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Structure and Reactions of Light Exotic Nuclei
By: Kalman Varga, Yasuyuki Suzuki, Rezso G. Lovas, Kazuhiro Yabana
Hardcover | 6 February 2003 | Edition Number 1
At a Glance
608 Pages
23.9 x 16.2 x 3.9
Hardcover
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Preface | p. xi |
Introduction | p. 1 |
Reactions with Light Exotic Nuclei | p. 9 |
Introduction to Part I | p. 11 |
Potential scattering | p. 19 |
Elements of scattering theory | p. 19 |
Scattering wave function | p. 19 |
Integral equation for scattering | p. 20 |
Flux conservation and optical theorem | p. 21 |
The eikonal approximation | p. 25 |
Derivation | p. 25 |
Treatment of the spin-orbit potential | p. 33 |
Projectile-rest frame | p. 35 |
Illustrative examples | p. 37 |
Square-well potential | p. 37 |
Coulomb scattering | p. 40 |
Glauber theory for composite-particle scattering | p. 43 |
Some kinematics | p. 43 |
Glauber theory | p. 46 |
Formal treatment | p. 46 |
Eikonal approximation | p. 50 |
Cross sections and reaction probabilities | p. 53 |
Nucleus+nucleus collision | p. 56 |
Profile function | p. 60 |
Optical-limit approximation to the phase-shift function | p. 62 |
Nucleon-nucleus case | p. 62 |
Nucleus-nucleus case | p. 67 |
Total reaction cross section | p. 69 |
Phase-shift function revisited | p. 74 |
Complete calculation | p. 74 |
Effective profile function | p. 77 |
High-energy reactions of halo nuclei | p. 81 |
Simple model for halo nuclei | p. 81 |
Glauber theory for halo nuclei | p. 83 |
Cross section formulae | p. 83 |
Relations between cross sections | p. 87 |
Optical-limit approximation for halo nuclei | p. 90 |
Applications | p. 96 |
Medium-energy reactions of halo nuclei | p. 101 |
Elastic scattering of stable nuclei | p. 101 |
Optical model | p. 101 |
Folding model | p. 103 |
Few-body direct reaction model | p. 109 |
The model | p. 109 |
Eikonal approximation | p. 111 |
Cross sections and reaction probabilities | p. 113 |
Applications | p. 115 |
Deuteron reactions | p. 115 |
Reactions with [superscript 11]Be: integrated cross sections | p. 119 |
Reactions with [superscript 11]Be: differential cross sections | p. 122 |
Reactions with other nuclei | p. 125 |
Fragment momentum distribution in reactions with halo nuclei | p. 127 |
Momentum distribution of projectile fragments | p. 127 |
Formalism | p. 131 |
Fundamentals | p. 131 |
Elastic breakup | p. 134 |
Inelastic breakup | p. 135 |
Derivation in the Glauber theory | p. 138 |
Applications | p. 142 |
A reaction with [superscript 11]Be | p. 142 |
A reaction with [superscript 8]B | p. 144 |
Coulomb breakup reactions of halo nuclei | p. 147 |
Soft dipole mode | p. 147 |
Dipole strength function | p. 147 |
Sum rule | p. 151 |
Zero-range potential model | p. 152 |
Equivalent-photon method | p. 157 |
Theory of the Coulomb breakup | p. 160 |
Eikonal approximation | p. 160 |
Perturbative theory | p. 165 |
Coulomb breakup reaction of [superscript 11]Be | p. 169 |
Postacceleration phenomena | p. 174 |
Structure of Light Exotic Nuclei | p. 177 |
Introduction to Part II | p. 179 |
Overview | p. 179 |
Description of exotic structure | p. 184 |
Cluster approach with Gaussians | p. 189 |
Correlated Gaussian approach | p. 193 |
Preliminary notes | p. 193 |
Motivation | p. 193 |
Essentials | p. 195 |
Coordinates and correlations | p. 198 |
Variational trial function | p. 201 |
Formulation in terms of relative coordinates | p. 201 |
Formulation without reference to relative coordinates | p. 204 |
Full form | p. 209 |
Generating function | p. 211 |
Definition | p. 211 |
Generating a correlated Gaussian | p. 214 |
Gaussian wave packets | p. 216 |
Correlated Gaussian from single-particle states | p. 219 |
Evaluation of matrix elements | p. 221 |
Uncoupling | p. 221 |
Including the centre of mass | p. 224 |
Generic forms of determinantal matrix elements | p. 227 |
Translation-invariant matrix elements | p. 228 |
Physical quantities | p. 231 |
One-body operators | p. 231 |
Two-body operators | p. 239 |
Variational procedure | p. 243 |
Basis optimization | p. 243 |
Stochastic optimization | p. 246 |
Random basis and sorting | p. 246 |
Trial-and-error search | p. 248 |
Refining | p. 250 |
Description of excited states | p. 252 |
Short-range and long-range behaviour | p. 255 |
Description of unbound states | p. 260 |
Classification | p. 260 |
Localization of resonances | p. 264 |
Analytic continuation in the coupling constant | p. 269 |
Pole trajectories | p. 269 |
Analytic continuation of pole trajectories | p. 273 |
Cluster models | p. 277 |
Preliminary notes | p. 277 |
Basic concepts of clustering | p. 279 |
Theory of clustering | p. 282 |
Cluster subspace | p. 282 |
Projection to the cluster subspace | p. 284 |
Amplitudes related to clustering | p. 288 |
Calculation of the clustering properties | p. 292 |
Basic concepts of cluster models | p. 293 |
Overview | p. 293 |
Intercluster relative motion | p. 294 |
The resonating-group method | p. 300 |
Essentials | p. 301 |
Matrix elements | p. 305 |
The harmonic-oscillator cluster model | p. 310 |
The model | p. 310 |
Eigenvalue problem of the norm operator | p. 314 |
The generator-coordinate method and the two-centre shell model | p. 315 |
Generator-coordinate method | p. 315 |
The method of complex generator coordinates | p. 321 |
Two-centre shell model | p. 324 |
Cluster distortion | p. 327 |
The orthogonality-condition model | p. 332 |
The nonlocality problem | p. 333 |
Local intercluster potential | p. 336 |
Microscopic versus macroscopic approach | p. 340 |
Observables | p. 340 |
The fishbone model | p. 343 |
Three-cluster system | p. 344 |
Cluster model in the correlated Gaussian approach | p. 351 |
Multicluster approximation | p. 351 |
Model space and interactions | p. 356 |
Characteristics of the state space | p. 357 |
Clustering in light nuclei | p. 358 |
Effective force | p. 360 |
Cluster correlations | p. 367 |
Correlated versus uncorrelated description | p. 367 |
Clustering in A-nucleon calculations | p. 370 |
Application to exotic nuclei | p. 379 |
The structure of [superscript 6]He and [superscript 6]Li | p. 379 |
Exposition | p. 379 |
State spaces | p. 381 |
Test of the approach | p. 386 |
Observables | p. 390 |
The structure of [superscript 8]He | p. 396 |
The mirror nuclei ([superscript 7]Li, [superscript 7]Be), ([superscript 8]Li, [superscript 8]B) and ([superscript 9]Li, [superscript 9]C) | p. 402 |
Exposition | p. 402 |
The structure of [superscript 7]Li and [superscript 7]Be | p. 403 |
The structure of [superscript 8]Li and [superscript 8]B | p. 404 |
The structure of [superscript 9]Li and [superscript 9]C | p. 408 |
Magnetic moments of mirror nuclei | p. 410 |
Summary | p. 416 |
The mirror nuclei [superscript 9]Be and [superscript 9]B | p. 417 |
Exposition | p. 417 |
State spaces and energies | p. 418 |
Radii and electromagnetic properties | p. 423 |
Beta-decay of [superscript 9]Li to [superscript 9]Be | p. 427 |
Summary | p. 428 |
The states of [superscript 10]Be | p. 429 |
Exposition | p. 429 |
Model | p. 430 |
Spectroscopy of states | p. 431 |
Density distributions | p. 434 |
The sequence of Be isotopes | p. 438 |
The parity inversion in the mirror nuclei [superscript 11]Be and [superscript 11]N | p. 439 |
The nuclei [superscript 10,11]Li | p. 446 |
Facts and speculations | p. 446 |
Theoretical approaches | p. 450 |
Overview of exotic structure | p. 456 |
Structure calculations with realistic nuclear forces | p. 460 |
Realistic forces | p. 461 |
Stochastic variational solution | p. 463 |
The triton and the alpha-particle | p. 464 |
The description of [superscript 6]Li | p. 465 |
Reaction calculations with correlated Gaussians | p. 468 |
Exposition | p. 468 |
High-energy p+[superscript 6]He scattering | p. 469 |
High-energy [superscript 6]He+[superscript 12]C scattering | p. 474 |
Low-energy [alpha]+[superscript 6]He scattering | p. 477 |
Appendices | p. 483 |
Overview of reaction theories | p. 483 |
Conventional cluster Jacobi coordinates | p. 491 |
Borromean and Efimov states | p. 497 |
Antisymmetrization | p. 503 |
Matrix elements between Slater determinants | p. 509 |
Unit operator | p. 509 |
One-body operators | p. 510 |
Two-body operators | p. 513 |
Many-body operators | p. 516 |
Matrix elements between correlated Gaussians | p. 523 |
Other matrix elements | p. 533 |
Successive coupling | p. 533 |
Unnatural parity states | p. 534 |
Calculation of the amplitudes related to clustering | p. 539 |
An [alpha]+n+n three-cluster model for [superscript 6]He | p. 547 |
The nuclear SU(3) symmetry | p. 553 |
Bibliography | p. 563 |
Glossary of symbols | p. 581 |
Index | p. 587 |
Abbreviations | p. 592 |
Table of Contents provided by Ingram. All Rights Reserved. |
ISBN: 9780415308724
ISBN-10: 0415308720
Published: 6th February 2003
Format: Hardcover
Language: English
Number of Pages: 608
Audience: General Adult
Publisher: Taylor & Francis Ltd
Country of Publication: GB
Edition Number: 1
Dimensions (cm): 23.9 x 16.2 x 3.9
Weight (kg): 1.02
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