Nuclear Physics 1

Оглавление

Ibrahima Sakho. Nuclear Physics 1

Table of Contents

Guide

List of Illustrations

List of Tables

Pages

Nuclear Physics 1. Nuclear Deexcitations, Spontaneous Nuclear Reactions

Preface

1. Overview of the Nucleus

1.1. Discovery of the electron. 1.1.1. Hittorf and Crookes experiments

Box 1.1. Hittorf (1824–1914); Crookes (1832–1919)

1.1.2. Perrin and Thomson experiments

Box 1.2. Stoney (1826–1911); Thomson (1856–1940); Perrin (1870–1942)

1.1.3. Millikan experiment

Box 1.3. Millikan (1868–1953)

1.2. The birth of the nucleus. 1.2.1. Perrin and Thomson atomic model

1.2.2. Geiger and Marsden experiment

Box 1.4. Geiger (1882–1945); Marsden (1889–1970)

1.2.3. Rutherford scattering: Planetary atomic model

1.2.4. Rutherford’s differential effective cross-section

Box 1.5.Rutherford (1871–1937)

1.3. Composition of the nucleus. 1.3.1. Discovery of the proton

Box 1.6. Blackett (1897–1974); Bothe (1891–1954)

1.3.2. Discovery of the neutron

Box 1.7.Chadwick (1891–1974)

1.3.3. Internal structure of nucleons: u and d quarks

Box 1.8. Gell-Mann (1929–2019); Zweig (born 1937)

1.3.4. Isospin

1.3.5. Nuclear spin

1.3.6. Nuclear magnetic moment

1.4. Nucleus dimensions. 1.4.1. Nuclear radius

1.4.2. Nuclear density, skin thickness

Box 1.9. Saxon (1920–2005)

1.5. Nomenclature of nuclides. 1.5.1. Isotopes, isobars, isotones

Box 1.10. Soddy (1877-1956)

1.5.2. Mirror nuclei, Magic nuclei

1.6. Nucleus stability. 1.6.1. Atomic mass unit

1.6.2. Segrè diagram, nuclear energy surface

Box 1.11. Segrè (1905–1989)

1.6.3. Mass defect, binding energy

1.6.4. Binding energy per nucleon, Aston curve

Box 1.12. Aston (1877-1945)

1.6.5. Separation energy of a nucleon

1.6.6. Nuclear forces

1.7. Exercises

Box 1.13. Goldstein (1850–1930)

1.8. Solutions to exercises

2. Nuclear Deexcitations

2.1. Nuclear shell model. 2.1.1. Overview of nuclear models

2.1.2. Individual state of a nucleon

2.1.3. Form of the harmonic potential

2.1.4. Shell structure derived from a harmonic potential

2.1.5. Shell structure derived from a Woods–Saxon potential

Box 2.1. Yukawa (1905–1981); Goeppert-Mayer (1906–1970); Jensen (1907–1973)

2.2. Angular momentum and parity. 2.2.1. Angular momentum and parity of ground state

2.2.2. Angular momentum and parity of an excited state

2.3. Gamma deexcitation. 2.3.1. Definition, deexcitation energy

2.3.2. Angular momentum and multipole order of γ-radiation

2.3.3. Classification of γ-transitions, parity of γ-radiation

2.3.4. γ-transition probabilities, Weisskopf estimates

2.3.5. Conserving angular momentum and parity

Box 2.2. Weisskopf (1908–2002)

2.4. Internal conversion. 2.4.1. Definition

2.4.2. Internal conversion coefficients

2.4.3. Partial conversion coefficients

2.4.4. K-shell conversion

2.5. Deexcitation by nucleon emission. 2.5.1. Definition

2.5.2. Energy balance

2.5.3. Bound levels and virtual levels

2.5.4. Study of an example of delayed-neutron emission

2.6. Bethe–Weizsäcker semi-empirical mass formula. 2.6.1. Presentation of the liquid-drop model

2.6.2. Bethe–Weizsäcker formula, binding energy

2.6.3. Volume energy, surface energy

2.6.4. Coulomb energy

2.6.5. Asymmetry energy, pairing energy

2.6.6. Principle of semi-empirical evaluation of coefficients in Bethe–Weizsäcker form

2.6.7. Isobar binding energy, the most stable isobar

2.7. Mass parabola equation for odd A. 2.7.1. Expression

2.7.2. Determining the nuclear charge of the most stable isobar from the decay energy

2.7.3. Mass parabola equation for even A

Box 2.3. Bethe (1906–2005); Weizsäcker (1912–2007)

2.8. Nuclear potential barrier. 2.8.1. Definition, model of the rectangular potential well

2.8.2. Modifying the model of the rectangular potential well

2.9. Exercises

2.10. Solutions to exercises

3. Alpha Radioactivity

3.1. Experimental facts. 3.1.1. Becquerel’s observations, radioactivity

Box 3.1. Becquerel (1852–1908)

3.1.2. Discovery of α radioactivity and β − radioactivity

Box 3.2. Marie Curie (1867–1934); Pierre Curie (1859–1906); Soddy (1877–1956)

3.1.3. Discovery of the positron

Box 3.3. Anderson (1905–1991); Neddermeyer (1907–1988)

3.1.4. Discovery of the neutrino, Cowan and Reines experiment

Box 3.4. Cowan (1919–1974); Reines (1918–1998)

3.1.5. Highlighting α, β and γ radiation

3.2. Radioactive decay. 3.2.1. Rutherford and Soddy’s empirical law

3.2.2. Radioactive half-life

3.2.3. Average lifetime of a radioactive nucleus

3.2.4. Activity of a radioactive source

3.3. α radioactivity. 3.3.1. Balanced equation

3.3.2. Mass defect (loss of matter), decay energy

3.3.3. Decay energy diagram

3.3.4. Fine structure of α lines

3.3.5. Geiger–Nuttall law

3.3.6. Quantum model ofα emission by tunnel effect

3.3.7. Estimating the radioactive half-life, Gamow factor

Box 3.5. Gamow (1906–1968); Gurney (1898–1953); Condon (1902–1974)

3.4. Exercises

3.5. Solutions to exercises

4. Beta Radioactivity, Radioactive Family Tree

4.1. Beta radioactivity. 4.1.1. Experiment of Frédéric and Irène Joliot-Curie: discovery of artificial radioactivity

Box 4.1. Irène Joliot (1897–1956);Frédéric Joliot (1900–1958); Townsend (1868–1967)

4.1.2. Balanced equation, β decay energy

4.1.3. Continuous β emission spectrum

4.1.4. Sargent diagram, β transition selection rules

Box 4.2. Sargent (1906–1993); Teller (1908–2003)

4.1.5. Decay energy diagram

4.1.6. Condition of β + emission

4.1.7. Decay by electron capture

4.1.8. Double β decay, branching ratio

4.1.9. Atomic deexcitation, Auger effect

Box 4.3. Fermi (1901–1954); Siegbahn (1886–1978); Auger (1899–1993)

4.2. Radioactive family trees. 4.2.1. Definition

4.2.2. Simple two-body family tree

4.2.3. Multi-body family tree, Bateman equations

4.2.4. Secular equilibrium

Box 4.4. Bateman (1882−1946)

4.3. Radionuclide production by nuclear bombardment. 4.3.1. General aspects

4.3.2. Production rate of a radionuclide

4.3.3. Production yield of a radionuclide

4.4. Natural radioactive series. 4.4.1. Presentation

4.4.2. Thorium (4n) family

4.4.3. Neptunium (4n + 1) family

4.4.4. Uranium-235 (4n +2) family

4.4.5. Uranium-238 (4n + 3) family

4.5. Exercises

4.6. Solutions to exercises

Appendix 1. Quantified Energy of the Three-Dimensional Quantum Harmonic Oscillator

A1.1. Integration of the Schrödinger equation

A1.2. Use of creation and annihilation operators

Appendix 2. Atomic Masses of Several Nuclides

References

Index

A, B

C, D

E, F

G, H

I, J

L, M

N, O

P, Q

R, S

T, U

V, W

X, Y, Z

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Ibrahima Sakho

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Chapter 1 is reserved for general information regarding the atomic nucleus with a view to establishing the general properties of nuclei. It begins with a presentation of the experimental facts that led to the discovery of the electron (β− particle), the proton, the neutron and the nucleus itself. It then focuses on the study of the composition and dimensions of the nucleus. Next, the nomenclature of nuclides and the stability of nuclei are studied. The chapter culminates with a series of exercises with answers.

Chapter 2 is dedicated to the study of nuclear deexcitation processes. The nuclear shell model, which offers an understanding of the discrete structure of nuclear levels, is studied in detail. Subsequently, the study examines the properties of angular momentum and parity, the processes of gamma deexcitation and internal conversion and the phenomenon of deexcitation by nuclear emission. A detailed study of the Bethe–Weizsäcker semi-empirical mass formula via the liquid-drop model and of the mass parabola equation for odd A completes the chapter and is followed by a series of exercises complete with answers.

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