Nuclear Physics

504 Pages·2017·7.494 MB·English

by  R. Prasad

Nuclear Physics
R. PRASAD
formerly at
Aligarh Muslim University
Aligarh, India
Delhi • Chennai
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contents
Preface vii
About the Author x
Acknowledgements xi
1. The Birth of the Nucleus 1
1.1 Background 1
1.2 Geiger and Marsden’s Alpha Scattering Experiment 2
1.3 Rutherford’s Model of Nuclear Atom 3
1.4 Rutherford’s Scattering Formula 4
1.5 Nuclear Atom 11
1.6 Electron Cannot be a Constituent of the Nucleus 25
1.7 The Nucleus Today 28
2. Basic Properties of the Nucleus and Their Determination 30
2.1 Determination of Nuclear Charge 30
2.2 Determination of Nuclear Mass 36
2.3 Determination of Nuclear Radius 51
2.4 Nuclear Angular Momentum, Magnetic Dipole Moment, and Electric
Quadrupole Moment 64
2.5 Determination of Nuclear Angular Momentum I 73
2.6 Determination of Nuclear Magnetic Moment 81
2.7 Determination of the Nuclear Quadrupole Moment Q 87
3. Force between Nucleons 90
3.1 Introduction 90
3.2 Inadequacy of Classical Forces 90
3.3 Two-body Nucleon–Nucleon Force 91
3.4 Mediation of Nuclear Field 104
3.5 Spin–Orbit Dependence of Nuclear Force 108
3.6 Nucleon–Nucleon Potential 108
3.7 Quark and Gluon 111
4. Quantum Mechanical analysis of some Nuclear systems 114
4.1 Deuteron and Its Properties 114
4.2 Schrödinger Equations for a System of Two Spinless Particles in Spherical
Polar Coordinates 116
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iv Contents
4.3 Simple Quantum Mechanical Description of Deuteron 120
4.4 Quantum Mechanical Approach to Nucleon–Nucleon Scattering 131
4.5 One-dimensional Rectangular Barrier Transmission 155
5. characteristics of stable Nuclei and Nuclear Models 162
5.1 Systematic Trends in Stable and Long-lived Nuclides 162
5.2 Shell Model 168
5.3 Liquid Drop Model 178
5.4 Collective Models of the Nucleus 190
5.5 Fermi Gas Model of the Nucleus 194
6. radioactive Decay 201
6.1 Nuclear Stability 201
6.2 Radioactive Decay Chain 203
6.3 Two-step Decay 204
6.4 Activation Analysis 206
6.5 The ` Decay 211
6.6 The a Decay 220
6.7 The Electron Capture Decay (EC) 232
6.8 Non-conservation of Parity in a Decay 233
6.9 The Neutrino and Its Rest Mass 236
6.10 Gamma (f ) Decay 243
6.11 Resonance Fluorescence of f Rays 247
7. Nuclear radiations and Detectors 255
7.1 Attenuation Coefficients 255
7.2 Energy Loss by Electromagnetic Radiation 257
7.3 Energy Loss by Heavy Charged Particles 268
7.4 Energy Loss by Light Charged Particles 278
7.5 Energy Loss by Un-charged Nuclear Particles 282
7.6 Nuclear Detectors 284
7.7 Some Special Detectors 305
7.8 Detection of Neutron 308
7.9 Detection of Neutrino 310
7.10 Solid-state Nuclear Track Detectors (SSNTD) 313
7.11 Choosing a Detector 314
8. Nuclear reactions 318
8.1 Quantities Conserved in a Nuclear Reaction 319
8.2 Quantities that are not Conserved in Nuclear Reactions 323
8.3 The Q Equation 323
8.4 The Partial Wave Analysis of Nuclear Reaction Cross-section 329
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Contents v
8.5 Reaction Mechanism 331
8.6 Test of the Compound Reaction Mechanism: Excitation Functions and
Ghoshal’s Experiment 340
8.7 Pre-equilibrium (or Pre-compound) Emission in Statistical Nuclear Reactions 343
8.8 Heavy Ion (HI) Reactions 346
8.9 Optical Model Approach to Nuclear Reactions 351
8.10 Direct Reaction Mechanism 353
8.11 Interaction of Electromagnetic Radiations with the Nucleus 354
8.12 Nuclear Reactions Using Radioactive Ion Beams 357
8.13 Nuclear Reactions Responsible for Nucleosynthesis 359
9. Particle accelerators 367
9.1 Electrostatic Accelerators 368
9.2 The Cyclotron 371
9.3 Linear Accelerator (Linac) 377
9.4 The Betatron 379
9.5 The Synchrotron 381
9.6 Particle Collider Machines 383
9.7 Some Internationally Important Accelerators 384
10. Nuclear energy 389
10.1 Energy from Nuclear Fission 389
10.2 Fission Chain Reaction 392
10.3 Nuclear Fission Power Reactor 394
10.4 The Delayed Neutrons 398
10.5 Controlling Reactor Power or Reactivity: Important Role of Delayed
Neutrons 399
10.6 Essential Elements of a Reactor 399
10.7 Classification of Fission Reactors 400
10.8 Problems Associated with Fission Reactors 402
10.9 Fast and Thermal Breeder Reactors 403
10.10 Advantages of Fission Energy 403
10.11 Accelerator-driven Energy Amplifier 404
10.12 India’s Three-stage Program for Harnessing Nuclear Energy 405
10.13 Possibilities of Controlled Fusion 406
10.14 Global Status of Nuclear Energy 411
10.15 Heavy and Super Heavy (SHE) Elements: Transuranic/Actinide and
Trans-actinide Nuclides 412
10.16 Nuclear Weapons 413
11. Fundamentals of elementary Particles 419
11.1 Elementary Particles 419
11.2 The Eight-fold Way 421
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vi Contents
11.3 Quark Model of Hadrons 422
11.4 New Quarks 424
11.5 Intermediate Vector Bosons 424
11.6 Gluons 425
11.7 Standard Model 425
11.8 Higg’s Field and Higg’s Particle 425
11.9 Conservation Laws 426
11.10 The Fundamental Forces of Nature 430
11.11 Nucleon Resonances and Hyperons 432
11.12 Discovery of Muon and p -Meson 433
11.13 Measurement of the Spin and Parity of Pions 436
11.14 The CPT or Lüders–Pauli Theorem 439
11.15 Units in Particle Physics: The Natural Units 443
11.16 Introduction to Feynman’s Diagrams 445
12. cosmic rays 451
12.1 Discovery of Cosmic Rays 451
12.2 The East–West Asymmetry 456
12.3 The Latitude and Longitude Effects 457
12.4 Some Important Detector Setups Used in the Study of Cosmic Rays 459
12.5 Primary Cosmic Rays 461
12.6 Passage of Primary Cosmic Rays Through the Atmosphere 462
12.7 Cosmic Ray Showers 464
12.8 Generation of Showers 467
12.9 Source of Cosmic Rays and the Mechanism of Acceleration of Cosmic
Ray Particles 469
12.10 How Cosmic Rays Affect Us? 470
Solutions to Numerical Problems 477
Index 487
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Preface
Nuclear Physics has been written for graduates and postgraduates, especially the ones studying
‘nuclear physics’ or ‘nuclear, particle and cosmic ray physics’. Written in a simple language, the
book comprises a judicial balance between theory and experiments. It includes latest topics like
the heavy ion reactions, radioactive ion beams, pre-equilibrium emission, complete and incom-
plete fusion, reactions important for nucleon synthesis, Higg’s mechanism and God particle,
Feynman diagrams etc. An attempt has been made to develop each topic from the very funda-
mental level to the higher level which may join smoothly with the requirements of advanced stud-
ies in the subject. Many solved examples, with a graded level of difficulty, have been included
for the practice of the students. A very special feature of the book is the inclusion of MCQs
(multiple-choice questions) after every chapter. Some of these questions have more than one cor-
rect alternative. A complete answer, in such cases, requires picking up all the correct alternatives
that ensures comprehensive understanding of the subject.
The book contains twelve chapters. The first chapter, titled ‘The birth of the nucleus’, gives a
brief review of the scientific temper and important scientific discoveries made till the time when
pioneering alpha scattering experiments were carried out by Rutherford and his group. This
may help in appreciate the ingenuity of the alpha scattering experiments. Detailed and stepwise
derivation of Rutherford scattering formula is then derived using the basic conservation laws of
non-relativistic mechanics. The chapter ends with an introduction to the basic properties of the
nucleus and the modern quark model of the nucleus.
Having introduced the basic nuclear properties in chapter 1, more detailed description of these
properties and methods of their experimental determination have been discussed in chapter 2.
Energy and momentum filters are used not only in mass spectrographs but also in other nuclear
instruments like accelerators, atomic and molecular beam systems etc. A detailed discussion of
these is, therefore, included in this chapter. Any measurement is incomplete without an estimate
of the accuracy. It is with this view that the topic of doublet method of mass spectrometry is
discussed in details.
Nearly constant and exceptionally large density of nuclear matter points towards the special
nature of nucleon-nucleon force. Basic properties of charge—independence, charge symmetry,
spin dependence and saturation of two body nucleon-nucleon force as derived from the system-
atic of stable nuclei—have been discussed in chapter 3.
The properties of microscopic systems are adequately described only by the quantum mechan-
ical treatment. In order to prove this, quantum mechanical analysis of the simplest stable nucleus
‘deuteron’ has been worked out in chapter 4. Frequently required tool of partial wave analysis
has been discussed in sufficient details in this chapter. In nuclear interactions, involving charged
particles, the reactants face a Coulomb barrier. In classical physics, the reactants cannot cross
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viii Preface
through the barrier if their kinetic energy is less than the height of the barrier. However, in case
of quantum mechanical treatment it can be shown that there is a finite probability of barrier
transmission even when the kinetic energy is less than the barrier height. This very important
aspect of quantum mechanics, which explains many nuclear phenomena, has also been devel-
oped in chapter 4. Development of quantum mechanical treatment at this stage is essential for a
comprehensive understanding of other topics like the alpha decay, nuclear fission and fusion etc
that follow.
The characteristics of stable and radioactive nuclei provide a basic set of data that a good
nuclear model must be able to reproduce. An inventory of such characteristics is compiled in
chapter 5. Independent particle model with an ad hock assumption of spin-orbit coupling led
to the nuclear shell model that can explain the magic numbers. Similarly, liquid drop model,
based on the similarity between the drops of a liquid and the nucleus has been quite successful in
explaining nuclear fission. The Fermi gas model is one of the simplest nuclear models that may
correctly predict the dependence of the stability of a nucleus on the difference in the number of
neutrons and protons in it. On the other hand collective models, that involve collective motion of
several nucleons together, have been able to correctly predict the lower excited states of nuclei.
All these models, with details needed for each, have been discussed in chapter 5.
After discussing the characteristics and the models for stable nuclei, Chapter 6 deals with the
unstable radioactive nuclei. The chapter details the stability criteria for nuclei, neutron and pro-
ton drip lines, laws of natural radioactive decay and its application to the successive series decay
leading to the Batman equations. Methods of activation analysis using stacked foil technique
for the study of nuclear reactions and carbon-14 dating for determining the archeological age
of artifacts have been discussed in this chapter. With the help of tools developed in chapter 4,
the elementary theory of alpha, beta and gamma decays are also provided in this chapter. Non
conservation of parity in beta decay, its experimental verification and consequences are also
outlined. This chapter also includes description of Mossbauer effect and its use as an important
experimental tool in different branches of science.
Detecting of nuclear radiations, their identification, measurement of their intensity and energy
distribution etc are the basic requirements of experimental nuclear physics. A detailed discus-
sion of energy loss processes that play very important role in devising detectors, for different
nuclear radiations is presented in chapter 7. Characteristics of different detectors, their selection
criteria etc are also discussed in this chapter. Some special detector set-ups for special needs are
also discussed. Neutrinos, emitted in weak nuclear interactions have very little interaction with
matter and, therefore, are very difficult to detect. However, neutrinos carry valuable information
about their source of origin. Neutrinos created at the time of big bang are expected to be present
in the universe and earth, without any interaction/alteration, even today. In view of this, dedi-
cated efforts s worldwide, are being made to develop neutrino detection facilities. India has also
planned a large neutrino facility. Details of Indian initiative along with other international efforts
are also outlined in chapter 7.
Binary nuclear reactions and reaction mechanisms are discussed in chapter 8. After discuss-
ing the conservation laws with the help of some examples, reaction Q-equation is developed,
which is then used to discuss cases in which two groups of particles with different kinetic ener-
gies are emitted at a given angle. Reaction mechanisms, including compound reaction mecha-
nism, pre-equilibrium emission, direct reactions, optical model and thermodynamic approaches
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Preface ix
to nuclear reactions are discussed in this chapter in sufficient details. Elementary treatment of
Giant resonances produced as a result of the interaction of electromagnetic radiations with the
nucleus is also presented in this chapter. Detailed discussions of heavy ion reactions, complete
and incomplete fusion, reactions with radioactive ion beams, halo nuclei, and reactions impor-
tant for nucleosynthesis which has been discussed in chapter 8.
Chapter 9 describes both the direct current and the cyclic accelerators. Information about
important international accelerator facilities including the large hadron collider and associated
experimental setups etc is also provided in this chapter.
Release of energy in nuclear fission and fusion, fission reactors, role of fast and slow fission
neutrons, new concept of accelerator driven energy amplifiers, confinement of plasma, magnetic
and inertial confinement, uncontrolled nuclear devices etc have all been discussed in chapter 10
on nuclear energy.
The topics of elementary particles and cosmic rays are included in the nuclear physics syllabus
of some universities. Hence, in order to cover the entire course, chapter 11 titled ‘Fundamentals
of elementary particles’ and chapter 12 titled ‘Cosmic rays’ have been included. Discoveries of
some important elementary particles, their classification, eight-fold way, conservation laws,
characteristics of fundamental interactions, quark structure of hadrons, electro weak interactions
and unification, standard model, Higg’s field and God particle, natural units and an introduction
to Feynman diagrams etc have all been discussed in a simplified way in chapter 11.
The last chapter of the book gives a detailed account of the discovery, classification, com-
position, variation with different parameters, origin and impact of cosmic rays on human life.
Different experimental set-ups used to study different aspects of cosmic rays have also been
described in this chapter. The contribution of two well known Indian scientists, Prof. P.S. Gill and
Prof. H.J. Bhabha, in the field of cosmic rays, has also been highlighted in this chapter.
Comments and suggestions for further improvement of the book are most welcome.
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