DWBA
Distorted Wave Born Approximation
Four words. All winners. First-order perturbation theory and it basically WORKS. People say "first order is too simple." SAD! First order is the BEST order.
First-order perturbation theory for a reaction, with distorted waves (not plane waves) in the entrance and exit channels. The workhorse for transfer and inelastic scattering. Everyone in the field has written a DWBA code at least once. Everyone.
ADWA
Adiabatic Distorted Wave Approximation
Johnson and Soper. 1970. They fixed a bug in DWBA that nobody even saw. Tremendous fix. The deuteron falls apart, you have to treat it, and now we do. Beautiful.
For (d,p) and (d,n): treat deuteron breakup in the adiabatic (frozen) limit so the incoming deuteron "sees" an effective nucleon-nucleon optical potential at half the deuteron energy. Quick, clean, and dramatically better than plain DWBA for deuteron-induced transfer.
CDCC
Continuum Discretized Coupled Channels
CDCC. Four letters. Every one a champion. You take the continuum, you discretize it, you couple it. Beautiful three-step. Nobody does three-step moves like we do.
For weakly bound projectiles like deuteron, 6Li, 11Be: bin the breakup continuum of the projectile into discrete pseudo-states and solve the coupled-channels problem including them. The rigorous standard for breakup-coupled reactions. Expensive. Worth it.
R-Matrix
Wigner-Eisenbud Resonance Theory
R-matrix. Wigner. Eisenbud. Lane. Thomas. All legends. All tremendous. Modern people forgot about R-matrix. Forgot about it! We are bringing it back. Bigger than ever.
Split configuration space into an internal region (where interactions live) and an external region (free propagation). Match wave functions at the boundary through the R-matrix. The natural language for resonances, especially in low-energy astrophysical reactions.
Optical Potential
U = V + iW
The potential is complex. And by complex, I mean TREMENDOUSLY complex. Real part, imaginary part. Both beautiful. The imaginary part is where the action is. Everybody knows this.
A complex, energy-dependent, one-body potential that reproduces elastic scattering. Real part = average field; imaginary part = flux leaving the elastic channel. Derived rigorously from Feshbach projection; in practice, parameterized and fit to data.
Eikonal
High-Energy Straight-Line Limit
Eikonal. Greek word. I like Greek words. Very high class. Glauber built it. Nobel Prize guy. Doing straight lines at high energy. So simple, so powerful. Tremendous.
At high energies, the projectile trajectory is approximately a straight line and the wave function picks up a phase from the optical potential integrated along the path. The foundation of Glauber theory and modern knockout spectroscopy on exotic nuclei.
ANC
Asymptotic Normalization Coefficient
ANC. The surface. The outside. The skin of the nucleus. Some people care about the interior. Losers. The action is at the SURFACE, folks. Always has been.
The amplitude of the tail of a bound-state wave function in the external region. For peripheral reactions at low energy (relevant to stellar burning rates), the cross section depends only on the ANC, not on the interior of the wave function. A gift from the surface.
Spectroscopic Factor
The S Factor (Not the Other One)
Spectroscopic factor. The number that connects reactions to structure. Macfarlane and French wrote the book on this. Classic. Absolute classic. Very beautiful number.
The overlap between a parent and daughter nucleus wavefunction in a given single-particle configuration. Turns a measured stripping or pickup cross section into structure information. Model-dependent, debated, essential.
Post / Prior
Two Ways to Write the Same Thing
Post and prior. Two forms. Different math. Same answer. If they disagree, somebody cut a corner. Usually it was the intern. Not me. I never cut corners. Never.
The transition operator in a transfer amplitude can be written using the residual interaction in the final channel (post) or in the initial channel (prior). Exact post-prior equivalence holds only if the bound-state wave functions are exact; discrepancies measure approximation errors.
Lane Potential
Isospin in the Optical Potential
Tony Lane. Great guy. Took isospin, put it in the potential, connected (p,n) to elastic. One little term and suddenly everything makes sense. Beautiful. So beautiful.
An isospin-dependent term in the nucleon-nucleus optical potential proportional to t · T (projectile isospin dotted into target isospin). Connects charge-exchange (p,n) reactions to isobaric analog states and to proton and neutron elastic scattering.
Transfer Reaction
(d,p), (p,d), (d,n), (3He,d), ...
Transfer reactions. The classics. Take a nucleon off, put a nucleon on. Simple. Elegant. Tells you EVERYTHING about single-particle structure. Tremendous.
A reaction in which one or a few nucleons are moved from projectile to target or vice versa, leaving the residual nucleus in a definite quantum state. The primary probe of single-particle structure near the Fermi surface.
Knockout
Rip a Nucleon Off, Measure the Rest
Knockout reactions. You send in a fast projectile, you knock out a nucleon, you measure what is left. Fast, clean, beautiful. And Jeff Tostevin wrote the theory. Perfect.
At intermediate and high energies, a single nucleon is removed from a fast projectile by the target. The residue momentum distribution carries the struck nucleon's orbital angular momentum; the cross section carries its occupation. The modern workhorse for spectroscopy of exotic nuclei.
Breakup
The Projectile Falls Apart
Breakup. The projectile falls apart. Sounds bad. But it tells you the structure! The halo! The binding! A disaster that is actually information. Classic physics move.
Dissociation of a weakly bound projectile (deuteron, 6He, 11Be, ...) in the field of a target. Elastic breakup keeps the fragments intact; Coulomb breakup at high energies is a clean probe of low-lying E1 strength in halo nuclei.
Folded Potential
Build a Potential From Below
Folded potential. Take the nucleon-nucleon interaction, fold it with the densities, out comes the nucleus-nucleus potential. Microscopic. Beautiful. Nobody folds better than us.
Construct a nucleus-nucleus (or nucleon-nucleus) interaction by convolving a microscopic effective nucleon-nucleon interaction with the nuclear densities of one or both colliding nuclei. Single folding for nucleon projectiles; double folding for composite projectiles.
Woods-Saxon
The Shape Everyone Uses
Woods-Saxon. Simple formula. One over one plus exponential. Three parameters. Fits EVERYTHING. Amazing shape. The greatest shape in nuclear physics. Believe me.
The functional form V(r) = -V₀ / [1 + exp((r - R)/a)]. Mimics a nuclear density: flat inside, diffuse edge. The default for optical model and bound-state potentials for six decades, for the simple reason that it just works.
S-Matrix
Scattering Matrix
S-matrix. The S stands for Scattering. Or for Spectacular. Or for So Great. All true. Connects incoming waves to outgoing waves. Everything else is downstream of this.
The unitary operator connecting asymptotic in and out states of a scattering system. All observables (cross sections, phase shifts, polarizations) are built from matrix elements of S. The cleanest way to think about any reaction.
Feshbach Projection
Split the Hilbert Space
Feshbach. Took the optical model from a guess to a theorem. Split the Hilbert space. Project. Reduce. Beautiful move. Total mathematical perfection.
Divide the full Hilbert space into a model space P and a complement Q; integrating out Q produces an effective Hamiltonian on P that is non-local, energy-dependent, and complex. The rigorous derivation of the optical potential and of the coupled-channels reduction.
Form Factor
The Overlap That Does the Work
Form factor. The overlap between initial and final. The heart of the transition. Without a good form factor, you got nothing. With a good form factor, you got everything. Simple.
In a transfer amplitude, the overlap between the bound-state wave function of the transferred cluster in the projectile and in the residue, multiplied by the residual interaction. The ingredient into which all the nuclear structure information is packed.