Introduction to Nuclear Reactions

Bertulani, C.A.

Preface -- 1 Classical and quantum scattering -- 1.1 Experiments with nuclear particles -- 1.2 Theories and experiments -- 1.3 Reactions channels -- 1.3.1 Elastic channel -- 1.3.2 Inelastic channels -- 1.3.3 Reaction channels -- 1.4 Conservation laws -- 1.4.1 Baryonic number -- 1.4.2 Charge -- 1.4.3 Energy and linear momentum -- 1.4.4 Total angular momentum -- 1.4.5 Parity -- 1.4.6 Isospin -- 1.5 Kinematics of nuclear reactions -- 1.6 Cross sections, center of mass and laboratory frames -- 1.7 Classical scattering -- 1.8 The classical cross section -- 1.9 Example: Rutherford scattering -- 1.10 Orbiting, rainbow and glory scattering -- 1.11 Stationary scattering of a plane wave -- 1.12 Appendix A: Systems of units -- 1.12.1 Nuclear collisions -- 1.12.2 Collisions of atoms, ions or molecules -- 1.13 Appendix B: Useful constants and conversion factors -- 1.14 Exercises -- References -- 2 The partial-wave expansion method -- 2.1 The scattering wave function -- 2.2 Radial equation -- 2.3 Free particle in spherical coordinates -- 2.4 Phase shifts -- 2.5 Scattering amplitude and cross sections -- 2.6 Integral formulae for the phase shifts -- 2.7 Hard-sphere scattering -- 2.8 Resonances -- 2.9 Scattering from a square well -- 2.10 Low-energy scattering: scattering length -- 2.11 Scattering length for nucleon-nucleon scattering -- 2.12 The effective-range formula -- 2.13 Effective range for nucleon-nucleon scattering -- 2.14 Coulomb scattering -- 2.14.1 Partial-wave expansion -- 2.14.2 Coulomb plus short-range potentials -- 2.15 An illustration: a-a scattering -- 2.16 Appendix A: Absolute phase shifts and Levinson’s Theorem -- 2.17 Exercises -- References -- 3 Formal scattering theory -- 3.1 Introduction: Green functions -- 3.2 Free particle’s Green functions -- 3.3 Scattering amplitude -- 3.4 Born approximation -- 3.5 Transition and scattering matrices -- 3.6 The two-potential formula -- 3.7 Distorted wave Bom approximation -- 3.8 Partial-wave expansion of the 5-matrix -- 3.9 Partial-wave free-particle’s Green functions -- 3.10 Collision of particles with spin -- 3.11 Collisions of identical particles -- 3.12 Scattering of clusters of identical fermions -- 3.13 Imaginary potentials: absorption cross section -- 3.14 Appendix A: Analytical properties of the S-matrix -- 3.14.1 The Jost function -- 3.14.2 Analytical continuation in the complex k- and E-planes -- 3.14.3 Bound states -- 3.14.4 Resonances -- 3.14.5 Analytical continuation in the complex /-plane -- 3.15 Exercises -- References -- 4 Compound-nucleus reactions -- 4.1 Introduction -- 4.2 The nucleon-nucleon interaction -- 4.3 The nucleus as a strongly absorbing medium -- 4.4 Mean free path of a nucleon in nuclei -- 4.5 Fermi gas model -- 4.6 Formal theory of the optical potential -- 4.7 Empirical optical potential -- 4.8 Compound-nucleus formation -- 4.9 R-matrix -- 4.10 Average of the cross sections -- 4.11 Level densities in nuclei -- 4.12 Compound-nucleus decay: the Weisskopf-Ewing theory -- 4.13 Reciprocity theorem -- 4.14 The Hauser-Feshbach theory -- 4.15 Appendix A: The shell model -- 4.16 Exercises -- References -- 5 Fusion and Fission -- 5.1 Introduction -- 5.2 The liquid-drop model -- 5.3 General considerations on fusion reactions -- 5.4 The one-dimensional WKB approximation -- 5.4.1 Conditions of validity -- 5.5 Connection formulas in WKB -- 5.6 The three-dimensional WKB approximation -- 5.6.1 Phase-shift for short-range potentials -- 5.6.2 Phase-shift for long-range potentials -- 5.6.3 Short-range + Coulomb potential -- 5.7 Heavy-ion fusion reactions -- 5.8 Sub-barrier fusion -- 5.9 Super heavy elements -- 5.10 Occurrence of fission -- 5.11 Mass distribution of the fragments -- 5.12 Neutrons emitted in fission -- 5.13 Cross sections for fission -- 5.14 Energy distribution in fission -- 5.15 Isomeric fission -- 5.16 The nuclear reactor -- 5.17 Appendix A: The Nilsson model -- 5.18 Exercises -- References -- 6 Direct reactions -- 6.1 Introduction -- 6.2 Level width and Fermi’s golden rule -- 6.3 Direct reactions: a simple approach -- 6.4 Direct reactions: detailed calculations -- 6.5 Applications of the shell model -- 6.5.1 The extreme shell model -- 6.5.2 Extension of the shell model: contribution of more than one particle -- 6.5.3 Isobaric analog states -- 6.5.4 Energy levels with residual interaction -- 6.6 Direct reactions as a probe of the shell model -- 6.7 Nuclear vibrations -- 6.8 Photonuclear reactions—giant resonances -- 6.9 Coulomb excitation -- 6.10 Electromagnetic transition probabilities for nuclear vibrations -- 6.10.1 Electromagnetic transition probabilities -- 6.10.2 Sum rules -- 6.11 Nuclear excitation in the deformed potential model -- 6.12 Appendix A: Multipole moments and the electromagnetic interaction -- 6.12.1 Multipole moments -- 6.12.2 The electromagnetic interaction -- 6.13 Exercises -- References -- 7 Nuclear reactions in the cosmos -- 7.1 Cosmic rays -- 7.2 Stellar evolution: hydrogen and CNO cycles -- 7.3 White dwarfs and neutron stars -- 7.4 Synthesis of heavier elements -- 7.5 Supernova explosions -- 7.6 Thermonuclear cross sections and reaction rates -- 7.7 Reaction networks -- 7.8 Models for astrophysical nuclear cross sections -- 7.8.1 Microscopic models -- 7.8.2 The potential and DWBA models -- 7.8.3 Parameter fits -- 7.8.4 The statistical models -- 7.9 Slow and rapid capture processes -- 7.9.1 Hydrostatic burning stages in pre-supernova evolution -- 7.9.2 Explosive burning -- 7.10 Tests of the solar models -- 7.10.1 Neutrinos as solar thermometers -- 7.10.2 Neutrino-nucleus cross sections -- 7.10.3 Neutrino oscillations -- 7.11 Indirect methods for nuclear astrophysics reactions -- 7.11.1 Coulomb dissociation method -- 7.11.2 Transfer reactions -- 7.11.3 Trojan horse -- 7.11.4 Asymptotic normalization coefficients -- 7.11.5 Charge-exchange reactions -- 7.12 Exercises -- References -- 8 Intermediate-energy collisions -- 8.1 Introduction -- 8.2 Nucleons as billiard balls -- 8.3 Applications of the classical model -- 8.3.1 Reaction cross sections -- 8.3.2 Coulomb-modified trajectories and reaction cross sections -- 8.3.3 Isotope yield in high-energy collisions -- 8.4 The eikonal wavefunction -- 8.5 Elastic scattering -- 8.6 Coulomb amplitude and Coulomb eikonal phase -- 8.7 Total reaction cross sections -- 8.8 Scattering of particles with spin -- 8.9 The optical limit of Glauber theory -- 8.10 Pauli blocking of nucleon-nucleon scattering -- 8.10.1 Comparison with elastic scattering data -- 8.11 Glauber theory of multiple scattering -- 8.12 Coulomb excitation -- 8.12.1 Semiclassical limit of the Coulomb excitation amplitudes -- 8.12.2 Coulomb excitation of giant dipole resonances -- 8.12.3 Excitation and photon decay of the GDR -- 8.13 Inelastic scattering -- 8.14 Charge-exchange reactions -- 8.15 Exercises -- References -- 9 High-energy collisions -- 9.1 Unpacking the nucleus -- 9.2 The Boltzmann-Uehling-Uhlenbeck equation -- 9.3 Wigner function -- 9.4 Numerical treatment of transport equations -- 9.4.1 Head-on collisions -- 9.4.2 Semicentral reactions -- 9.4.3 Effects on observables -- 9.4.4 Mesons and expansion -- 9.5 Structure of hadrons -- 9.6 Quantum chromodynamics -- 9.7 The quark-gluon plasma -- 9.8 Exercises -- References -- Index.