Subatomic Physics

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Chapter 18 Collective Model Although the shell model describes the magic numbers and the properties of many levels very well, it has a number of failures. The most outstanding one is the fact that many quadrupole moments are much larger than those predicted by the shell model. (1) It was shown by Rainwater that such large quadrupole moments can be explained within the concept of a shell model if the closed-shell core is assumed to be deformed. (2) Indeed, if the core is ellipsoidal it acquires a quadrupole moment proportional to the deformation. A deformation of the core is evidence for manybody effects, and collective modes of excitation are possible. The appearance of such modes is not surprising. Lord Rayleigh investigated the stability and oscillations of electrically charged liquid drops in 1877, (3) and Niels Bohr and F. Kalckar showed in 1936 that a system of particles held together by their mutual attraction can perform collective oscillations. (4) A classical example of such collective effects is provided by plasma oscillations. (5) The existence of large nuclear quadrupole moments provides evidence for the possibility of collective effects in nuclei. From about 1950, Aage Bohr and Ben Mottelson started a systematic study of collective motions in nuclei; (6) over the years, they and their collaborators have improved the treatment so that today the model combines the desirable features of shell and collective models and is called the unified nuclear model. The salient facts can be discussed most easily by describing two extreme situations. Closed shell nuclei are spherically symmetric and not deformed. The primary collective motions of such nuclei are surface oscillations, like the surface waves on a liquid drop. For small oscillations, harmonic restoring forces are assumed, and equally spaced vibrational levels result. Far away from closed shells, the nucleons outside the core polarize the core, and the nucleus can acquire a permanent 1 C.H. Townes, H.M. Foley, and W. Low, Phys. Rev. 76, 1415 (1949). 2 J. Rainwater, Phys. Rev. 79, 432 (1950). 3 J.W.S. Rayleigh, The Theory of Sound, Vol. II, Macmillan, New York, 1877, §364. 4 N. Bohr, Nature 137, 344 (1936); N. Bohr and F. Kalckar, Kgl. Danske Videnskab. Selskab. Mat.-fys. Medd. 14, No. 10 (1937). 5 Feynman Lectures, II-7-5ff; Jackson, Chapter 7. 6 A. Bohr, Phys. Rev. 81, 134 (1951); A. Bohr and B.R. Mottelson, Kgl. Danske Videnskab. Selskab. Mat-fys. Medd. 27, No. 16 (1953). 543
544 Collective Model deformation. The entire deformed nucleus can rotate, and this type of collective excitation leads to the appearance of rotational bands. The deformed nucleus acts as a nonspherical potential for the much more rapid single-particle motion; the energy levels of a single particle in such a potential can be investigated, and the result is the Nilsson model, (7) already mentioned at the end of the previous chapter. We shall begin the discussion in the present chapter with deformations and rotational excitations because these two features are easiest to understand and give the most spectacular effects. 18.1 Nuclear Deformations As early as 1935 optical spectra revealed the existence of nuclear quadrupole moments. (8) We have encountered the quadrupole moment in Section 14.5, and we have seen there that it measures the deviation of the shape of the nuclear charge distribution from a sphere. The existence of a quadrupole moment hence implies nonspherical (deformed) nuclei. For the discussion of nuclear models, the sign and magnitude of the deformation are important. As we shall see below, the quadrupole moments far away from closed shells are so large that they cannot be due to a single particle and thus cannot be explained by the naive shell model. The discrepancy is particularly clear around A ≈ 25 (Al, Mg), 150
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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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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
Page 514 and 515: 15.9. Outlook and Problems 493 wher
Page 516 and 517: 15.10. References 495 On a more adv
Page 518 and 519: 15.10. References 497 where J± = J
Page 520 and 521: 15.10. References 499 (b) Apply the
Page 522 and 523: Chapter 16 Liquid Drop Model, Fermi
Page 524 and 525: 16.1. The Liquid Drop Model 503 Fig
Page 526 and 527: 16.1. The Liquid Drop Model 505 Bey
Page 528 and 529: 16.2. The Fermi Gas Model 507 N = V
Page 530 and 531: E/A(MeV) 16.3. Heavy Ion Reactions
Page 532 and 533: 16.4. Relativistic Heavy Ion Collis
Page 534 and 535: 16.4. Relativistic Heavy Ion Collis
Page 536 and 537: 16.5. References 515 medium (i.e. s
Page 538 and 539: 16.5. References 517 16.12. Symmetr
Page 540 and 541: 16.5. References 519 16.25. At RHIC
Page 542 and 543: Chapter 17 The Shell Model The liqu
Page 544 and 545: 17.1. The Magic Numbers 523 The res
Page 546 and 547: 17.2. The Closed Shells 525 solved
Page 548 and 549: 17.2. The Closed Shells 527 Figure
Page 550 and 551: 17.3. The Spin-Orbit Interaction 52
Page 552 and 553: 17.4. The Single-Particle Shell Mod
Page 554 and 555: 17.5. Generalization of the Single-
Page 556 and 557: 17.6. Isobaric Analog Resonances 53
Page 558 and 559: 17.7. Nuclei Far From the Valley of
Page 560 and 561: 17.8. References 539 An elementary
Page 562 and 563: 17.8. References 541 (b) N odd. (c)
Page 566 and 567: 18.1. Nuclear Deformations 545 spin
Page 568 and 569: 18.2. Rotational Spectra of Spinles
Page 570 and 571: 18.2. Rotational Spectra of Spinles
Page 572 and 573: 18.3. Rotational Families 551 A spi
Page 574 and 575: 18.3. Rotational Families 553 2. Th
Page 576 and 577: 18.4. One-Particle Motion in Deform
Page 578 and 579: 18.4. One-Particle Motion in Deform
Page 580 and 581: 18.5. Vibrational States in Spheric
Page 582 and 583: 18.5. Vibrational States in Spheric
Page 584 and 585: 18.6. The Interacting Boson Model 5
Page 586 and 587: 18.7. Highly Excited States; Giant
Page 588 and 589: 18.8. Nuclear Models—Concluding R
Page 590 and 591: 18.8. Nuclear Models—Concluding R
Page 592 and 593: 18.9. References 571 J. S. Vaagen,
Page 594 and 595: 18.9. References 573 18.13. Verify
Page 596 and 597: 18.9. References 575 18.33. Conside
Page 598 and 599: 18.9. References 577 18.51. (a) In
Page 600 and 601: Chapter 19 Nuclear and Particle Ast
Page 602 and 603: 19.1. The Beginning of the Universe
Page 604 and 605: 19.1. The Beginning of the Universe
Page 606 and 607: 19.2. Primordial Nucleosynthesis 58
Page 608 and 609: 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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