Principles Of Radiation Interaction In Matter And Detection

P R I N C I P L E S

OF

Radiation Interaction Matter and Detection

P R I N C I P L E S

OF

\ Rddidtion Interaction 1N

\

Matter and Detection

Claude Leroy University of Montreal, Montreal, Canada

Pier-Giorgio Rancoita Istituto Nazionale di Fisica Nucleare, Milan, Italy

Y§£ World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • S H A N G H A I • H O N G K O N G ' T A I P E I • CHENNAI

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PRINCIPLES OF RADIATION INTERACTION IN MATTER AND DETECTION Copyright © 2004 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.

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ISBN 981-238-909-1

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To Our Families For their patience and encouragement

Preface This book originates from lectures given to undergraduate and graduate students over several academic years. Students questions and interests have driven the need to make systematic and comprehensive (we hope) the presentation of the basic principles of a field which is under continuous development. The physics principles of radiation interaction with matter are introduced as a general knowledge background needed to understand how radiation can be detected. Technical developments are making available detectors and detecting media of increasing complexity. Historically, the first nuclear particle detectors (like those based on X-rays films) were very simple. In the course of time, the detectors have become more and more sophisticated. In addition, complex systems of detectors generally targeting a wide range of physics goals led to large experimental apparata often constituted by several sub-detectors. These large detector assemblies require dedicated methods of reconstruction and analysis of data to decrease the experimental errors. Therefore, both detectors and detection methods are fields of developments and investigations. To be detected, radiation and particles have to interact during their passage through a medium. Therefore, the first chapters are dealing with collision and radiation energy losses by charged particles, photon absorption and nuclear collision in matter. A particular attention has been given to the discussion of both the energy loss and the energy straggling, and the absorption of photons and hadrons in media. The second part of the book covers the particle energy determination, solid state, wire chambers and droplet detectors, and applications in the field of nuclear medicine. Detailed examples are presented which illustrate the operation of the various types of detectors, and help the understanding of the optimization factors. We are grateful for the help received from individuals and groups of students in writing this book. The chapters on electromagnetic and hadron interactions in matter have taken advantage of discussions with undergradvii

viii

Principles of Radiation Interaction in Matter and Detection

uate and graduate students of the University of Milan and Montreal. Their questions have helped the shaping of the content of these chapters. Help for the drawing of some of the figures and assistance have been provided by Pasquale D'Angelo from the National Institute of Nuclear Physics (Milan) and Dr. Simonetta Pensotti from the University of Milano-Bicocca. The chapters on solid state and nuclear medicine benefitted from the input of Celine Lebel PhD student at the University of Montreal and Dr. Patrick Roy former PhD student at the Montreal University. We have to acknowledge our collaborators of the SICAPO collaboration for the scientific achievements in the field of high energy electromagnetic and hadronic shower propagation in matter presented in the chapter on particle energy determination. Sections of the chapter on droplet detectors present results obtained in the framework of the PICASSO experiment in Montreal. They are the result of collaboration with Profs. Louis Lessard and Viktor Zacek of Montreal University. Input on this chapter has also been provided by Marie-Helene Genest. The part of the chapter on wire chambers dealing with ionization chambers and their application in the measurement of liquid argon purity borrows material developed with our Dubna colleagues, in particular Drs. Alexander Tcheplakov and Victor Kukhtin. We wish to thank many Authors and Editors who permitted us to reproduce adapt figures from their articles or books. For their permission in reproducing materials and figures, we acknowledge the Annual Review of Nuclear Science, the American Physical Society (APS), Cambridge University Press, European Organization for Nuclear Research (CERN), Elsevier, the International Atomic Energy Agency (IAEA), the Institute of Physics (IoP), the National Academic Press (NAS), Zeitschrift fur Naturforschung, the Oxford University Press, Physica Scripta, the Italian Physical Society (IPS), and Springer-Verlag. We wish to thank for their collaboration Profs. A. Bohr, A. Fasso, R. Fernow, B. Mottelson, B. Povh, J.O. Rasmussen, K. Rith, G.B. Yodh, F. Zetsche, the Particle Data Group at Lawrence Berkeley National Laboratory, and the American Institute of Physics responsible for the succession of E. Segre. The permissions are indicated in figure captions according to the indications from Editors. C. Leroy Universite de Montreal (Quebec) Canada H3C3J7

P.G. Rancoita Istituto Nazionale di Fisica Nucleare 1-20126 Milan Italy 19 March 2004

Contents

vii

Preface 1.

2.

Introduction

1

1.1 Radiation and Particle Interactions 1.2 Particles and Types of Interaction 1.2.1 Quarks and Leptons 1.3 Relativistic Kinematics 1.3.1 The Two-Body Scattering 1.3.2 The Invariant Mass 1.4 Cross Section and Differential Cross Section 1.4.1 Atomic Weight and Atomic Mass Unit 1.5 Detectors and Large Experimental Apparata 1.5.1 Trigger, Monitoring, Data Acquisition, Slow Control 1.5.2 General Features of Particle Detectors and Detection Media

18

Electromagnetic Interaction of Radiation in Matter

27

2.1 Passage of Ionizing Particles through Matter 2.1.1 The Collision Energy Loss of Massive Charged Particles 2.1.1.1 The Shell Correction Term 2.1.1.2 The Density Effect and Relativistic Rise . . 2.1.1.3 Restricted Energy Loss and Fermi Plateau . 2.1.1.4 Energy-Loss Formula for Compound Materials 2.1.2 Energy Loss Fluctuations 2.1.2.1

p"=p-p'

p"2 =p2+p'2-2pp'cos9.

(1.11)

Equation (1.11) can be rewritten taking into account Eq. (1.9): pll2 =p2+

(Ek+meS)2-my

_

2 p c o s

^+mec^r^

which becomes, after substituting p" obtained from Eq. (1.10) and squaring both sides of that equation,

Ek^p2c2+m2c4

= -Ekmec2

+pccos9y(Ek

+ mec2)2 - m2^,

from which we get IE2 + 2EkmeC2 pccos 9J — r^

V

2 r^pr- 5-j fn&cr + VP c + m c »

=

^fc

and finally, by squaring both sides of the equation, we can derive the expression for the kinetic energy Ek of the scattered target particle, we have p -frfc =

2 m e c V cos2 6 ~1. • (m e c 2 + y/p2c2 + m2c4) — p2c2cos2 9

I1-12)

The kinetic energy Ek of the recoiling target particle is the amount of transferred energy in the interaction. From Eq. (1.12), we note that the maximum energy transfer Wm is for 6 = 0, i.e., when a head-on collision occurs. For 9 = 0, Eq. (1.12) becomes: o2c2 m

~~ \mec2 + i (m2/me)

c2 + y/p2c2 + m2c4'

(1.13)

10

Principles of Radiation Interaction in Matter and Detection

From Eq. (1.5), the incoming particle energy Ei is: Ei = mjc2 = y/p2c2 + m2c4. We can rewrite Eq. (1.13) as:

Wm = 2 m e c W [l + ( ^ ) 2 + 2 7 ^ 1 - 1 .

(1.14)

For massive particles (e.g., proton,* K, TT etc.), whose masses are much larger than the electron (or positron) mass, we have m 3> me ( « 0.511 MeV/c 2 ). At sufficiently high energies, for which the incoming momentum p is ^$> ln^c (for instance for an incoming TT with momentum 3> 36 GeV/c, or an incoming proton with momentum ;» 1.7 TeV/c), Eq. (1.13) becomes:

In the extreme relativistic case, a massive particle can transfer all its energy to the target electron in a head-on collision, i.e., a proton can be stopped by interacting with an electron. At lower energies, i.e., when p 2 is: Mli2 = V ( ^ ~ ) = ^j2^^-+m21c2

-V\ -Vl - 2P1P2COS9 + mlc2-2plP2cos9,

(1.19)

where & is the angle between the three-vectors pi and p 2 - F° r example, let us take a proton of 100 GeV incident on a target proton at rest, like in a high-energy physics fixed target experiment. From Eq. (1.19), because P2 = 0, E2 = m2c2, m\ = m 2 RS 1 GeV/c 2 , the available center of mass energy (i.e., the invariant mass) becomes Afi,2 « v / 200TTTT « 14.2 GeV/c 2 .

12

Principles of Radiation Interaction in Matter and Detection

In the scattering between an incoming particle 1 and a target particle 2, we indicate (with the variable s) the invariant quantity: s = (qi+ qif = m\