Nuclear Reactions, Scattering Theory, and Reaction Mechanisms
Quantum Scattering and the S-Matrix
Formalism
Nuclear reactions are described by asymptotic scattering states and the -matrix, with cross sections derived from amplitudes. Phase shifts, resonances, and bound-state poles encode the essential physics of low-energy collisions.
Resonances
A resonance often appears as a rapid phase-shift variation and a pole of the scattering amplitude near the real energy axis.
Reaction models
Direct reactions, compound-nucleus reactions, pre-equilibrium processes, and transfer reactions are treated using different approximations. Distorted-wave Born approximation, coupled-channels, and continuum-discretized coupled-channels methods are central tools.
Reaction regimes
Direct reaction
- Fast and selective
- Sensitive to single-particle structure
Compound nucleus
- Many intermediate states
- Statistical decay dominates
What does a rapid increase in scattering phase shift near an energy indicate?
A resonance is associated with strong temporary trapping of flux and a rapid phase variation.
Correct answer: A resonance
What is the role of the -matrix in scattering theory?
The -matrix is the central object of scattering theory because it encodes reaction amplitudes.
Correct answer: It connects incoming and outgoing asymptotic states and determines observable cross sections
Microscopic Reaction Theory and Ab Initio Reactions
From structure to reactions
A major frontier is deriving reaction observables from the same underlying Hamiltonians used for structure. This includes nucleon-nucleus scattering, transfer reactions, breakup, radiative capture, and weak-interaction processes, all with consistent many-body inputs.
Why are transfer reactions important in nuclear physics?
Transfer reactions are sensitive to overlaps between initial and final nuclear wave functions, making them useful probes of structure.
Correct answer: They can probe single-particle occupancies and spectroscopic information
Name one approximation commonly used for direct reaction calculations.
DWBA is a standard first approximation for many transfer and inelastic scattering problems.
Correct answer: Distorted-wave Born approximation