Chapter
2.2.3 Compound nucleus reactions
2.3.1 Non-relativistic kinematics
2.3.2 Relative and center-of-mass wave functions
2.3.3 Relativistic kinematics
2.4.1 Differential cross sections
2.4.2 Laboratory and center of mass measures
2.4.3 Experimental and theoretical cross sections
2.4.4 Cross sections and scattering amplitudes
3.1 Elastic scattering from spherical potentials
3.1.1 Partial-wave scattering from a finite spherical potential
3.1.2 Coulomb and nuclear potentials
3.1.3 Resonances and virtual states
3.1.4 Nuclear currents or flux
3.2 Multi-channel scattering
3.2.3 Unitarity of the multi-channel S matrix
3.3.1 Green's function methods
3.3.2 Vector-form T matrix for plane waves
3.3.3 Two-potential formula
3.3.4 Vector-form T matrix for distorted waves
3.3.5 Born series and approximations
3.4.2 Direct and exchange amplitudes in elastic scattering
3.4.3 Integrated cross sections
3.5 Electromagnetic channels
3.5.1 Maxwell equations and photon channels
3.5.2 Coupling photons and particles
3.5.3 Photon cross sections
3.5.4 Partial waves and vector spherical harmonics
3.5.5 Electric and magnetic parts in the Coulomb gauge
4.1.2 Global optical potentials
4.2 Single-nucleon binding potentials
4.2.1 Neutron and proton single-particle states in nuclei
4.2.2 Optical potentials extended to bound states
4.3.1 Multipole analysis of transition potentials
4.3.2 Spin-dependent potentials
4.4.1 Collective inelastic processes
4.4.2 Single-particle inelastic processes
4.5 Particle rearrangements
4.6.1 Charge-exchange reactions
4.6.2 Generalized multipole transitions
4.7 Photo-nuclear couplings
4.7.1 Single-photon reactions
4.7.2 Electric transitions using the Siegert theorem
4.7.3 Combining multiple-particle and γ channels
4.7.4 Connecting photon cross sections and B(EJ)
4.7.5 Magnetic transitions
5 Connecting structure with reactions
5.1 Summary of structure models
5.1.4 Collective nuclear-matter descriptions
5.2.3 Typical forms of effective interactions
5.3.1 Non-antisymmetrized theory
5.3.2 Antisymmetrized theory
5.4 General matrix elements
5.4.1 Coulomb and nuclear transitions
6.2.1 Local and non-local couplings
6.2.2 Simplified solutions
6.3 Multi-channel equations
6.3.2 Close-coupling methods for local couplings
6.3.3 Iterative solutions
6.3.4 Numerical iterations
6.3.5 Convergence of iterative methods
6.4 Multi-channel bound states
6.4.1 Coupled-channels eigenvalue problem
6.5.1 One-channel R-matrix expansions
6.5.2 The multi-channel R matrix
6.6 Coupled asymptotic wave functions
7.1 Few-body adiabatic scattering
7.1.1 Three-body adiabatic model
7.1.2 The Johnson and Soper potential for transfer reactions
7.1.3 The Johnson special three-body model
7.1.4 The adiabatic wave function for breakup
7.1.5 The adiabatic wave function for transfers
7.2.1 The eikonal wave function
7.2.2 Eikonal elastic scattering
7.2.3 Composite-body scattering and the optical limit
7.2.4 Eikonal cross sections
7.2.5 Stripping reactions
7.3 First-order semiclassical approximation
7.4.1 Coulomb penetration factors
8.1 Three-body wave equations
8.1.1 Wave function components
8.1.2 Three-component Faddeev equations
8.1.3 Reduction to one Jacobi set
8.2 Continuum Discretized Coupled Channel method
8.2.2 CDCC equations and couplings
8.2.3 Calculating differential cross sections
8.2.4 Model space and convergence of the CDCC equations
8.2.6 Three-body observables
8.3 Other breakup measures and methods
8.3.1 Momentum distributions
8.3.2 Inclusive measurements
8.3.3 Semiclassical and time-dependent methods
8.3.4 Transfer to the continuum
9.1 Definitions of halo and deeply bound states
9.2 Three-body models for bound states
9.2.1 The hyperspherical coordinates
9.2.2 Hyperspherical expansions
9.2.3 Coupled hyper-radial equations
9.4 Reactions with three-body projectiles
9.4.1 Born approximations
9.4.3 Three-body eikonal models
10 R-matrix phenomenology
10.2 Single-channel R matrix
10.2.1 Phase shifts from the one-channel R matrix
10.2.2 Isolated poles in single-channel scattering
10.2.3 Multiple poles in one channel
10.3 Coupled-channels R matrix
10.3.1 Revised derivation of the scattering S matrix
10.3.2 Level-matrix formulation
10.4 Combining direct and resonant contributions
11 Compound-nucleus averaging
11.1 Compound-nucleus phenomena
11.1.1 Porter-Thomas statistics
11.2 Approximations neglecting interference
11.2.1 Reich-Moore approximation
11.2.2 Multi-level Breit-Wigner approximation
11.3 Hauser-Feshbach models
11.3.1 Width fluctuation corrections
11.3.2 Transmission coefficients
11.3.3 Weisskopf-Ewing approximation
11.3.4 Strong couplings and overlapping resonances
11.5 Average amplitudes and the optical model
11.5.1 Sources of the optical potential
11.5.2 Effects of neglected direct-reaction channels
11.5.3 Effects of neglected compound-nucleus channels
12 Stellar reaction rates and networks
12.1.1 Reaction rates (συ) and lifetimes
12.1.2 Maxwell-Boltzmann distributions
12.1.4 Averaging over resonances
12.1.5 Neutron and photon reaction rates
12.1.6 Inverse reaction rates
12.1.7 Electron screening
12.2.1 Coupled rate equations
12.2.2 Explicit and implicit solution methods
12.3.1 Fixed points of the rate equations
12.3.3 Reactions with excited states
12.3.4 Nuclear statistical equilibrium
12.4 Sensitivities to nuclear data
13 Connection to experiments
13.1 New accelerators and their methods
13.1.2 An example of a fast-fragmentation facilty
13.1.3 An example of an ISOL facility
13.3.1 Charged-particle beams
14.1 Transfer spectroscopy
14.1.1 DWBA transfer theory
14.1.2 Q-value sensitivity
14.1.3 Angular momentum sensitivity
14.1.4 Extraction of asymptotic normalization coefficients
14.1.5 Extraction of spectroscopic factors
14.1.6 Dependence on optical potentials
14.1.7 Dependence on single-particle parameters
14.1.8 Higher-order corrections
14.2 Knockout spectroscopy
14.3 Inelastic spectroscopy
14.4 Breakup spectroscopy
14.4.1 Coulomb dissociation method
14.4.2 Extracting an asymptotic normalization coefficient
14.5 Charge-exchange spectroscopy
15.1.2 Multivariate theory
15.2 Fitting cross-section harmonic multipoles
15.3 Fitting optical potentials
15.3.2 Ambiguities in optical potentials
15.4 Multi-channel fitting
15.4.2 Fitting inelastic scattering
15.4.4 A Progressive Improvement Policy
15.5.2 Theoretical expectations and the Bayesian method
15.5.3 Error estimates from χ2 fitting
Appendix B Getting started with FRESCO
B.2 Learning through examples
B.2.2 Inelastic scattering
B.4 Fitting data: SFRESCO
B.5 System requirements, compilations and installation
Nuclear Reactions for Astrophysics
：Principles, Calculation and Applications of Low-Energy Reactions
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