Subatomic Physics

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8.8. References 237 8.4. Verify the steps in footnote 1. 8.5. Calculate the commutator (8.11). 8.6. Justify that the isospin of the deuteron is zero (a) By using experimental information. (b) By considering the generalized Pauli principle stating that the total wave function, assumed to be a product of space, spin, and isospin parts, must be antisymmetric under the exchange of the two nucleons. 8.7. The reaction dd −→ απ 0 has been observed (see E.J. Stephenson et al., Phys. Rev. Lett. 91, 142302 (2003)), but with a very small cross section. The isospin of the deuteron and the alpha particle are known to be zero. What does the abnormally small cross section of the reaction tell us? 8.8. Verify Eq. (8.37), Eq. (8.38). 8.9. ∗ Study the energy levels of the A =12isobars. (a) Sketch the energy level diagrams. (b) Justify that the ground state and the first few excited states of 12 Chave isospin zero. (c) Find the first I =1statein 12 C and justify that it forms an isospin triplet with the ground states of 12 Band 12 N. 8.10. Consider the reactions d 16 O −→ α 14 N d 12 C −→ p 13 C. Assume isospin invariance. What are the values of I of the states in 14 N and 13 C that can be reached by these reactions? ( 16 O, 12 C, α, andd denote ground states; 14 Nand 13 C can be excited.) 8.11. ∗ Consider the beta decay of 14 O to the first and second excited states in 14 N. Normally, a beta decay will have a lifetime that is approximately proportional to E −5 ,whereE is the maximum energy of the beta particles. Use isospin invariance to explain the observed branching ratio.
238 Angular Momentum and Isospin 8.12. ∗ Compare ∆ECoul for A =10, 80, and 200. Why is it more difficult (or impossible) to find all the members of an isospin multiplet in heavy nuclei than in light nuclei? 8.13. Consider the reactions γA −→ nA ′ dA −→ pA ′ dA −→ αA ′ 3 HeA ′′ −→ 3 HA ′ . If A is a self-conjugate (N = Z) nuclide, what are the isospin states in A ′ that can be reached by these reactions? The photon “carries” isospin 0 and 1. If A ′′ has isospin 0, or 1 3 2 ,or2 , what are the possible values of the isospin states in A ′ ? 8.14. (a) Prove the commutation relations [I±,I 2 ]=0, [I3,I±] =±I±, [I+,I−] =2I3. (b) Use these commutation relations and Eq. (8.24) to prove Eq. (8.27). 8.15. (a) Use the generalization of Eq. (8.30) to deduce the strangeness content of the D 0 meson of isospin 1/2, the ηc meson of isospin 0, the Λ + c baryon of isospin 0. Assume that B = T =0. (b) Repeat part (a) for bottomness content for the B− of isospin 1 2 ,ifC = T =0. 8.16. The angular distribution of neutral pions produced in the reaction np → dπ 0 is found to be (almost) symmetrical about 90 ◦ in the c.m. (see A.K. Opper et al., Phys. Rev. Lett. 91, 212302 (2003)) Show that this follows from isospin conservation. 8.17. Projection operators have the properties that P |a〉 and P |b〉 =0if〈a|b〉 =0 and P 2 = P . In terms of the isospin operator I3,op determine a projection operator Pp for the proton and Pn for the neutron, such that Pp|p〉 =1, Pp|n〉 =0,Pn|n〉 =1,Pn|p〉 =0. (For isospin 1/2 I 2 3,op =1/4).
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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
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4.10. Calorimeters 69 Figure 4.18:
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4.11. Counter Electronics 71 Figure
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4.13. References 73 Table 4.1: Func
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4.13. References 75 4.6. Sketch the
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Part II Particles and Nuclei The si
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Chapter 5 The Subatomic Zoo A conve
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5.1. Mass and Spin. Fermions and Bo
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5.1. Mass and Spin. Fermions and Bo
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5.2. Electric Charge and Magnetic D
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5.3. Mass Measurements 87 Figure 5.
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5.3. Mass Measurements 89 Figure 5.
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5.3. Mass Measurements 91 Earlier,
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5.4. A First Glance at the Subatomi
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5.5. Gauge Bosons 95 Figure 5.13: A
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5.6. Leptons 97 to its momentum, re
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5.7. Decays 99 Figure 5.15: Exponen
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5.7. Decays 101 The function g(ω)
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5.8. Mesons 103 5.8 Mesons Table 5.
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5.9. Baryon Ground States 105 Japan
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5.9. Baryon Ground States 107 neutr
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5.10. Particles and Antiparticles 1
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5.10. Particles and Antiparticles 1
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5.11. Quarks, Gluons, and Intermedi
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5.12. Excited States and Resonances
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5.12. Excited States and Resonances
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5.13. Excited States of Baryons 123
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5.14. References 129 in Section 5.5
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5.14. References 131 5.14. Use the
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5.14. References 133 5.32. ∗ What
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Chapter 6 Structure of Subatomic Pa
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6.2. Rutherford and Mott Scattering
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6.2. Rutherford and Mott Scattering
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6.3. Form Factors 141 The scatterin
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6.4. The Charge Distribution of Sph
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6.4. The Charge Distribution of Sph
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6.5. Leptons Are Point Particles 14
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6.6. Nucleon Elastic Form Factors 1
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6.8. Inelastic Electron and Muon Sc
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6.8. Inelastic Electron and Muon Sc
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6.9. Deep Inelastic Electron Scatte
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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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Page 208 and 209: 6.11. More Details on Scattering an
Page 210 and 211: 6.12. References 189 Some character
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Page 216 and 217: Part III Symmetries and Conservatio
Page 218 and 219: Chapter 7 Additive Conservation Law
Page 220 and 221: 7.1. Conserved Quantities and Symme
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Page 224 and 225: 7.2. The Electric Charge 203 7.2 Th
Page 226 and 227: 7.2. The Electric Charge 205 or [Q,
Page 228 and 229: 7.3. The Baryon Number 207 antineut
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Page 238 and 239: 7.7. References 217 There are also
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Page 242 and 243: Chapter 8 Angular Momentum and Isos
Page 244 and 245: 8.2. Symmetry Breaking by a Magneti
Page 246 and 247: 8.4. The Nucleon Isospin 225 8.4 Th
Page 248 and 249: 8.5. Isospin Invariance 227 magneti
Page 250 and 251: 8.6. Isospin of Particles 229 the v
Page 252 and 253: 8.6. Isospin of Particles 231 The a
Page 254 and 255: 8.7. Isospin in Nuclei 233 If the e
Page 256 and 257: 8.8. References 235 Isospin doublet
Page 260 and 261: Chapter 9 P , C, CP, andT In the pr
Page 262 and 263: 9.1. The Parity Operation 241 P is
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Page 268 and 269: 9.3. Conservation and Breakdown of
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Page 276 and 277: 9.4. Charge Conjugation 255 The π
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Page 292 and 293: 9.9. References 271 • There are t
Page 294 and 295: 9.9. References 273 9.8. * Find inf
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Page 298 and 299: 9.9. References 277 9.39. Compare t
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Page 302 and 303: Chapter 10 The Electromagnetic Inte
Page 304 and 305: 10.1. The Golden Rule 283 Schrödin
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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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