Particles and Nuclei: An Introduction to the Physical Concepts

393 Pages·2006·7.19 MB·English

by  Professor Dr. Bogdan Povh, Professor Dr. Klaus Rith, Dr. Christoph Scholz, Dr. Frank Zetsche (auth.)

ParticlesandNuclei
An Introduction to the Physical Concepts
Bogdan Povh Klaus Rith
Christoph Scholz Frank Zetsche
Particles
and Nuclei
An Introduction
to the Physical Concepts
TranslatedbyMartinLavelle
FifthEdition
With148Figures,11Tables,and58ProblemsandSolutions
123
ProfessorDr.BogdanPovh ProfessorDr.KlausRith
Max-Planck-InstitutfürKernphysik PhysikalischesInstitut
Postfach103980 derUniversitätErlangen-Nürnberg
69029Heidelberg,Germany Erwin-Rommel-Strasse1
91058Erlangen,Germany
Dr.ChristophScholz Dr.FrankZetsche
SAPAG UniversitätHamburgund
Postfach1461 DeutschesElektronen-Synchrotron
69185Walldorf,Germany Notkestrasse85
22603Hamburg,Germany
Translator:
Dr.MartinLavelle
InstitutdeFísicad’AltesEnergies
FacultatdeCiències
UniversitatAutònomadeBarcelona
08193Bellaterra(Barcelona),Spain
TitleoftheoriginalGermanEdition:
B.Povh,K.Rith,C.Scholz,F.Zetsche:TeilchenundKerne
EineEinführungindiephysikalischenKonzepte.
(7.Auflage)
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ISBN-10 3-540-36683-0 5thEditionSpringerBerlinHeidelbergNewYork
ISBN-13 978-3-540-36683-6 5thEditionSpringerBerlinHeidelbergNewYork
ISBN 3-540-20168-8 4thEditionSpringerBerlinHeidelbergNewYork
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Preface
In the last two editions we included new results on the neutrino oscillations
as evidence for a non-vanishing mass of the neutrinos.
In the present edition we have rewritten the chapter on “Phenomenology
oftheWeakInteraction”(Chapter10)inordertogiveacoherentpresentation
oftheneutrinoproperties.Furthermore,weextendedthechapteron“Nuclear
Thermodynamics” (Chapter 19).
Heidelberg, July 2006 Bogdan Povh
Preface to the First Edition
The aim of Particles and Nuclei is to give a unified description of
nuclear and particle physics because the experiments which have uncovered
thesubstructureofatomicnucleiandnucleonsareconceptuallysimilar.With
theprogressofexperimentalandtheoreticalmethods,atoms,nuclei,nucleons,
and finally quarks have been analysed during the course of this century. The
intuitive assumption that our world is composed of a few constituents — an
idea which seems attractive, but could not be taken for granted — appears
to be confirmed. Moreover, the interactions between these constituents of
matter can be formulated elegantly, and are well understood conceptionally,
within the so-called “standard model”.
Once we have arrived at this underlying theory we are immediately faced
withthequestionofhowthecomplexstructuresaroundusareproducedbyit.
Onthewayfromelementaryparticlestonucleonsandnucleiwelearnthatthe
“fundamental” laws of the interaction between elementary particles are less
and less recognisable in composite systems because many-body interactions
cause greater and greater complexity for larger systems.
This book is therefore divided into two parts. In the first part we deal
with the reduction of matter in all its complication to a few elementary con-
stituentsandinteractions,whilethesecondpartisdevotedtothecomposition
of hadrons and nuclei from their constituents.
We put special emphasis on the description of the experimental concepts
but we mostly refrain from explaining technical details. The appendix con-
tains a short description of the principles of accelerators and detectors. The
exercises predominantly aim at giving the students a feeling for the sizes of
the phenomena of nuclear and particle physics.
Whereverpossible,werefertothesimilaritiesbetweenatoms,nuclei,and
hadrons, because applying analogies has not only turned out to be a very
effectiveresearchtoolbutisalsoveryhelpfulforunderstandingthecharacter
of the underlying physics.
We have aimed at a concise description but have taken care that all the
fundamental concepts are clearly described. Regarding our selection of top-
ics, we were guided by pedagogical considerations. This is why we describe
experiments which — from today’s point of view — can be interpreted in a
straightforwardway.Manyhistoricallysignificantexperiments,whoseresults
can nowadays be much more simply obtained, were deliberately omitted.
Particles and Nuclei(Teilchen und Kerne)isbasedonlectureson
nuclearandparticlephysicsgivenattheUniversityofHeidelbergtostudents
in their 6th semester and conveys the fundamental knowledge in this area,
which is required of a student majoring in physics. On traditional grounds
these lectures, and therefore this book, strongly emphasise the physical con-
cepts.
We are particularly grateful to J. Hu¨fner (Heidelberg) and M. Rosina
(Ljubljana)fortheirvaluablecontributionstothenuclearphysicspartofthe
book.WewouldliketothankD.Dubbers(Heidelberg),A.Fa¨ßler(Tu¨bingen),
G. Garvey (Los Alamos), H. Koch (Bochum), K. Ko¨nigsmann (Freiburg),
U. Lynen (GSI Darmstadt), G. Mairle (Mannheim), O. Nachtmann (Hei-
delberg), H.J. Pirner (Heidelberg), B. Stech (Heidelberg), and Th. Walcher
(Mainz) for their critical reading and helpful comments on some sections.
Many students who attended our lecture in the 1991 and 1992 summer
semesters helped us through their criticism to correct mistakes and improve
unclearpassages.WeowespecialthankstoM.Beck,Ch.Bu¨scher,S.Fabian,
Th. Haller, A. Laser, A. Mu¨cklich, W. Wander, and E. Wittmann.
M.Lavelle(Barcelona)hastranslatedthemajorpartofthebookandput
itinthepresentlinguisticform.Wemuchappreciatedhisclosecollaboration
with us. The English translation of this book was started by H. Hahn and
M. Moinester (Tel Aviv) whom we greatly thank.
NumerousfiguresfromtheGermantexthavebeenadaptedfortheEnglish
edition by J. Bockholt, V. Tra¨umer, and G. Vogt of the Max-Planck-Institut
fu¨r Kernphysik in Heidelberg.
We would like to extend our thanks to Springer-Verlag, in particular
W. Beiglbo¨ck for his support and advice during the preparation of the Ger-
man and, later on, the English editions of this book.
Heidelberg, May 1995 Bogdan Povh
Klaus Rith
Christoph Scholz
Frank Zetsche
Table of Contents
1 Hors d’œuvre............................................. 1
1.1 Fundamental Constituents of Matter...................... 1
1.2 Fundamental Interactions................................ 2
1.3 Symmetries and Conservation Laws....................... 4
1.4 Experiments ........................................... 5
1.5 Units ................................................. 6
Part I Analysis: The Building Blocks of Matter
2 Global Properties of Nuclei............................... 11
2.1 The Atom and its Constituents........................... 11
2.2 Nuclides............................................... 13
2.3 Parametrisation of Binding Energies ...................... 18
2.4 Charge Independence of the Nuclear Force and Isospin ...... 21
Problem ................................................... 23
3 Nuclear Stability ......................................... 25
3.1 β-Decay............................................... 26
3.2 α-Decay............................................... 31
3.3 Nuclear Fission ........................................ 33
3.4 Decay of Excited Nuclear States.......................... 35
Problems .................................................. 39
4 Scattering ................................................ 41
4.1 General Observations About Scattering Processes........... 41
4.2 Cross Sections ......................................... 44
4.3 The “Golden Rule” ..................................... 48
4.4 Feynman Diagrams ..................................... 49
Problems .................................................. 52
5 Geometric Shapes of Nuclei .............................. 53
5.1 Kinematics of Electron Scattering ........................ 53
5.2 The Rutherford Cross-Section............................ 56
5.3 The Mott Cross-Section ................................. 60
X Table of Contents
5.4 Nuclear Form Factors ................................... 61
5.5 Inelastic Nuclear Excitations............................. 69
Problems .................................................. 71
6 Elastic Scattering off Nucleons............................ 73
6.1 Form Factors of the Nucleons ............................ 73
6.2 Quasi-elastic Scattering ................................. 78
6.3 Charge Radii of Pions and Kaons......................... 80
Problems .................................................. 82
7 Deep Inelastic Scattering ................................. 83
7.1 Excited States of the Nucleons ........................... 83
7.2 Structure Functions..................................... 85
7.3 The Parton Model...................................... 88
7.4 Interpretation of Structure Functions in the Parton Model ... 91
Problems .................................................. 94
8 Quarks, Gluons, and the Strong Interaction .............. 97
8.1 The Quark Structure of Nucleons......................... 97
8.2 Quarks in Hadrons ..................................... 102
8.3 The Quark–Gluon Interaction............................ 103
8.4 Scaling Violations of the Structure Functions .............. 107
Problem ................................................... 111
9 Particle Production in e+e− Collisions.................... 113
9.1 Lepton Pair Production ................................. 114
9.2 Resonances ............................................ 118
9.3 Non-resonant Hadron Production......................... 123
9.4 Gluon Emission ........................................ 125
Problems .................................................. 126
10 Phenomenology of the Weak Interaction.................. 127
10.1 Properties of Leptons ................................... 128
10.2 The Types of Weak Interactions.......................... 132
10.3 Coupling Strength of the Weak Interaction ................ 134
10.4 The Quark Families..................................... 139
10.5 The Lepton families .................................... 142
10.6 Majorana Neutrino? .................................... 144
10.7 Parity Violation........................................ 144
10.8 Deep Inelastic Neutrino Scattering........................ 147
Problems .................................................. 150
Table of Contents XI
11 Exchange Bosons of the Weak Interaction ................ 151
11.1 Real W and Z Bosons................................... 151
11.2 Electroweak Unification ................................. 156
Problem ................................................... 163
12 The Standard Model ..................................... 165
Part II Synthesis: Composite Systems
13 Quarkonia ................................................ 171
13.1 The Hydrogen Atom and Positronium Analogues ........... 171
13.2 Charmonium........................................... 174
13.3 Quark–Antiquark Potential .............................. 177
13.4 The Chromomagnetic Interaction......................... 180
13.5 Bottonium and Toponium ............................... 181
13.6 The Decay Channels of Heavy Quarkonia.................. 183
13.7 Decay Widths as a Test of QCD.......................... 185
Problems .................................................. 187
14 Mesons Made from Light Quarks ......................... 189
14.1 Mesonic Multiplets ..................................... 189
14.2 Meson Masses.......................................... 193
14.3 Decay Channels ........................................ 195
14.4 Neutral Kaon Decay .................................... 197
Problems .................................................. 199
15 The Baryons.............................................. 201
15.1 The Production and Detection of Baryons ................. 201
15.2 Baryon Multiplets ...................................... 207
15.3 Baryon Masses ......................................... 210
15.4 Magnetic Moments ..................................... 213
15.5 Semileptonic Baryon Decays ............................. 217
15.6 How Good is the Constituent Quark Concept? ............. 225
Problems .................................................. 226
16 The Nuclear Force........................................ 229
16.1 Nucleon–Nucleon Scattering ............................. 230
16.2 The Deuteron.......................................... 234
16.3 Nature of the Nuclear Force ............................. 237
Problems .................................................. 243
XII Table of Contents
17 The Structure of Nuclei .................................. 245
17.1 The Fermi Gas Model................................... 245
17.2 Hypernuclei............................................ 250
17.3 The Shell Model........................................ 253
17.4 Deformed Nuclei ....................................... 261
17.5 Spectroscopy Through Nuclear Reactions.................. 264
17.6 β-Decay of the Nucleus.................................. 271
17.7 Double β-decay ........................................ 279
Problems .................................................. 283
18 Collective Nuclear Excitations ............................ 285
18.1 Electromagnetic Transitions ............................. 286
18.2 Dipole Oscillations...................................... 289
18.3 Shape Oscillations ...................................... 297
18.4 Rotation States ........................................ 300
Problems .................................................. 309
19 Nuclear Thermodynamics ................................ 311
19.1 Thermodynamical Description of Nuclei ................... 312
19.2 Compound Nuclei and Quantum Chaos ................... 314
19.3 The Phases of Nuclear Matter............................ 317
19.4 Particle Physics and Thermodynamics in the Early Universe . 322
19.5 Stellar Evolution and Element Synthesis................... 330
Problems .................................................. 336
20 Many-Body Systems in the Strong Interaction............ 337
A Appendix................................................. 341
A.1 Accelerators ........................................... 341
A.2 Detectors.............................................. 348
A.3 Combining Angular Momenta ............................ 358
A.4 Physical Constants ..................................... 360
Solutions to the Problems .................................... 361
References.................................................... 385