Nuclear and Particle Physics E-Book

Brian R. Martin

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 995

Veröffentlichungsjahr: 2019

Beschreibung

Updated and expanded edition of this well-known Physics textbook provides an excellent Undergraduate introduction to the field

This new edition of Nuclear and Particle Physics continues the standards established by its predecessors, offering a comprehensive and highly readable overview of both the theoretical and experimental areas of these fields. The updated and expanded text covers a very wide range of topics in particle and nuclear physics, with an emphasis on the phenomenological approach to understanding experimental data. It is one of the few publications currently available that gives equal treatment to both fields, while remaining accessible to undergraduates.

Early chapters cover basic concepts of nuclear and particle physics, before describing their respective phenomenologies and experimental methods. Later chapters interpret data through models and theories, such as the standard model of particle physics, and the liquid drop and shell models of nuclear physics, and also discuss many applications of both fields. The concluding two chapters deal with practical applications and outstanding issues, including extensions to the standard model, implications for particle astrophysics, improvements in medical imaging, and prospects for power production. There are a number of useful appendices. Other notable features include:

• New or expanded coverage of developments in relevant fields, such as the discovery of the Higgs boson, recent results in neutrino physics, research to test theories beyond the standard model (such as supersymmetry), and important technical advances, such as Penning traps used for high-precision measurements of nuclear masses.
• Practice problems at the end of chapters (excluding the last chapter) with solutions to selected problems provided in an appendix, as well as an extensive list of references for further reading.
• Companion website with solutions (odd-numbered problems for students, all problems for instructors), PowerPoint lecture slides, and other resources.

As with previous editions, the balanced coverage and additional resources provided, makes Nuclear and Particle Physics an excellent foundation for advanced undergraduate courses, or a valuable general reference text for early graduate studies. 

Leseprobe

Nuclear and Particle Physics

An Introduction

Third Edition

B.R. MARTIN

Department of Physics and Astronomy University College London, UK

G. SHAW

School of Physics and AstronomyManchester University, Manchester, UK

This edition first published 2019

© 2019 John Wiley & Sons Ltd

Edition History

Nuclear and Particle Physics - An introduction Wiley - 2006, Nuclear and Particle Physics - Second Edition Wiley 2009.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

The right of B.R. Martin and G. Shaw to be identified as the authors of this work has been asserted in accordance with law.

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Library of Congress Cataloging-in-Publication Data

Names: Martin, B. R. (Brian Robert), author. ∣ Shaw, G. (Graham), 1942– author.

Title: Nuclear and particle physics : an introduction / Brian R. Martin (Department of Physics and Astronomy, University College London, UK), Graham Shaw (School of Physics and Astronomy, University of Manchester, Manchester, UK).

Description: Third edition. ∣ Hoboken, NJ : Wiley, 2019. ∣ Includes index. ∣

Identifiers: LCCN 2018043095 (print) ∣ LCCN 2018058046 (ebook) ∣ ISBN 9781119344629 (Adobe PDF) ∣ ISBN 9781119344636 (ePub) ∣ ISBN 9781119344612 (pbk.)

Subjects: LCSH: Nuclear physics–Textbooks. ∣ Particles (Nuclear physics)–Textbooks.

Classification: LCC QC776 (ebook) ∣ LCC QC776 .M34 2019 (print) ∣ DDC 539.7/2–dc23

LC record available at https://lccn.loc.gov/2018043095

Cover Design: Wiley

Cover Images: Courtesy of Brookhaven National Laboratory

CONTENTS

Cover

Preface

Notes

1 Basic concepts

1.1 History

1.2 Relativity and antiparticles

1.3 Space-time symmetries and conservation laws

1.4 Interactions and Feynman diagrams

1.5 Particle exchange: forces and potentials

1.6 Observable quantities: cross-sections and decay rates

1.7 Units

Problems 1

Notes

2 Nuclear phenomenology

2.1 Mass spectroscopy

2.2 Nuclear shapes and sizes

2.3 Semi-empirical mass formula: the liquid drop model

2.4 Nuclear instability

2.5 Decay chains

2.6

β

decay phenomenology

2.7 Fission

2.8

γ

decays

2.9 Nuclear reactions

Problems 2

Notes

3 Particle phenomenology

3.1 Leptons

3.2 Quarks

3.3 Hadrons

Problems 3

Notes

4 Experimental methods

4.1 Overview

4.2 Accelerators and beams

4.3 Particle interactions with matter

4.4 Particle detectors

4.5 Detector Systems

Problems 4

Notes

5 Quark dynamics: the strong interaction

5.1 Colour

5.2 Quantum chromodynamics (QCD)

5.3 New forms of matter

5.4 Jets and gluons

5.5 Deep inelastic scattering and nucleon structure

5.6 Other processes

5.7 Current and constituent quarks

Problems 5

Notes

6 Weak interactions and electroweak unification

6.1 Charged and neutral currents

6.2 Charged current reactions

6.3 The third generation

6.4 Neutral currents and the unified theory

6.5 Gauge invariance and the Higgs boson

Problems 6

Notes

7 Symmetry breaking in the weak interaction

7.1

P

violation,

C

violation, and

CP

conservation

7.2 Spin structure of the weak interactions

7.3 Neutral kaons: particle–antiparticle mixing and

CP

violation

7.4

CP

violation and flavour oscillations in

B

decays

7.5

CP

violation in the standard model

Problems 7

Notes

8 Models and theories of nuclear physics

8.1 The nucleon–nucleon potential

8.2 Fermi gas model

8.3 Shell model

8.4 Nonspherical nuclei

8.5 Summary of nuclear structure models

8.6 α decay

8.7

β

decay

8.8

γ

decay

Problems 8

Notes

9 Applications of nuclear and particle physics

9.1 Fission

9.2 Fusion

9.3 Nuclear weapons

9.4 Biomedical applications

9.5 Further applications

Problems 9

Notes

10 Some outstanding questions and future prospects

10.1 Overview

10.2 Hadrons and nuclei

10.3 Unification schemes

10.4 The nature of the neutrino

10.5 Particle astrophysics

Notes

A Some results in quantum mechanics

A.1 Barrier penetration

A.2 Density of states

A.3 Perturbation theory and the Second Golden Rule

A.4 Isospin formalism

Problems A

Notes

B Relativistic kinematics

B.1 Lorentz transformations and four-vectors

B.2 Frames of reference

B.3 Invariants

Problems B

Notes

C Rutherford scattering

C.1 Classical physics

C.2 Quantum mechanics

Problems C

Note

D Gauge theories

D.1 Gauge invariance and the standard model

D.2 Particle masses and the Higgs field

Problems D

Notes

E Short answers to selected problems

Problems 1

Problems 2

Problems 3

Problems 4

Problems 5

Problems 6

Problems 7

Problems 8

Problems 9

Problems A

Problems B

Problems C

References

Index

End User License Agreement

List of Tables

Chapter 2

Table 2.1

Chapter 3

Table 3.1

Table 3.2

Table 3.3

Table 3.4

Table 3.5

Table 3.6

Table 3.7

Table 3.8

Table 3.9

Chapter 5

Table 5.1

Chapter 6

Table 6.1

Table 6.2

Chapter 8

Table 8.1

Table 8.2

Chapter 9

Table 9.1

Chapter 10

Table 10.1

Table 10.2

List of Illustrations

Chapter 1

Figure 1.1 The observed electron energy distribution

d

N

/d

E

in

β

decay (dashed line) as a f...

Figure 1.2 Some examples of electromagnetic processes: (a) single-photon exchange in

e

−

 + ...

Figure 1.3 The forbidden vertex

e

−

 → 

e

+

 + 

γ

.

Figure 1.4 Contributions to the elastic weak scattering reaction

e

−

 + 

ν

e

 → 

e

−

 + 

ν

e

by (a) ...

Figure 1.5 (a) The decay of a neutron via an intermediate

W

boson; (b) single

π

0

exchange ...

Figure 1.6 Exchange of a particle

X

in the reaction

A

 + 

B

 → 

A

 + 

B

.

Figure 1.7 Two-photon exchange in the reaction

e

−

 + 

e

−

 → 

e

−

 + 

e

−

.

Figure 1.8 Geometry of the differential cross-section. A beam of particles, shown in green...

Figure 1.9 The Breit–Wigner formula (1.82).

Figure 1.10 Formation and decay of a resonance

R

in the reaction

1 + 2 → 

f

.

Figure 1.11 Formation and decay of a resonance

R

in the reaction

1 + 2 → 

f

.

Chapter 2

Figure 2.1 Schematic diagram of a deflection mass spectrometer.

Figure 2.2 Schematic diagram of a deflection mass spectrometer.

Figure 2.3 Schematic diagram of a deflection mass spectrometer.

Figure 2.4 Schematic diagram of a deflection mass spectrometer.

Figure 2.5 Schematic diagram of a deflection mass spectrometer.

Figure 2.6 Schematic diagram of a deflection mass spectrometer.

Figure 2.7 Schematic diagram of a deflection mass spectrometer.

Figure 2.8 Schematic diagram of a deflection mass spectrometer.

Figure 2.9 Binding energy per nucleon as a function of mass number

A

for stable and long-l...

Figure 2.10 Schematic diagram of nuclear energy levels near the highest filled levels.

Figure 2.11 Fit to the binding energy data (shown as green circles) for odd-

A

and even-

A

nu...

Figure 2.12 Contributions to the binding energy per nucleon as a function of mass number fo...

Figure 2.13 Contributions to the binding energy per nucleon as a function of mass number fo...

Figure 2.14 Time variation of the relative numbers of nuclei in the decay chain (2.69).

Figure 2.15 (a) Mass parabola of the

A

 = 111

isobars. (b) Mass parabolas of the

A

 = 102

iso...

Figure 2.16 (a) Mass parabola of the

A

 = 111

isobars. (b) Mass parabolas of the

A

 = 102

iso...

Figure 2.17 Deformation of a heavy nucleus.

Figure 2.18 Potential energy during different stages of a fission reaction.

Figure 2.19 Energy-level diagram showing the excitation of a compound nucleus

C

 *

and its s...

Figure 2.20 Energy-level diagram showing the excitation of a compound nucleus

C

 *

and its s...

Figure 2.21 Direct and compound nucleus reactions in nuclear reactions initiated by protons...

Figure 2.22 Direct and compound nucleus reactions in nuclear reactions initiated by protons...

Figure 2.23 Direct and compound nucleus reactions in nuclear reactions initiated by protons...

Chapter 3

Figure 3.1 Single-photon exchange in the reaction

e

+

e

−

 → 

μ

+

μ

−

.

Figure 3.2 Dominant Feynman diagram for the decay .

Figure 3.3 Dominant Feynman diagram for the decay .

Figure 3.4 Dominant Feynman diagram for the decay .

Figure 3.5 Dominant Feynman diagram for the decay .

Figure 3.6 Dominant Feynman diagram for the decay .

Figure 3.7 Three-neutrino squared-mass spectra in both the ‘normal’ and ‘inverted’ mass hi...

Figure 3.8 A Feynman diagram contributing to the decay

τ

−

 → 

μ

−

 + 

γ

. There are two other di...

Figure 3.9 A Feynman diagram contributing to the decay

τ

−

 → 

μ

−

 + 

γ

. There are two other di...

Figure 3.10 Mechanism for two-jet production in

e

+

e

−

annihilation reaction.

Figure 3.11 Quark Feynman diagram for the decay in the spectator model.

Figure 3.12 Production mechanism for the reaction .

Figure 3.13 Production mechanism for the reaction .

Figure 3.14 Total cross-sections for

π

−

p

and

π

+

p

scattering.

Figure 3.15 The lowest-lying states with (a)

J

P

 = 0

−

and (b)

J

P

 = 1

−

that are composed of

u...

Figure 3.16 The lowest-lying states with (a)

J

P

 = 1/2

+

and (b)

J

 = 3/2

+

that are composed o...

Figure 3.17 The

J

 = 3/2

+

baryon states composed of

u

,

d

,

s,

and

c

quarks.

Figure 3.18 Feyman diagrams for the decays (a)

K

 *+

 → 

K

 0

 + 

π

+

, (b)

π

+

 → 

μ

+

 + 

ν

μ

, and (c) Λ...

Figure 3.19 Mechanism for the formation of mesons

V

 0

with quantum numbers

J

PC

 = 1

−−

in ele...

Figure 3.20 Mechanism for the formation of mesons

V

 0

with quantum numbers

J

PC

 = 1

−−

in ele...

Figure 3.21 Quark diagrams for (

a

) the decay of a charmonium state to a pair of charmed mes...

Figure 3.22 The states of charmonium () and bottomonium () ...

Figure 3.23 Patterns of

S

- and

P

-wave energy levels arising from (a) Coulomb-like

(

r

−1

)

and...

Figure 3.24 Heavy quark–antiquark potentials obtained from fitting the energy levels of cha...

Chapter 4

Figure 4.1 Principle of the tandem Van de Graaff accelerator (see text for a detailed desc...

Figure 4.2 Acceleration in a linear ion accelerator.

Figure 4.3 Acceleration in a linear ion accelerator.

Figure 4.4 Cross-section of: (a) a typical bending (dipole) magnet; (b) a focusing (quadru...

Figure 4.5 Magnitude of the electric field as a function of time at a fixed point in the r...

Figure 4.6 Magnitude of the electric field as a function of time at a fixed point in the r...

Figure 4.7 Magnitude of the electric field as a function of time at a fixed point in the r...

Figure 4.8 Magnitude of the electric field as a function of time at a fixed point in the r...

Figure 4.9 Total and elastic cross-sections for

π

−

p

scattering as functions of the pion la...

Figure 4.10 Total and elastic cross-sections for

π

−

p

scattering as functions of the pion la...

Figure 4.11 Dominant Feynman diagrams for the bremsstrahlung process

e

−

 + (

Z

,

A

) → 

e

−

 + 

γ

 +...

Figure 4.12 Dominant Feynman diagrams for the bremsstrahlung process

e

−

 + (

Z

,

A

) → 

e

−

 + 

γ

 +...

Figure 4.13 The pair production process

γ

 + (

Z

,

A

) → 

e

−

 + 

e

+

 + (

Z

,

A

)

.

Figure 4.14 Gas amplification factor as a function of voltage

V

applied in a single-wire ga...

Figure 4.15 Gas amplification factor as a function of voltage

V

applied in a single-wire ga...

Figure 4.16 Gas amplification factor as a function of voltage

V

applied in a single-wire ga...

Figure 4.17 Schematic diagram of a resistive-plate chamber.

Figure 4.18 Schematic diagram of a resistive-plate chamber.

Figure 4.19 A particle P, produced from the target, emits Čerenkov radiation on traversing ...

Figure 4.20 Approximate development of an electromagnetic shower in a sampling calorimeter ...

Figure 4.21 Approximate development of an electromagnetic shower in a sampling calorimeter ...

Figure 4.22 Approximate development of an electromagnetic shower in a sampling calorimeter ...

Figure 4.23 Approximate development of an electromagnetic shower in a sampling calorimeter ...

Figure 4.24 Approximate development of an electromagnetic shower in a sampling calorimeter ...

Chapter 5

Figure 5.1 Example of quark–quark scattering by gluon exchange. In this diagram, the quark...

Figure 5.2 The three lowest-order contributions to gluon–gluon scattering in QCD: (a) and ...

Figure 5.3 Values of the running coupling constant

α

s

obtained from the following sources:...

Figure 5.4 OZI-suppressed decay of a

C

 = −1

charmonium state below the th...

Figure 5.5 (a) The simplest quantum fluctuation of an electron and (b) the associated exch...

Figure 5.6 (a) A more complicated quantum fluctuation of the electron and (b) the associat...

Figure 5.7 The two lowest-order vacuum polarisation corrections to one-gluon exchange in q...

Figure 5.8 The two lowest-order vacuum polarisation corrections to one-gluon exchange in q...

Figure 5.9 Schematic diagram of possible tetraquark structures: (a) a molecular quark stat...

Figure 5.10 Schematic diagram of possible tetraquark structures: (a) a molecular quark stat...

Figure 5.11 Schematic diagram of possible tetraquark structures: (a) a molecular quark stat...

Figure 5.12 Stages in the formation of a quark–gluon plasma and subsequent hadron emission:...

Figure 5.13 View of a 200 GeV gold–gold interaction in the STAR detector at the RHIC accele...

Figure 5.14 Dimuon invariant–mass distributions in PbPb (left) and

pp

(right) data at a tot...

Figure 5.15 Basic mechanism of a two-jet production in electron–positron annihilation.

Figure 5.16 Basic mechanism of a two-jet production in electron–positron annihilation.

Figure 5.17 Dominant mechanism for electron–positron annihilation to muon pairs.

Figure 5.18 Measured values of the cross-section ratio

R

and the theoretical prediction (5....

Figure 5.19 Dominant one-photon exchange mechanism for inelastic lepton–proton scattering, ...

Figure 5.20 Dominant one-photon exchange mechanism for inelastic lepton–proton scattering, ...

Figure 5.21 Dominant one-photon exchange mechanism for inelastic lepton–proton scattering w...

Figure 5.22 (a) The interaction of the exchanged photon with the struck quark in the parton...

Figure 5.23 Quark and antiquark distributions (5.34a), together with the valence quark dist...

Figure 5.24 Dominant contribution to deep inelastic neutrino scattering in the parton model...

Figure 5.25 Mechanism for producing

W

±

and

Z

 0

bosons in proton–antiproton annihilations.

Figure 5.26 Mechanism for producing

W

±

and

Z

 0

bosons in proton–antiproton annihilations.

Figure 5.27 Sketch of a final-state charged lepton and the associated jet produced by the m...

Figure 5.28 The dominant mechanism for di-jet production in proton–proton collisions. The d...

Figure 5.29 Sketch of the two high-

p

T

jets

j

1

and

j

2

produced by the mechanism of Figure 5....

Figure 5.30 The Drell–Yan mechanism for charged lepton-pair production in proton–proton col...

Figure 5.31 Dilepton invariant mass spectrum, in the mass region

15 < 

M

 < 600 GeV/

c

2

. The v...

Figure 5.32 Schematic representation of the evolution of the quark content of the proton wi...

Figure 5.33 Measured charm mass

m

c

(

μ

)

in the scheme. The red square at sca...

Chapter 6

Figure 6.1 Feynman diagram for the weak neutral current reaction

ν

μ

 + 

N

 → 

ν

μ

 + 

X

.

Figure 6.2 Feynman diagram for the weak neutral current reaction

ν

μ

 + 

N

 → 

ν

μ

 + 

X

.

Figure 6.3 The basic vertex for electron–photon interactions, together with two of the bas...

Figure 6.4 One of the two basic vertices for

W

 ±

 – lepton interactions, together with two ...

Figure 6.5 The second basic vertex for

W

 ±

 – lepton interactions, together with two of the...

Figure 6.6 Example of a vertex that violates lepton number conservation, together with two...

Figure 6.7 Dominant diagram for neutron decay (6.7).

Figure 6.8 Dominant diagrams for Λ decay (6.6).

Figure 6.9 The

W

 ±

quark vertices obtained from lepton–quark symmetry when quark mixing is...

Figure 6.10 Feynman diagrams for the semileptonic decays: (a) and (b)

Figure 6.11 The

ud

′

W

vertex and its interpretation in terms of

udW

and

usW

vertices.

Figure 6.12 The additional vertices arising from lepton–quark symmetry when quark mixing is...

Figure 6.13 Cabibbo-allowed decays from (6.22a) and (6.22b) of a charmed quark.

Figure 6.14 Feynman diagram for the decays .

Figure 6.15 The dominant mechanism for the decay of

W

 ±

bosons into hadrons.

Figure 6.16 Mechanism for the decay .

Figure 6.17 Mechanism for the decay .

Figure 6.18 The dominant decays of the

b

quark to lighter quarks and leptons. Here ℓ = 

e

,

μ...

Figure 6.19 The dominant decays of the

τ

lepton to quarks and leptons. Here ℓ = 

e

  or   

μ

a...

Figure 6.20 The mechanism for

t

quark decays. The decays that lead to

b

quarks are overwhel...

Figure 6.21 Production of hadron jets from the decay

t

 → 

b

 + 

W

 +

where the

W

boson decays t...

Figure 6.22 Higher-order contribution to the reaction

e

+

μ

−

 → 

e

+

μ

−

from the exchange of two ...

Figure 6.23 Two of the higher-order contributions to inverse muon decay that were neglected...

Figure 6.24 Two of the higher-order contributions to inverse muon decay that were neglected...

Figure 6.25 The two dominant contributions to the reaction

e

+

 + 

e

−

 → 

μ

+

+ 

μ

−

in the unified ...

Figure 6.26 Qualitative sketch of the observed total cross-section for the reaction

e

+

e

−

 → ...

Figure 6.27 The basic vertices for Higgs boson–fermion interactions. The fermion

f

can be a...

Figure 6.28 The basic first-order vertices for Higgs boson–boson interactions.

Figure 6.29 The basic second-order vertices for Higgs boson–boson interactions.

Figure 6.30 The dominant mechanism for the decay .

Figure 6.31 The dominant mechanism for the decay

H

 0

 → 

g

 + 

g

.

Figure 6.32 The dominant mechanisms for the rare decay

H

 0

 → 

γ

 + 

γ

.

Figure 6.33 The dominant mechanisms for the reactions (6.80a), (6.80b), and (6.80c), respec...

Figure 6.34 The dominant mechanisms for the reactions (6.80a), (6.80b), and (6.80c), respec...

Figure 6.35 Gluon fusion production mechanism for the reaction

p

 + 

p

 → 

H

 0

 + 

X

at the LHC.

Figure 6.36 Production mechanisms for the Higgs boson at the LHC.

Figure 6.37 Production mechanisms for the Higgs boson at the LHC.

Figure 6.38 Dominant background processes producing

2

γ

final states.

Figure 6.39 Dominant background processes producing

2

γ

final states.

Figure 6.40 Dominant mechanism for the decay

H

 0

 → ℓ

+

 + ℓ

−

 + ℓ′

+

 + ℓ′

−

  (ℓ = 

e

,

μ

; ℓ′ = 

e

, ...

Figure 6.41 Dominant mechanism for the decay

H

 0

 → ℓ

+

 + ℓ

−

 + ℓ′

+

 + ℓ′

−

  (ℓ = 

e

,

μ

; ℓ′ = 

e

, ...

Figure 6.42 Dominant mechanism for the decay

H

 0

 → ℓ

+

 + ℓ

−

 + ℓ′

+

 + ℓ′

−

  (ℓ = 

e

,

μ

; ℓ′ = 

e

, ...

Figure 6.43 Feynman diagram for the reaction

e

+

e

−

 → 

μ

+

μ

−

via the exchange of a single Higgs...

Chapter 7

Figure 7.1 Effect of a parity transformation on

60

Co decay. The thick arrows indicate the ...

Figure 7.2 Effect of a parity transformation on muon decays. The thick arrows indicate the...

Figure 7.3 Photon and

Z

 0

exchange in Möller scattering.

Figure 7.4 (a) Möller scattering; (b) the effect of a parity transformation on the configu...

Figure 7.5 Helicity states of a spin-1/2 particle. The long thin arrows represent the mome...

Figure 7.6 Effect of

C

,

P,

and

CP

transformations. Only the states shown in boxes are obse...

Figure 7.7 Possible helicities of the photon and neutrinos emitted in the reaction

e

−

 + 

15...

Figure 7.8 Helicities of the charged leptons in pion decays. The short arrows denote spin ...

Figure 7.9 Muon decays in which electrons of the highest possible energy are emitted (a) i...

Figure 7.10 Example of a process that can convert a

K

 0

state to a state. ...

Figure 7.11 Example of a process that can convert a

K

 0

state to a state. ...

Figure 7.12 Predicted variation with time of the intensities

I

(

K

 0

 → 

K

 0

) (solid line) and ...

Figure 7.13 Predicted variation with time of the intensities

I

(

K

 0

 → 

K

 0

) (solid line) and ...

Figure 7.14 Quark diagrams for the decay

B

 0

 → 

K

 +

 + 

π

−

in lowest order weak interactions. ...

Figure 7.15 Example of a process that can convert a state into a

Figure 7.16 Mechanism for the decay of the 4S state ϒ(10.58);

q

 = 

u

or

d

.

Figure 7.17 Mechanism for the decay of the 4S state ϒ(10.58);

q

 = 

u

or

d

.

Figure 7.18 Mechanism for the decay of the 4S state ϒ(10.58);

q

 = 

u

or

d

.

Figure 7.19 The tree (a) and penguin (b) diagrams for the decays , where in...

Figure 7.20 The leading tree and penguin diagrams for the decays and...

Chapter 8

Figure 8.1 Idealised square well representation of the strong interaction nucleon–nucleon ...

Figure 8.2 Proton and neutron potentials and states in the Fermi gas model.

Figure 8.3 The black line shows the binding energy per nucleon for even values of

A

. The g...

Figure 8.4 Low-lying energy levels in a single-particle shell model using a Woods–Saxon po...

Figure 8.5 Magnetic moments for odd-

N

, even-

Z

nuclei (left diagram) and odd-

Z

, even-

N

(rig...

Figure 8.6 Shapes of nuclei leading to (a)

Q

 > 0

(prolate) and (b)

Q

 < 0

(oblate).

Figure 8.7 Some measured electric quadrupole moments for odd-

A

nuclei, normalised by divid...

Figure 8.8 Comparison of the Geiger–Nuttall relation with experimental data for some

α

emi...

Figure 8.9 Schematic diagram of the potential energy of an

α

particle as a function of its...

Figure 8.10 Predicted electron spectra:

Z

 = 0

, without the Fermi screening factor;

β

±

, with...

Figure 8.11 Predicted electron spectra:

Z

 = 0

, without the Fermi screening factor;

β

±

, with...

Figure 8.12 Predicted Kurie plot for tritium decay very close to the end point of the elect...

Figure 8.13 Predicted Kurie plot for tritium decay very close to the end point of the elect...

Figure 8.14 Transition rates using the single-particle shell model formulas of Weisskopf as...

Chapter 9

Figure 9.1 Transition rates using the single-particle shell model formulas of Weisskopf as...

Figure 9.2 Transition rates using the single-particle shell model formulas of Weisskopf as...

Figure 9.3 Sketch of the elements of the core of a reactor.

Figure 9.4 Sketch of the elements of the core of a reactor.

Figure 9.5 Possible energy flows in an energy amplifier system of the Rubbia design. The c...

Figure 9.6 (a) The dashed curve increasing with energy is proportional to the barrier pene...

Figure 9.7 The function

τ

2

 exp(−

τ

) of (9.31) for the

p–p

and

p

 – 

12

C

fusion reactions.

Figure 9.8 Typical values of the thermal reactivity 〈

συ

〉 for the

d–t

reaction (9.51) and t...

Figure 9.9 Typical values of the thermal reactivity 〈

συ

〉 for the

d–t

reaction (9.51) and t...

Figure 9.10 Schematic diagrams of: (a) gun assembly and (b) implosion assembly technique fo...

Figure 9.11 Schematic diagram of the Teller-Ulam staged explosion technique for an idealise...

Figure 9.12 Relative absorption of photons and protons as functions of equivalent depth of ...

Figure 9.13 Treatment plans for an extensive non-small-cell lung cancer (shown in brown) us...

Figure 9.14 Treatment plans for an extensive non-small-cell lung cancer (shown in brown) us...

Figure 9.15 Basic layout for imaging using an external source.

Figure 9.16 Schematic diagram of a gamma camera.

Figure 9.17 Schematic diagram of a gamma camera.

Figure 9.18 Schematic diagram of the arrangement for a CT X-ray scanner.

Figure 9.19 Schematic diagram of the arrangement for a CT X-ray scanner.

Figure 9.20 Schematic diagram of the arrangement of a PET scanner.

Figure 9.21 Schematic diagram of the arrangement of a PET scanner.

Figure 9.22 (a) Precession of the magnetisation M in the

xy

plane under the action of a tor...

Figure 9.23 (a) Precession of the magnetisation M in the

xy

plane under the action of a tor...

Chapter 10

Figure 10.1 (a) Precession of the magnetisation M in the

xy

plane under the action of a tor...

Figure 10.2 Idealised behaviour of the strong and electroweak coupling as functions of the ...

Figure 10.3 Fundamental vertices that can occur for the multiplet of particles in (10.2a).

Figure 10.4 The three fundamental vertices involving

X

and

Y

bosons that are predicted by t...

Figure 10.5 Examples of processes that contribute to the proton decay reaction

p

 → 

π

0

 + 

e

+

....

Figure 10.6 The zero-range approximation to an

X

boson exchange process.

Figure 10.7 (a) Double

β

decay

ββ

2

ν

(allowed in the standard model); (b) neutrinoless doubl...

Figure 10.8 Energy spectra for the two electrons in

ββ

2

ν

and

ββ

0

ν

decays as a function of

E...

Figure 10.9 The predicted values of the effective neutrino Majorana mass

m

ββ

, as a function...

Figure 10.10 The predicted values of the effective neutrino Majorana mass

m

ββ

, as a function...

Figure 10.11 The predicted values of the effective neutrino Majorana mass

m

ββ

, as a function...

Figure 10.12 Data for neutrinos from SN1987A detected in the Kamiokande and IMB experiments....

Figure 10.13 Data for neutrinos from SN1987A detected in the Kamiokande and IMB experiments....

Figure 10.14 Motion of the Sun and Earth through the dark matter background.

Figure 10.15 Motion of the Sun and Earth through the dark matter background.

Figure 10.16 (a) An example of a diagram involving superparticles that can lead to a nonzero...

Figure 10.17 (a) An example of a diagram involving superparticles that can lead to a nonzero...

Chapter a

Figure A.1: (a) Rectangular barrier with wavefunction solutions. (b) Form of the real parts...

Figure A.2: The function .

Chapter c

Figure C.1: Kinematics of the Geiger and Marsden experiment.

Figure C.2: Kinematics of Rutherford scattering.

Chapter d

Figure D.1: The potential energy density

V

(

η

)

, as given by (D.22), for

λ

 > 0

.

Guide

Cover

Table of Contents

Preface

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I

E1

Preface

It is common practice to teach nuclear physics and particle physics together in an introductory undergraduate course, and it is for such a course that this book has been written. The material is presented so that different selections can be made for a short course of about 25–30 lectures depending on the lecturer's preferences and the students' backgrounds. On the latter, students should have taken a first course in quantum physics, covering the traditional topics in nonrelativistic quantum mechanics and atomic physics. No prior knowledge of nuclear and particle physics is assumed. A few lectures on relativistic kinematics would also be useful, but this is not essential, as the necessary background is given in an appendix and is only used in a few places in the book.

We have not presented proofs or derivations of all the statements in the text. Rather, we have taken the view that it is more important that students see an overview of the subject, which for many, probably the majority, will be the only time they study nuclear and particle physics. For future specialists, the details will form part of more advanced courses. We have tried to take a direct approach throughout, focusing on the interpretation of experimental data in terms of current models and theories. Space restrictions have still meant that it has been necessary to make a choice of topics, and doubtless other equally valid choices could have been made. This is particularly true in Chapter 9, which deals with applications of nuclear and particle physics.

Since publication of the Second Edition of this book, there have been many important developments in both nuclear and particle physics. These include: the long-awaited discovery of the Higgs boson; substantial progress in neutrino physics and symmetry breaking in the weak interaction; a better understanding of stellar evolution and cosmology; high-precision nuclear mass measurements; increased developments in applying nuclear and particle physics techniques to clinical science; and tighter constraints on difficult-to-measure quantities, such as possible electric dipole moments and the masses of hypothetical particles, which are important for testing new theories of particle physics. Our aim in producing this Third Edition is again to bring the book up-to-date throughout, while leaving its basic philosophy unchanged. In doing this we are grateful to John Wiley and Sons for permission to use material from other books that we have published with them.

Finally, a word about footnotes: readers often have strong views about these (‘Notes are often necessary, but they are necessary evils’ – Samuel Johnson), so, as in previous editions, in this book they are designed to provide ‘non-essential’ information only. For those readers who prefer not to have the flow disrupted, ignoring the footnotes should not detract from understanding the text. Nuclear and particle physics have been, and still are, very important parts of the entire subject of physics and its practitioners have won an impressive number of Nobel Prizes. For historical interest, the footnotes also record many of these awards.

Brian Martin and Graham Shaw

July 2018

Notes

References

References are referred to in the text in the form of a name and date, for example Jones (1997). A list of references with full publication details is given at the end of the book.

Data

Tabulations of nuclear and particle physics data, such as masses, quantum numbers, decay modes, etc., are now readily available at the ‘click of a mouse’ from a number of sites and it is useful for students to get some familiarity with such sources. They are also needed to solve some end-of-chapter problems in the book. Many physical quantities are also readily found by a simple Internet search.

For particle physics, a comprehensive compilation of data, plus brief critical reviews of a number of current topics, may be found in the biannual publications of the Particle Data Group (PDG). The 2018 edition of their definitive Review of Particle Properties is referred to in Tanabashi et al. (Particle Data Group) (). Physical Review D98, 030001 in the references, and also as Particle Data Group (). The PDG Review is available online at http://pdg.lbl.gov and this site also contains links to other sites where compilations of specific particle data may be found.

Nuclear physics does not have the equivalent of the PDG review, but extensive compilations of nuclear data are available from a number of sources. Examples are: the Berkeley Laboratory Isotopes Project (http://ie.lbl.gov/education/isotopes.htm); the National Nuclear Data Center (NNDC), based at Brookhaven National Laboratory, USA (http://www.nndc.bnl.gov); the Nuclear Data Centre of the Japan Atomic Energy Research Institute (http://wwwndc.tokai-sc.jaea.go.jp/NuC); and the Nuclear Data Evaluation Laboratory of the Korea Atomic Energy Research Institute (http://atom.kaeri.re.kr). All four sites have links to other data compilations.

Problems

Problems are provided for Chapters 1 to 9 and Appendices A to D; they are an integral part of the text. The problems are sometimes numerical and require values of physical constants that are given on the inside rear cover. Some also require data that may be found in the reference sites listed above. Short answers to selected problems are given at the end of the book in Appendix E. Readers may access the full solutions to odd-numbered problems on the book's website given below, and instructors can access there the full solutions for all problems.

Illustrations

Some illustrations in the text have been adapted from, or are based on, diagrams that have been published elsewhere. We acknowledge, with thanks, permission to use such illustrations from the relevant copyright holders, as stated in the captions.

Website

www.wiley.com/go/martin/nuclear3

Instructors may access PowerPoint slides of all the illustrations from the text on the accompanying website. As indicated above, solutions for all the problems are also available to Instructors, with odd-numbered solutions available to all Readers. Any misprints or other necessary corrections brought to the author's notice will be listed. We would also be grateful for any other comments about the book, which should initially be sent to the Publishers ([email protected]).

1Basic concepts

1.1 History

Although this book will not follow a strictly historical development, to ‘set the scene’ this first chapter will start with a brief review of the most important discoveries that led to the separation of nuclear physics from atomic physics as a subject in its own right, and later work that in its turn led to the emergence of particle physics from nuclear physics.1

1.1.1 The origins of nuclear physics

In 1896 Becquerel observed that photographic plates were being fogged by an unknown radiation emanating from uranium ores. He had accidentally discovered radioactivity, the fact that some chemical elements spontaneously emit radiation. The name was coined by Marie Curie two years later to distinguish this phenomenon from induced forms of radiation. In the years that followed, radioactivity was extensively investigated, notably by the husband and wife team of Pierre and Marie Curie, and by Rutherford and his collaborators.2 Other radioactive sources were quickly found, including the hitherto unknown chemical elements polonium and radium, discovered by the Curies in 1897.3 It was soon established that there were two distinct types of radiation involved, named by Rutherford α and β rays. We know now that β rays are electrons (the name ‘electron’ had been coined in 1894 by Stoney) and α rays are doubly ionised helium atoms. In 1900 a third type of decay was discovered by Villard that involved the emission of photons, the quanta of electromagnetic radiation, referred to in this context as γ rays. These historical names are still commonly used.

The revolutionary implications of these experimental discoveries did not become fully apparent until 1902. Prior to this, atoms were still believed to be immutable – indestructible and unchanging – an idea with its origin in Greek philosophy and, for example, embodied in Dalton's atomic theory of chemistry in 1804. This causes a big problem: if the atoms in a radioactive source remain unchanged, where does the energy carried away by the radiation come from? Typically, early attempts to explain the phenomena of radioactivity assumed that the energy was absorbed from the atmosphere or, when that failed, that energy conservation was violated in radioactive processes. However, Rutherford had shown in 1900 that the intensity of the radiation emitted from a radioactive source was not constant, but reduced by a factor of two in a fixed time that was characteristic of the source, but independent of its amount. This is called its half-life. In 1902, together with Soddy, he put forward the correct explanation, called the transformation theory, according to which the atoms of any radioactive element decay with a characteristic half-life, emitting radiation, and in so doing are transformed into the atoms of a different chemical element. The centuries old belief in the immutability of atoms was shattered forever.

An important question not answered by the transformation theory is: which elements are radioactive and which are stable? An early attempt to solve this problem was made by J.J. Thomson, who was extending the work of Perrin and others on the radiation that had been observed to occur when an electric field was established between electrodes in an evacuated glass tube. In 1897 he was the first to definitively establish the nature of these ‘cathode rays’. We now know they consist of free electrons, denoted e− (the superscript denotes the electric charge) and Thomson measured their mass and charge.4 This gave rise to the speculation that atoms contained electrons in some way, and in 1903 Thomson suggested a model where the electrons were embedded and free to move in a region of positive charge filling the entire volume of the atom – the so-called plum pudding model. This model could account for the stability of atoms, but gave no explanation for the discrete wavelengths observed in the spectra of light emitted from excited atoms.

The plum pudding model was finally ruled out by a classic series of experiments suggested by Rutherford and carried out by his collaborators Geiger and Marsden starting in 1909. This consisted of scattering α particles from very thin gold foils. In the Thomson model, most of the α particles would pass through the foil, with only a few suffering deflections through small angles. However, Geiger and Marsden found that some particles were scattered through very large angles, even greater than 90°. As Rutherford later recalled, ‘It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you’.5 He then showed that this behaviour was not due to multiple small-angle deflections, but could only be the result of the α particles encountering a very small, very heavy, positively charged central nucleus. (The reason for these two different behaviours is discussed in Appendix C.)

To explain these results, Rutherford in 1911 proposed the nuclear model of the atom. In this model, the atom was likened to a planetary system, with the light electrons (the ‘planets’) orbiting about a tiny but heavy central positively charged nucleus (the ‘sun’). The size of the atom is thus determined by the radii of the electrons' orbits, with the mass of the atom arising almost entirely from the mass of the nucleus. In the simplest case of hydrogen, a single electron orbits a nucleus, now called the proton (p), with electric charge +e, where e is the magnitude of the charge on the electron, to ensure that hydrogen atoms are electrically neutral. Alpha particles are just the nuclei of helium, while heavier atoms were considered to have more electrons orbiting heavier nuclei. At about the same time, Soddy showed that a given chemical element often contained atoms with different atomic masses but identical chemical properties. He called this isotopism and the members of such families isotopes. Their discovery led to a revival of interest in Prout's Law of 1815, which claimed that all the elements had integer atomic mass in units of the mass of the hydrogen atom, called atomic weights. This holds to a good approximation for many elements, like carbon and nitrogen, with atomic weights of approximately 12.0 and 14.0 in these units, but does not hold for other elements, like chlorine, which has an atomic weight of approximately 35.5. However, such fractional values could be explained if the naturally occurring elements consisted of mixtures of isotopes. Chlorine, for example, is now known to consist of a mixture of isotopes with atomic weights of approximately 35.0 and 37.0, giving an average value of 35.5 overall.6

Although the planetary model explained the α particle scattering experiments, there remained the problem of reconciling it with the observation of stable atoms. In classical physics, the electrons in the planetary model would be continuously accelerating and would therefore lose energy by radiation, leading to the collapse of the atom. This problem was solved by Bohr in 1913, who revolutionised the study of atomic physics by applying the newly emerging quantum theory. The result was the Bohr–Rutherford model of the atom, in which the motion of the electrons is confined to a set of discrete orbits. Because photons of a definite energy would be emitted when electrons moved from one orbit to another, this model could explain the discrete nature of the observed electromagnetic spectra when excited atoms decayed. In the same year, Moseley extended these ideas to a study of X-ray spectra and conclusively demonstrated that the charge on the nucleus is +Ze, where the integer Z was the atomic number of the element concerned, and implying Z orbiting electrons for electrical neutrality. In this way he laid the foundation of a physical explanation of Mendeleev's periodic table and in the process predicted the existence of no less than seven unknown chemical elements, which were all later discovered.7

The phenomena of atomic physics are controlled by the behaviour of the orbiting electrons and are explained in detail by refined modern versions of the Bohr–Rutherford model, including relativistic effects described by the Dirac equation, the relativistic analogue of the Schrödinger equation that applies to electrons, which is discussed in Section 1.2. However, following the work of Bohr and Moseley it was quickly realised that radioactivity was a nuclear phenomenon. In the Bohr–Rutherford and later models, different isotopes of a given element have different nuclei with different nuclear masses, but their orbiting electrons have virtually identical chemical properties because these nuclei all carry the same charge +Ze. The fact that such isotopes often have dramatically different radioactive decay properties is therefore a clear indication that these decays are nuclear in origin. In addition, since electrons were emitted in β decays, it seemed natural to assume that nuclei contained electrons as well as protons, and the first model of nuclear structure, which emerged in 1914, assumed that the nucleus of an isotope of an element with atomic number Z and mass number A was itself a tightly bound compound of A protons and A − Z electrons. This provided an explanation of the existence of isotopes and of the approximate validity of Prout's law when applied to isotopes, because the electron mass is negligible compared to that of the proton. However, although this model persisted for some time, it was subsequently ruled out by detailed measurements of the spins of nuclei (cf. Problem 1.1).

The correct explanation of isotopes and nuclear structure had to wait almost twenty years, until a classic discovery by Chadwick, in 1932. His work followed earlier experiments by Irène Curie (the daughter of Pierre and Marie Curie) and her husband Frédéric Joliot. They had observed that neutral radiation was emitted when α particles bombarded beryllium, and later work had studied the energy of protons emitted when paraffin was exposed to this neutral radiation. Chadwick refined and extended these experiments and demonstrated that they implied the existence of an electrically neutral particle of approximately the same mass as the proton, called the neutron (n).8 The discovery of the neutron led immediately to the correct formulation of nuclear structure, in which an isotope of atomic number Z and mass number A is a bound state of Z protons and A − Z neutrons. There are no electrons bound inside nuclei.

Finally, to complete this historical account, we must go back to another major result: the discovery of the continuous β - decay spectrum by Chadwick in 1914. At that time, nuclear decays were all viewed as a parent nucleus decaying via α, β, or γ decay to give a daughter nucleus plus either an alpha particle, an electron or a photon, respectively. As each possibility would be a two-body decay, energy and momentum conservation implies that the emitted particle would have a unique energy, depending on the masses of the parent and daughter nucleons, which would be the same for all observed decays of a given type. This behaviour is precisely what is observed for α decays and γ decays and the earliest experiments erroneously suggested the same held for β decays. However, when Chadwick measured the energies of the electrons from samples of nuclei he found that the electrons emitted in a given β-decay process had a continuous energy distribution, as shown in Figure 1.1.

Figure 1.1 The observed electron energy distribution dN/dE in β decay (dashed line) as a function of E/Q, where E is the kinetic energy of the electron and Q is the total energy released. Also shown is the expected energy distribution if β decay were a two-body process (solid line).

After a hiatus due to the first world war, various ideas were suggested to explain this unexpected result, including a remarkable proposal by Bohr in 1929 that energy conservation was violated in β decays, but later abandoned by him in favour of the correct hypothesis proposed by Pauli in 1930. Pauli proposed that an additional, and hitherto unknown, neutral particle was emitted in β decays and shared the energy released with the electron. This particle had to be very light, since the most energetic electrons in the observed continuous distribution carried off almost all the energy released in the decay, as can be seen in Figure 1.1; it had also to interact so weakly with matter that it invariably escaped detection. Despite this, its existence was rapidly accepted, largely because of its crucial role in the highly successful theory of β decay proposed in 1932 by Fermi, who used the name neutrino (meaning ‘little neutral one’) for the new particle after his close friend and colleague Amaldi jokingly suggested it to distinguish Pauli's particle from Chadwick's ‘big neutral one’, the neutron.9

In conclusion, by 1932 physicists had arrived at a model of the nucleus in which an isotope of atomic number Z and mass number A is a bound state of Z protons and A − Z neutrons. Later workers, including Heisenberg, another of the founders of quantum theory, applied quantum mechanics to the nucleus, now viewed as a collection of neutrons and protons, collectively called nucleons. In this case, however, the force binding the nucleus is not the electromagnetic force that holds electrons in their orbits, but a much stronger force that does not depend on the charge of the nucleon (i.e. is charge-independent) and with a very short effective range. This binding interaction is called the strong nuclear force. In addition, there is a third force, much weaker than the electromagnetic force, called the weak interaction, responsible for β decays, where neutrinos as well as electrons are emitted. These ideas form the essential framework of our understanding of the nucleus today. Nevertheless, there is still no single theory that is capable of explaining all the data of nuclear physics and we shall see that different models are used to interpret different classes of phenomena.

1.1.2 The emergence of particle physics: hadrons and quarks

By the early 1930s, the nineteenth century view of atoms as indivisible elementary particles had been replaced and a smaller group of subatomic particles now enjoyed this status: electrons, protons and neutrons. To these we must add two electrically neutral particles: the photon (γ) and the neutrino (ν). However, this simple picture was not to last, because of the discovery of many new subatomic particles, initially in cosmic rays and later in experiments using particle accelerators.

We start with cosmic rays, which may be conveniently divided into two types: primaries, which are high-energy particles, mostly protons, incident on the Earth's atmosphere from all directions in space; and secondaries, which are produced when the primaries collide with nuclei in the Earth's atmosphere, with some penetrating to sea level. It was among these secondaries that the new particles were discovered, mainly using a detector devised by C.T.R. Wilson, called the cloud chamber. It consisted of a vessel filled with air almost saturated with water vapour and fitted with an expansion piston. When the vessel was suddenly expanded, the air was cooled and became supersaturated. Droplets were then formed preferentially along the trails of ions left by charged particles passing through the chamber. Immediately after the expansion, the chamber was illuminated by a flash of light and the tracks of droplets so revealed were photographed before they had time to disperse. The use of these chambers in cosmic ray studies led to many important discoveries, including, in 1932, the detection of antiparticles, to be discussed in Section 1.2.10 However, the birth of particle physics as a new subject, distinct from atomic and nuclear physics, dates from 1947 with the discovery of pions and of strange particles by cosmic ray groups at Bristol and Manchester Universities, respectively. We will consider these in turn.

The discovery of pions was not unexpected, since Yukawa had famously predicted their existence in a theory of the strong nuclear forces proposed in 1934. We will return to this in Section 1.5. Here we will simply note that the range of the nuclear force required the pions to have a mass of around one seventh of the proton mass, while the charge independence of the nuclear force required there to be three charge states, denoted π+, π− π0, with charges +e, − e and zero, respectively. This gave rise to a search for these particles in cosmic ray secondaries, and in 1936 Anderson and Neddermeier discovered new subatomic particles that were initially thought to be pions, but are now known to be particles called muons. As we shall see in Chapter 3, muons are rather like heavy electrons and, like both electrons and neutrinos, do not interact via the strong force that holds the nucleus together. Charged pions with suitable properties were finally detected in 1947 using photographic emulsions containing a silver halide. The ionisation energy deposited by a charged particle passing through the emulsion causes the formation of a latent image, and the silver grains resulting from subsequent development form a visual record of the path of the particle. The neutral pion was detected somewhat later in 1950.11 Pions interact with each other and with nucleons via forces comparable in strength to the strong nuclear interaction between nucleons and in future we will refer to all such forces as strong interactions, reserving the term strong nuclear interaction to the special case of nucleon–nucleon interactions. Particles that interact by the strong force are now called hadrons. Thus pions and nucleons are examples of hadrons, while electrons, muons and neutrinos are not.

Further work using cloud chambers to detect cosmic ray secondaries led to the discovery in 1947 by Rochester and Butler of new particles, named kaons, which, in contrast to the discovery of pions, was totally unexpected. Kaons were almost immediately recognised as a completely new form of matter, because they had supposedly ‘strange’ properties, which will be discussed further in Section 3.3. Other strange particles