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Elastic scattering

A projectile wave meets a nucleus that both bends it and swallows part of it. The surface shows the wave itself: behind the nucleus a shadow forms, from absorption and from interference of the bent waves.

Projectile

Target

E_lab

W ×1.00

Kinematics

Optical potential

Scope

The target is treated as spin 0 and inert: no target spin, no excitation (a warning gives its NUBASE2020 J^π when that is not 0⁺); targets must be NUBASE2020 nuclides. The result is shape (direct) elastic scattering only: compound-nucleus elastic, which adds to the measured elastic cross section at low incident energies (KD02 Sec. 2.3), is not included, so at low energies a measured elastic cross section can lie above the curve for that reason alone.

Rendering

What is drawn: the surface height is Re(ψ e^−iωt) (exaggerated vertically, ω not to scale) and its colour is |ψ|² on a log scale (|ψ|² = 1 is the undisturbed beam; darker blue is shadow, gold is focus). The water look (sky reflections at the Fresnel factor of water, a key-light glint, troughs tinted deeper, light through the crests) is lighting only, and the reflection is capped so the colour stays readable. The glass sphere has the radius R_V of the real potential; the amber glow inside it is the absorptive potential −W(r) as solved (volume plus surface term, times W ×), drawn as emission proportional to −W along the line of sight, upper half only; at W × 0 it is empty. The basin, plinth, beam source and lights are decoration.

Potentials: n, p from Koning & Delaroche, Nucl. Phys. A 713, 231 (2003), transcribed from Koning's kd02.f; d from Han, Shi & Shen, Phys. Rev. C 74, 044615 (2006), Eqs. (1) to (13) and Table I; α from Avrigeanu, Avrigeanu & Mănăilescu, Phys. Rev. C 90, 044612 (2014), Table II. Solved live: Numerov in each (l, j), matched to Coulomb functions (Steed's method). Checked against ECIS-06 (the code KD02 was fitted with) in 14 configurations, relativistic and non-relativistic, n, p, d, α to 200 MeV: k, μ, η to 5×10⁻¹¹, σ_R to 4×10⁻⁸, and up to 52 MeV dσ/dΩ to 5×10⁻⁵ and A_y, iT₁₁ to 4×10⁻⁵. At 100 to 200 MeV the two differ at back angles by the step error of each: against its own finest step, this solver converges as h⁴ (Numerov) down to about 10⁻⁴, ECIS as h³ (shown for p and n + ²⁰⁸Pb at 200 MeV and d + ²⁰⁸Pb at 140 MeV). Against FRESCO in 14 configurations (non-relativistic, and relativistic for neutrons): σ_R to 1×10⁻⁶, dσ/dΩ to 5×10⁻⁵, iT₁₁ to 3×10⁻⁵. In the nine configurations tested (n, p, d, α, 19 to 200 MeV), the step, matching radius and partial waves used here put σ_R within 4×10⁻⁵, dσ/dΩ within 10⁻³ and iT₁₁ within 2×10⁻⁴ of converged values; other configurations are not covered by these numbers. Data: EXFOR, each table cross-checked against the IAEA's own parse.

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