Subatomic Physics

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5.12. Excited States and Resonances 119 Figure 5.29: Energy levels in a square well. The ground state is sharp. The excited states can decay to the ground state by photon emission, and they display a natural line width. States with positive energy form a continuum. treating the square well. Consider a particle with mass m in a square well as shown in Fig. 5.29. It is straightforward to solve the Schrödinger equation for this problem and to find the allowed energy levels. First consider the case E
120 The <strong>Subatomic</strong> Zoo Figure 5.30: Scattering of a particle with energy E from a one-dimensional potential well. Classically, all incident particles will be transmitted. Quantum mechanically, at small energies, the transmission coefficient T is unity only at certain energies. The appearance of transmission resonances in the behavior of the transmission as a function of particle energy E is shown at the right. 1 T =1+ V 2 4E(E + |V |) sin2 ka, (5.66) where E is the kinetic energy of the incident particles, V (< 0) the depth, and a the width of the potential well. The wave number k is given by k 2 = 2m (E + |V |). (5.67) �2 Equations (5.66) and (5.67) demonstrate that the transmission coefficient T is unity only at certain energies. The behavior of T as a function of E is sketched in Fig. 5.30, where the appearance of transmission resonances is evident. The behavior of a particle with an energy Er corresponding to maximum transmission can be investigated by using wave packets rather than plane waves to describe the incident beam. It turns out that the incident particle remains in the well region for a time that is much longer than that expected from classical mechanics. (44) The mean time spent in the well region, τ, and the width of the corresponding resonance, Γ, satisfy Eq. (5.46). Mathematically, the existence of a resonance at the energy Er can again be described, in analogy to Eq. (5.36), by introducing a complex energy, E = Er − 1 2 iΓ. Here Er is positive, and Γ can be comparable to Er. The appearance of a resonance in the continuum is not restricted to the simple one-dimensional case just discussed but is a more general phenomenon. To treat 44 Detailed discussions can be found in Merzbacher, Chapter 6, and in D. Bohm, Quantum Theory, Prentice Hall, Englewood Cliffs, N. J., 1951, Chapters 11 and 12.
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SUBAT MIC PHYSICS Third Edition
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SUBAT MIC PHYSICS Ernest M Henley A
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To Elaine and Viviana
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Acknowledgments In writing the pres
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Preface to the First Edition Subato
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Preface to the Third Edition Subato
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General Bibliography The reader of
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Contents Dedication v Acknowledgmen
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Contents xvii 6 Structure of Subato
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Contents xix 12.5 GeneralReferences
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Chapter 1 Background and Language H
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1.2. Units 3 1.2 Units Table 1.1: B
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1.3. Special Relativity, Feynman Di
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1.3. Special Relativity, Feynman Di
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1.4. References 9 Problems 1.1. ∗
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Part I Tools One of the most frustr
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Chapter 2 Accelerators 2.1 Why Acce
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2.1. Why Accelerators? 15 particle
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2.2. Cross Sections and Luminosity
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2.3. Electrostatic Generators (Van
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2.4. Linear Accelerators (Linacs) 2
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2.5. Beam Optics 23 Figure 2.8: Rec
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2.6. Synchrotrons 25 Figure 2.10: E
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2.6. Synchrotrons 27 Photo 3: The p
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2.7. Laboratory and Center-of-Momen
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2.8. Colliding Beams 31 or with Eqs
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2.10. Beam Storage and Cooling 33 l
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2.11. References 35 and in E. Byckl
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2.11. References 37 (b) Extreme rel
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Chapter 3 Passage of Radiation Thro
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3.2. Heavy Charged Particles 41 Fig
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3.2. Heavy Charged Particles 43 −
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3.3. Photons 45 Equation (3.2) also
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3.4. Electrons 47 Figure 3.8: Passa
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3.5. Nuclear Interactions 49 Figure
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3.6. References 51 3.8. A beam of 1
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Chapter 4 Detectors What would a ph
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4.1. Scintillation Counters 55 The
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4.2. Statistical Aspects 57 Or, to
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4.3. Semiconductor Detectors 59 kno
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4.3. Semiconductor Detectors 61 Fig
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4.4. Bubble Chambers 63 Photo 5: Bu
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4.6. Wire Chambers 65 voltage suppl
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4.8. Time Projection Chambers 67 Fi
Page 90 and 91: 4.10. Calorimeters 69 Figure 4.18:
Page 92 and 93: 4.11. Counter Electronics 71 Figure
Page 94 and 95: 4.13. References 73 Table 4.1: Func
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Page 98 and 99: Part II Particles and Nuclei The si
Page 100 and 101: Chapter 5 The Subatomic Zoo A conve
Page 102 and 103: 5.1. Mass and Spin. Fermions and Bo
Page 104 and 105: 5.1. Mass and Spin. Fermions and Bo
Page 106 and 107: 5.2. Electric Charge and Magnetic D
Page 108 and 109: 5.3. Mass Measurements 87 Figure 5.
Page 110 and 111: 5.3. Mass Measurements 89 Figure 5.
Page 112 and 113: 5.3. Mass Measurements 91 Earlier,
Page 114 and 115: 5.4. A First Glance at the Subatomi
Page 116 and 117: 5.5. Gauge Bosons 95 Figure 5.13: A
Page 118 and 119: 5.6. Leptons 97 to its momentum, re
Page 120 and 121: 5.7. Decays 99 Figure 5.15: Exponen
Page 122 and 123: 5.7. Decays 101 The function g(ω)
Page 124 and 125: 5.8. Mesons 103 5.8 Mesons Table 5.
Page 126 and 127: 5.9. Baryon Ground States 105 Japan
Page 128 and 129: 5.9. Baryon Ground States 107 neutr
Page 130 and 131: 5.10. Particles and Antiparticles 1
Page 132 and 133: 5.10. Particles and Antiparticles 1
Page 134 and 135: 5.11. Quarks, Gluons, and Intermedi
Page 142 and 143: 5.12. Excited States and Resonances
Page 144 and 145: 5.13. Excited States of Baryons 123
Page 150 and 151: 5.14. References 129 in Section 5.5
Page 152 and 153: 5.14. References 131 5.14. Use the
Page 154 and 155: 5.14. References 133 5.32. ∗ What
Page 156 and 157: Chapter 6 Structure of Subatomic Pa
Page 158 and 159: 6.2. Rutherford and Mott Scattering
Page 160 and 161: 6.2. Rutherford and Mott Scattering
Page 162 and 163: 6.3. Form Factors 141 The scatterin
Page 164 and 165: 6.4. The Charge Distribution of Sph
Page 166 and 167: 6.4. The Charge Distribution of Sph
Page 168 and 169: 6.5. Leptons Are Point Particles 14
Page 174 and 175: 6.6. Nucleon Elastic Form Factors 1
Page 182 and 183: 6.8. Inelastic Electron and Muon Sc
Page 184 and 185: 6.8. Inelastic Electron and Muon Sc
Page 186 and 187: 6.9. Deep Inelastic Electron Scatte
Page 188 and 189: 6.10. Quark-Parton Model for Deep I
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6.10. Quark-Parton Model for Deep I
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6.10. Quark-Parton Model for Deep I
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6.11. More Details on Scattering an
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6.12. References 189 Some character
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6.12. References 191 (c) Show that
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6.12. References 193 6.23. Show tha
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Part III Symmetries and Conservatio
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Chapter 7 Additive Conservation Law
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7.1. Conserved Quantities and Symme
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7.1. Conserved Quantities and Symme
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7.2. The Electric Charge 203 7.2 Th
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7.2. The Electric Charge 205 or [Q,
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7.3. The Baryon Number 207 antineut
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7.4. Lepton and Lepton Flavor Numbe
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7.5. Strangeness Flavor 211 all bel
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7.5. Strangeness Flavor 213 Positiv
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7.6. Additive Quantum Numbers of Qu
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7.7. References 217 There are also
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7.7. References 219 7.12. Follow th
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Chapter 8 Angular Momentum and Isos
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8.2. Symmetry Breaking by a Magneti
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8.4. The Nucleon Isospin 225 8.4 Th
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8.5. Isospin Invariance 227 magneti
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8.6. Isospin of Particles 229 the v
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8.6. Isospin of Particles 231 The a
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8.7. Isospin in Nuclei 233 If the e
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8.8. References 235 Isospin doublet
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8.8. References 237 8.4. Verify the
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Chapter 9 P , C, CP, andT In the pr
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9.1. The Parity Operation 241 P is
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9.2. The Intrinsic Parities of Suba
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9.2. The Intrinsic Parities of Suba
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9.3. Conservation and Breakdown of
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9.4. Charge Conjugation 253 “Is t
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9.4. Charge Conjugation 255 The π
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9.5. Time Reversal 257 if Tψ(t) an
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9.5. Time Reversal 259 found to be
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9.6. The Two-State Problem 261 Hami
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9.7. The Neutral Kaons 263 9.7 The
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9.7. The Neutral Kaons 265 3. The s
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9.7. The Neutral Kaons 267 and only
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9.8. The Fall of CP Invariance 269
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9.9. References 271 • There are t
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9.9. References 273 9.8. * Find inf
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9.9. References 275 9.27. Assume th
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9.9. References 277 9.39. Compare t
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Part IV Interactions In the previou
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Chapter 10 The Electromagnetic Inte
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10.1. The Golden Rule 283 Schrödin
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10.1. The Golden Rule 285 where it
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10.2. Phase Space 287 Figure 10.4:
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10.3. The Classical Electromagnetic
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10.3. The Classical Electromagnetic
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10.4. Photon Emission 293 is a twof
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10.4. Photon Emission 295 the form
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10.4. Photon Emission 297 where V (
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10.5. Multipole Radiation 299 The t
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10.5. Multipole Radiation 301 Figur
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10.6. Electromagnetic Scattering of
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10.6. Electromagnetic Scattering of
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10.7. Vector Mesons as Mediators of
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10.7. Vector Mesons as Mediators of
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10.8. Colliding Beams 311 10.8 Coll
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10.8. Colliding Beams 313 Figure 10
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10.9. Electron-Positron Collisions
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10.10. The Photon-Hadron Interactio
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10.11. Magnetic Monopoles 323 The s
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10.12. References 325 Quantum Elect
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10.12. References 327 (b) Compare t
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10.12. References 329 (a) How would
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Chapter 11 The Weak Interaction Thi
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11.1. The Continuous Beta Spectrum
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11.2. Beta Decay Lifetimes 335 The
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11.3. The Current-Current Interacti
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11.4. A Variety of Weak Processes 3
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11.4. A Variety of Weak Processes 3
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11.5. The Muon Decay 347 Linac Pion
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11.6. The Weak Current of Leptons 3
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11.6. The Weak Current of Leptons 3
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11.7. Chirality versus Helicity 353
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11.9. Weak Decays of Quarks and the
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11.10. Weak Currents in Nuclear Phy
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11.10. Weak Currents in Nuclear Phy
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11.11. Inverse Beta Decay: Reines a
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11.12. Massive Neutrinos 363 11.12
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11.13. Majorana versus Dirac Neutri
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11.14. The Weak Current of Hadrons
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11.15. References 375 11.15 Referen
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11.15. References 377 11.5. Beta sp
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11.15. References 379 (b) * Discuss
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11.15. References 381 11.41. For nu
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Chapter 12 Introduction to Gauge Th
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12.1. Introduction 385 D0 ≡ 1 ∂
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12.2. Potentials in Quantum Mechani
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12.3. Gauge Invariance for Non-Abel
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12.3. Gauge Invariance for Non-Abel
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12.4. The Higgs Mechanism; Spontane
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12.5. General References 401 12.5 G
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Chapter 13 The Electroweak Theory o
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13.2. The Gauge Bosons and Weak Iso
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13.2. The Gauge Bosons and Weak Iso
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13.3. The Electroweak Interaction 4
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13.4. Tests of the Standard Model 4
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13.4. Tests of the Standard Model 4
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13.5. References 419 Physics. 112,
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Chapter 14 Strong Interactions All
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14.1. Range and Strength of the Low
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14.2. The Pion-Nucleon Interaction
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14.3. The Form of the Pion-Nucleon
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14.4. The Yukawa Theory of Nuclear
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14.5. Low-Energy Nucleon-Nucleon Fo
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14.6. Meson Theory of the Nucleon-N
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14.7. Strong Processes at High Ener
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14.8. The Standard Model, Quantum C
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14.9. QCD at Low Energies 457 An ex
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14.10. Grand Unified Theories, Supe
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14.11. References 461 and Partons,
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14.11. References 463 Fig. 14.28 14
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14.11. References 465 14.25. The lo
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14.11. References 467 (b) What comb
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Part V Models “A model is like an
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Chapter 15 Quark Models of Mesons a
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15.2. Quarks as Building Blocks of
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15.4. Mesons as Bound Quark States
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15.4. Mesons as Bound Quark States
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15.5. Baryons as Bound Quark States
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15.6. The Hadron Masses 481 Figure
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15.7. QCD and Quark Models of the H
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15.8. Heavy Mesons: Charmonium, Ups
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15.9. Outlook and Problems 493 wher
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15.10. References 495 On a more adv
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15.10. References 497 where J± = J
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15.10. References 499 (b) Apply the
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Chapter 16 Liquid Drop Model, Fermi
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16.1. The Liquid Drop Model 503 Fig
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16.1. The Liquid Drop Model 505 Bey
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16.2. The Fermi Gas Model 507 N = V
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E/A(MeV) 16.3. Heavy Ion Reactions
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16.4. Relativistic Heavy Ion Collis
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16.4. Relativistic Heavy Ion Collis
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16.5. References 515 medium (i.e. s
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16.5. References 517 16.12. Symmetr
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16.5. References 519 16.25. At RHIC
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Chapter 17 The Shell Model The liqu
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17.1. The Magic Numbers 523 The res
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17.2. The Closed Shells 525 solved
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17.2. The Closed Shells 527 Figure
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17.3. The Spin-Orbit Interaction 52
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17.4. The Single-Particle Shell Mod
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17.5. Generalization of the Single-
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17.6. Isobaric Analog Resonances 53
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17.7. Nuclei Far From the Valley of
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17.8. References 539 An elementary
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17.8. References 541 (b) N odd. (c)
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Chapter 18 Collective Model Althoug
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18.1. Nuclear Deformations 545 spin
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18.2. Rotational Spectra of Spinles
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18.2. Rotational Spectra of Spinles
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18.3. Rotational Families 551 A spi
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18.3. Rotational Families 553 2. Th
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18.4. One-Particle Motion in Deform
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18.4. One-Particle Motion in Deform
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18.5. Vibrational States in Spheric
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18.5. Vibrational States in Spheric
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18.6. The Interacting Boson Model 5
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18.7. Highly Excited States; Giant
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18.8. Nuclear Models—Concluding R
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18.8. Nuclear Models—Concluding R
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18.9. References 571 J. S. Vaagen,
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18.9. References 573 18.13. Verify
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18.9. References 575 18.33. Conside
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18.9. References 577 18.51. (a) In
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Chapter 19 Nuclear and Particle Ast
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19.1. The Beginning of the Universe
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19.1. The Beginning of the Universe
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19.2. Primordial Nucleosynthesis 58
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19.3. Stellar Energy and Nucleosynt
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19.4. Stellar Collapse and Neutron
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19.4. Stellar Collapse and Neutron
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19.5. Cosmic Rays 597 We are consta
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19.5. Cosmic Rays 599 Figure 19.11:
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19.6. Neutrino Astronomy and Cosmol
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19.8. References 603 baryon excess
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19.8. References 605 Neutron Stars
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19.8. References 607 (a) What is th
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Index Abundance, 585-586 Accelerato
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Index 611 drift chambers, 66-67 ele
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Index 613 diagrams, 279 electromagn
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Index 615 outlook, 567 Nuclear stru
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Index 617 poles, 494 recurrences, 4
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Index 619 TCP theorem, 269, 448 Tem
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