Introduction to Nuclear Reactions

Until the publication of Introduction to Nuclear Reactions, an introductory reference on nonrelativistic nuclear reactions had been unavailable. Providing a concise overview of nuclear reactions, this reference discusses the main formalisms, ranging from basic laws to the final formulae used to calculate measurable quantities.

Well known in their fields, the authors begin with a discussion of scattering theory followed by a study of its applications to specific nuclear reactions. Early chapters give a framework of scattering theory that can be easily understood by the novice. These chapters also serve as an introduction to the underlying physical ideas. The largest section of the book comprises the physical models that have been developed to account for the various aspects of nuclear reaction phenomena. The final chapters survey applications of the eikonal wavefunction to nuclear reactions as well as examine the important branch of nuclear transport equations.

By combining a thorough theoretical approach with applications to recent experimental data, Introduction to Nuclear Reactions helps you understand the results of experimental measurements rather than describe how they are made. A clear treatment of the topics and coherent organization make this information understandable to students and professionals with a solid foundation in physics as well as to those with a more general science and technology background.

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.

Bertulani, C.A.