Structure and reactions of light exotic nuclei / Yasuyuki Suzuki ... [and others].

Format:

Book

Contributor:

Suzuki, Yasuyuki, 1945-

Language:

English

Subjects (All):

Exotic nuclei.

Physical Description:

xv, 591 pages : illustrations ; 25 cm

Place of Publication:

London ; New York : Taylor & Francis, 2003.

Summary:

Since the mid-1980s increasing effort has been put into light exotic nuclei, that is light nuclei of unusual composition. The research of the exotic nuclei began with the advent of accelerated beams of such nuclei. This new technique has revitalized nuclear physics, and the facilities producing radioactive ion beams now offer opportunities for pioneering research. This book considers the theory of collisions of light exotic nuclei and puts forth a multi-cluster model in which the inter-cluster motion is treated accurately. Current hot topics are included, as are more advanced areas of the theory. Structure and Reactions of Light Exotic Nuclei is intended for both experimental and theoretical physicists of graduate level and above.

Contents:

I Reactions with Light Exotic Nuclei 9

2 Potential scattering 19

2.1 Elements of scattering theory 19

2.1.1 Scattering wave function 19

2.1.2 Integral equation for scattering 20

2.1.3 Flux conservation and optical theorem 21

2.2 The eikonal approximation 25

2.2.1 Derivation 25

2.2.2 Treatment of the spin-orbit potential 33

2.2.3 Projectile-rest frame 35

2.3 Illustrative examples 37

2.3.1 Square-well potential 37

2.3.2 Coulomb scattering 40

3 Glauber theory for composite-particle scattering 43

3.1 Some kinematics 43

3.2 Glauber theory 46

3.2.1 Formal treatment 46

3.2.2 Eikonal approximation 50

3.2.3 Cross sections and reaction probabilities 53

3.2.4 Nucleus+nucleus collision 56

3.2.5 Profile function 60

3.3 Optical-limit approximation to the phase-shift function 62

3.3.1 Nucleon-nucleus case 62

3.3.2 Nucleus-nucleus case 67

3.4 Total reaction cross section 69

3.5 Phase-shift function revisited 74

3.5.1 Complete calculation 74

3.5.2 Effective profile function 77

4 High-energy reactions of halo nuclei 81

4.1 Simple model for halo nuclei 81

4.2 Glauber theory for halo nuclei 83

4.2.1 Cross section formulae 83

4.2.2 Relations between cross sections 87

4.2.3 Optical-limit approximation for halo nuclei 90

4.3 Applications 96

5 Medium-energy reactions of halo nuclei 101

5.1 Elastic scattering of stable nuclei 101

5.1.1 Optical model 101

5.1.2 Folding model 103

5.2 Few-body direct reaction model 109

5.2.1 The model 109

5.2.2 Eikonal approximation 111

5.2.3 Cross sections and reaction probabilities 113

5.3 Applications 115

5.3.1 Deuteron reactions 115

5.3.2 Reactions with [superscript 11]Be: integrated cross sections 119

5.3.3 Reactions with [superscript 11]Be: differential cross sections 122

5.3.4 Reactions with other nuclei 125

6 Fragment momentum distribution in reactions with halo nuclei 127

6.1 Momentum distribution of projectile fragments 127

6.2 Formalism 131

6.2.1 Fundamentals 131

6.2.2 Elastic breakup 134

6.2.3 Inelastic breakup 135

6.2.4 Derivation in the Glauber theory 138

6.3 Applications 142

6.3.1 A reaction with [superscript 11]Be 142

6.3.2 A reaction with [superscript 8]B 144

7 Coulomb breakup reactions of halo nuclei 147

7.1 Soft dipole mode 147

7.1.1 Dipole strength function 147

7.1.2 Sum rule 151

7.1.3 Zero-range potential model 152

7.2 Equivalent-photon method 157

7.3 Theory of the Coulomb breakup 160

7.3.1 Eikonal approximation 160

7.3.2 Perturbative theory 165

7.4 Coulomb breakup reaction of [superscript 11]Be 169

7.5 Postacceleration phenomena 174

II Structure of Light Exotic Nuclei 177

8.2 Description of exotic structure 184

8.3 Cluster approach with Gaussians 189

9 Correlated Gaussian approach 193

9.1 Preliminary notes 193

9.1.1 Motivation 193

9.1.3 Coordinates and correlations 198

9.2 Variational trial function 201

9.2.1 Formulation in terms of relative coordinates 201

9.2.2 Formulation without reference to relative coordinates 204

9.2.3 Full form 209

9.3 Generating function 211

9.3.2 Generating a correlated Gaussian 214

9.3.3 Gaussian wave packets 216

9.3.4 Correlated Gaussian from single-particle states 219

9.4 Evaluation of matrix elements 221

9.4.1 Uncoupling 221

9.4.2 Including the centre of mass 224

9.4.3 Generic forms of determinantal matrix elements 227

9.4.4 Translation-invariant matrix elements 228

9.5 Physical quantities 231

9.5.1 One-body operators 231

9.5.2 Two-body operators 239

10 Variational procedure 243

10.1 Basis optimization 243

10.2 Stochastic optimization 246

10.2.1 Random basis and sorting 246

10.2.2 Trial-and-error search 248

10.2.3 Refining 250

10.2.4 Description of excited states 252

10.3 Short-range and long-range behaviour 255

10.4 Description of unbound states 260

10.4.1 Classification 260

10.4.2 Localization of resonances 264

10.5 Analytic continuation in the coupling constant 269

10.5.1 Pole trajectories 269

10.5.2 Analytic continuation of pole trajectories 273

11 Cluster models 277

11.1 Preliminary notes 277

11.2 Basic concepts of clustering 279

11.3 Theory of clustering 282

11.3.1 Cluster subspace 282

11.3.2 Projection to the cluster subspace 284

11.3.3 Amplitudes related to clustering 288

11.3.4 Calculation of the clustering properties 292

11.4 Basic concepts of cluster models 293

11.4.2 Intercluster relative motion 294

11.5 The resonating-group method 300

11.5.2 Matrix elements 305

11.6 The harmonic-oscillator cluster model 310

11.6.1 The model 310

11.6.2 Eigenvalue problem of the norm operator 314

11.7 The generator-coordinate method and the two-centre shell model 315

11.7.1 Generator-coordinate method 315

11.7.2 The method of complex generator coordinates 321

11.7.3 Two-centre shell model 324

11.7.4 Cluster distortion 327

11.8 The orthogonality-condition model 332

11.8.1 The nonlocality problem 333

11.8.2 Local intercluster potential 336

11.9 Microscopic versus macroscopic approach 340

11.9.1 Observables 340

11.9.2 The fishbone model 343

11.9.3 Three-cluster system 344

12 Cluster model in the correlated Gaussian approach 351

12.1 Multicluster approximation 351

12.2 Model space and interactions 356

12.2.1 Characteristics of the state space 357

12.2.2 Clustering in light nuclei 358

12.2.3 Effective force 360

12.3 Cluster correlations 367

12.3.1 Correlated versus uncorrelated description 367

12.3.2 Clustering in A-nucleon calculations 370

13 Application to exotic nuclei 379

13.1 The structure of [superscript 6]He and [superscript 6]Li 379

13.1.1 Exposition 379

13.1.2 State spaces 381

13.1.3 Test of the approach 386

13.1.4 Observables 390

13.2 The structure of [superscript 8]He 396

13.3 The mirror nuclei ([superscript 7]Li, [superscript 7]Be), ([superscript 8]Li, [superscript 8]B) and ([superscript 9]Li, [superscript 9]C) 402

13.3.1 Exposition 402

13.3.2 The structure of [superscript 7]Li and [superscript 7]Be 403

13.3.3 The structure of [superscript 8]Li and [superscript 8]B 404

13.3.4 The structure of [superscript 9]Li and [superscript 9]C 408

13.3.5 Magnetic moments of mirror nuclei 410

13.4 The mirror nuclei [superscript 9]Be and [superscript 9]B 417

13.4.1 Exposition 417

13.4.2 State spaces and energies 418

13.4.3 Radii and electromagnetic properties 423

13.4.4 Beta-decay of [superscript 9]Li to [superscript 9]Be 427

13.5 The states of [superscript 10]Be 429

13.5.1 Exposition 429

13.5.2 Model 430

13.5.3 Spectroscopy of states 431

13.5.4 Density distributions 434

13.5.5 The sequence of Be isotopes 438

13.6 The parity inversion in the mirror nuclei [superscript 11]Be and [superscript 11]N 439

13.7 The nuclei [superscript 10,11]Li 446

13.7.1 Facts and speculations 446

13.7.2 Theoretical approaches 450

13.8 Overview of exotic structure 456

13.9 Structure calculations with realistic nuclear forces 460

13.9.1 Realistic forces 461

13.9.2 Stochastic variational solution 463

13.9.3 The triton and the alpha-particle 464

13.9.4 The description of [superscript 6]Li 465

13.10 Reaction calculations with correlated Gaussians 468

13.10.1 Exposition 468

13.10.2 High-energy p+[superscript 6]He scattering 469

13.10.3 High-energy [superscript 6]He+[superscript 12]C scattering 474

13.10.4 Low-energy [alpha]+[superscript 6]He scattering 477

A Overview of reaction theories 483

B Conventional cluster Jacobi coordinates 491

C Borromean and Efimov states 497

D Antisymmetrization 503

E Matrix elements between Slater determinants 509

E.1 Unit operator 509

E.2 One-body operators 510

E.3 Two-body

operators 513

E.4 Many-body operators 516

F Matrix elements between correlated Gaussians 523

G Other matrix elements 533

G.1 Successive coupling 533

G.2 Unnatural parity states 534

G.3 Calculation of the amplitudes related to clustering 539

H An [alpha]+n+n three-cluster model for [superscript 6]He 547

I The nuclear SU(3) symmetry 553.

Notes:

Includes bibliographical references (pages [563]-580) and index.

ISBN:

0415308720

OCLC:

52097726