-ray spectroscopic measurements of the K−p system

can be related to a theoretical framework. The third chapter is dedicated to thedescription of the SIDDHARTA experiment on the DAΦNE collider, the Φ-factoryof the LNF-INFN. A detailed description of the different parts of the experimentalapparatus is given, highlighting how the KH physical processes constraints theexperimental part. The fourth chapter presents the KH analysis result. In order toextract the most precise value of � and Γ parameters, several studies and correctionsare needed before apply the final analysis technique. In particular the data-handlingprocedures to remove the cross-talk events and to correct the ADC fluctuations,the correct evaluation of the detectors response function and the definition andoptimization of cuts criteria are necessary. In this work the final result on � andΓis extracted using Kaonic Deuterium (KD) collected data too, in order to preciselyevaluate the background contribution in the KH spectrum. The final chapterpresents the obtained final result, where the total error is reduced by the 17 % on� and the 13 % on Γ with respect to the already published SIDDHARTA data, themost precise so far. The consistency study obtained by applying different analysistechniques data is then presented, demonstrating the good agreement among verydifferent analysis methods. The estimation of the systematic error contributions isdescribed in detail in the last part of the chapter. A discussion on the obtainedresults concludes the work.

14 Introduction14 Introduction

High precision X-ray spectroscopic measurements of the K−p system

can be related to a theoretical framework. The third chapter is dedicated to thedescription of the SIDDHARTA experiment on the DAΦNE collider, the Φ-factoryof the LNF-INFN. A detailed description of the different parts of the experimentalapparatus is given, highlighting how the KH physical processes constraints theexperimental part. The fourth chapter presents the KH analysis result. In order toextract the most precise value of � and Γ parameters, several studies and correctionsare needed before apply the final analysis technique. In particular the data-handlingprocedures to remove the cross-talk events and to correct the ADC fluctuations,the correct evaluation of the detectors response function and the definition andoptimization of cuts criteria are necessary. In this work the final result on � andΓis extracted using Kaonic Deuterium (KD) collected data too, in order to preciselyevaluate the background contribution in the KH spectrum. The final chapterpresents the obtained final result, where the total error is reduced by the 17 % on� and the 13 % on Γ with respect to the already published SIDDHARTA data, themost precise so far. The consistency study obtained by applying different analysistechniques data is then presented, demonstrating the good agreement among verydifferent analysis methods. The estimation of the systematic error contributions isdescribed in detail in the last part of the chapter. A discussion on the obtainedresults concludes the work.

14 IntroductionThe strong interaction in light kaonic atoms

The strong interaction in light kaonic atoms

In this chapter the theoretical approach to the hadronic interaction in lightkaonic atoms is reviewed. The chapter is organized in three main parts. Thefirst one is dedicated to a short introduction to the exotic atom physics, includingthe historical point of view. The second part is dedicated to the capture, thequantum cascade and the competitors processes which constraint the experimentaltechnique, with a focus on the KH case. The last part presents the theoreticaldescription of the strong interactions in kaonic atoms. A review on Deser-typeformulae is followed by the description of the optical potential approach to thehadronic atoms.

2.1 The kaonic hydrogen and the exotic atoms scenario

An exotic atom is an atom which captured a negative charged long-lived particle(a lepton or a hadron) in an atomic orbit. Postulated since early 40’s [3][4][5], theexistence of such systems was first established only in 1951 by the observation ofAuger electrons from pionic and muonic silver and bromine in photographic emul-sions (see fig 1), exposed in the stratosphere on board of meteorological balloons [6].

Figure 1: The original caption of ref. [6]: “Mosaic of a π-meson and anassociated low energy electron. The meson track goes to the rightand down. A clump of silver grains can be seen at the end of themeson track which is indicated by an arrow. The track of a 45 keVelectron can be seen below the meson track.” (Source : W.F. Fry(1951) Phys. Rev. 83, 594− 597)

Since the beginning the X-ray spectroscopy of these bound systems was usedto study the properties and the fundamental interactions of the nucleons and thecaptured particles.

15

Chapter II

15

High precision X-ray spectroscopic measurements of the K−p system

Let us consider the expressions for the binding energies (eq. 1), the Bohr radius(eq. 2) and its expectation value (eq. 3) of such systems:

Bn = μ c2α2Z2

2n2 (1)

rB = �cμc2αZ (2)

�rn� = rB

[3n2 − �(�+1)

2

](3)

where the symbols α, Z, n and � denote the fine structure constant (α−1 =137.036), the nuclear charge, the principal quantum number and the angularmomentum respectively. The reduced mass μ is defined as μ = (mAmH)/(mA +mH), where mA is the nucleus mass and mH the hadron mass. Equation 1 showsthe linear dependence of Bn on the reduced mass μ of the system, whilst theequation 2 and the equation 3 point out the inverse dependence of the Bohr radiusand its expectation value on μ. Therefore, when the captured particle comes tolower levels (small n), the geometrical dimension of the bound system may becompared to the dimensions of a nucleus, allowing to perform a large variety ofstudies. In particular [7]:

• strong interaction at very low energies (hadronic atoms)

• masses and magnetic moments of negatively charged particles

• test of electro-weak interactions (muonic atoms)

• muon-catalyzed fusion

The major motivation for the hadronic atoms study is the investigation ofthe strong interaction at very low energies. Since the hadron-nucleon scatteringprocesses require a low-energy extrapolation to perform such investigation, thehadronic atoms have always been fundamental in the field, because no such extrap-olation is required. This characteristic is due to the kinetic energy of the hadronin the last transitions, which is of the order of few keV. For example, in the kaonichydrogen, the comparison of such energy (6 keV circa for the 2p → 1s transition)with the K− mass (493.667 MeV), shows the kaon can be considered almost atrest when it strongly interacts with the proton. The information about the stronginteraction in hadronic atoms naturally emerges by comparing their transitions tolow-lying bound states, dictated by both electromagnetic and strong interactions,with the pure EM calculated transitions. In particular the hadronic hydrogen anddeuterium give access to fundamental low energy parameters: the hadron-protonand the hadron-neutron scattering lengths respectively.The theoretical descriptions of hadronic atoms have followed the different ap-proaches developed to describe the low-energy strong interactions, in particularthe optical potential, the meson exchange and the chiral perturbation theory (χPT).

16 High Precision X–Ray Spectroscopic Measurements of the K-P System16 High Precision X–Ray Spectroscopic Measurements of the K–P System

High precision X-ray spectroscopic measurements of the K−p system

Let us consider the expressions for the binding energies (eq. 1), the Bohr radius(eq. 2) and its expectation value (eq. 3) of such systems:

Bn = μ c2α2Z2

2n2 (1)

rB = �cμc2αZ (2)

�rn� = rB

[3n2 − �(�+1)

2

](3)

where the symbols α, Z, n and � denote the fine structure constant (α−1 =137.036), the nuclear charge, the principal quantum number and the angularmomentum respectively. The reduced mass μ is defined as μ = (mAmH)/(mA +mH), where mA is the nucleus mass and mH the hadron mass. Equation 1 showsthe linear dependence of Bn on the reduced mass μ of the system, whilst theequation 2 and the equation 3 point out the inverse dependence of the Bohr radiusand its expectation value on μ. Therefore, when the captured particle comes tolower levels (small n), the geometrical dimension of the bound system may becompared to the dimensions of a nucleus, allowing to perform a large variety ofstudies. In particular [7]:

• strong interaction at very low energies (hadronic atoms)

• masses and magnetic moments of negatively charged particles

• test of electro-weak interactions (muonic atoms)

• muon-catalyzed fusion

The major motivation for the hadronic atoms study is the investigation ofthe strong interaction at very low energies. Since the hadron-nucleon scatteringprocesses require a low-energy extrapolation to perform such investigation, thehadronic atoms have always been fundamental in the field, because no such extrap-olation is required. This characteristic is due to the kinetic energy of the hadronin the last transitions, which is of the order of few keV. For example, in the kaonichydrogen, the comparison of such energy (6 keV circa for the 2p → 1s transition)with the K− mass (493.667 MeV), shows the kaon can be considered almost atrest when it strongly interacts with the proton. The information about the stronginteraction in hadronic atoms naturally emerges by comparing their transitions tolow-lying bound states, dictated by both electromagnetic and strong interactions,with the pure EM calculated transitions. In particular the hadronic hydrogen anddeuterium give access to fundamental low energy parameters: the hadron-protonand the hadron-neutron scattering lengths respectively.The theoretical descriptions of hadronic atoms have followed the different ap-proaches developed to describe the low-energy strong interactions, in particularthe optical potential, the meson exchange and the chiral perturbation theory (χPT).

16 High Precision X–Ray Spectroscopic Measurements of the K-P SystemThe strong interaction in light kaonic atoms

The latter, an effective-theory inspired by QCD properties, can be tested with highprecision using kaonic hydrogen (KH) and deuterium (KD). The captured K−

opens the access to the strangeness sector indeed, making KH and KD two suitableframeworks to test the three-flavour χPT.Since the introduction of high-resolution semiconductors detectors, the kaonichydrogen X-ray spectroscopy belongs to the field of high precision physics1.

Basics concepts of the exotic atom physics: As already introduced, anexotic atom is formed when a negative charged long-lived particle X− is capturedin an external atomic orbital. During the capture process the X− particle replacesthe atomic electron of the capturing-orbital by ejecting it, forming the new exoticsystem. The binding energies scale approximately as the ratio of the negativeparticle mass and the electron one (mX−/me). Therefore the new principal quantumnumber n0 is given by the formula [8][9]:

n0 =

√μ

me≈ ne

√mX−

me(4)

where ne is the principal quantum number of the outermost electron shell2. Fromthe n0 level the hadron starts a series of electromagnetic transitions towards thelower levels (quantum-cascade). If Z > 1, the electron shells beneath are depletedthrough Auger emission till the formation of a hydrogenoid system X−-nucleus.From this point to the end of the cascade process, in an ideal case, all the transitionswould be radiative. In the last ones, when the hadron is closer to the nucleus andthe strong interactions are not negligible, X-rays are emitted. The presence of thestrong interaction causes an energy shift (�) and a broadening of the width (Γ) ofthe transition line respect to a pure EM interaction, experimentally measured byusing X-ray spectroscopy techniques. The link with the theoretical side is givenby the Deser-type formulae (see subsection 2.3.1), where � and Γ are, in a firstapproximation, recognized as the real and the imaginary part of a complex s-wavehadron-nucleon scattering length (Z=1), a parameter which can be calculated indifferent theoretical frameworks. The last phase, namely the nuclear absorption,takes place after the last X-ray transitions, ending the lifetime of the bound system.

2.1.1 From the capture to the quantum cascade

In this paragraph we describe in detail the physical processes which take placeduring the lifetime of an exotic bound system. The most important ones, whichconstrain some parts of the experimental technique, are the capture and the cascadeprocesses.

1The early experiments before the introduction of semiconductors detectors measured X-raysfrom several tens of keV to the MeV range by using NaI(Tl) scintillators [7].

2Let us consider as an example the kaonic hydrogen case. When the K− replace the atomicelectron (n = 1), the new principal quantum number of the bound system is n0 = 29, accordingto the eqn. 4

17II. The strong interaction in light kaonic atoms 17ii. The strong interaction in light kaonic atoms