XAS / EXAFS — X-ray Absorption & Extended X-ray Absorption Fine Structure L1-147

SpectroscopyInner-shell X-ray absorption + multiple scattering oscillationsδ=5 · challengingL_DAG = 3📋 Stub — not mineable

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Unclaimed Principle — open for contribution

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Forward model E

m u (E) = m u_{0} (E) \cdot [1 + c hi (k)]; c hi (k) = j \sum (N_{j} S_{0}^{2} / (k R_{j}^{2})) \cdot F_{j} (k) \cdot e x p (- 2 σ_{j}^{2} k^{2}) \cdot s in (2 k R_{j} + p h i_{j} (k))

Above an absorption edge (K, L1-3), an X-ray photon ejects a core-level photoelectron whose outgoing spherical wave back-scatters off neighboring atoms, interfering with the outgoing wave. This creates oscillations chi(k) in the absorption coefficient vs. wavenumber k = sqrt(2m(E-E_0))/hbar. XANES (<50 eV above edge) probes oxidation/coordination; EXAFS (>50 eV) probes radial distribution functions.

L-DAG

L.absorb.photoionization -> L.scatter.multiple -> int.spectral

L.absorb.photoionizationL.scatter.multipleint.spectral

Well-posedness W

Existence:: true
Uniqueness:: structural parameters unique when Nyquist-sampled in k-space and shells non-degenerate
Stability:: conditional
κ:: 500

Fourier-transform EXAFS inversion is linear; parameter fitting (R_j, N_j, sigma_j^2) is nonlinear; correlation among N, S_0, sigma is a major ill-conditioning source.

Solvability C

Solver class:: FEFF path calculation + Artemis / IFEFFIT nonlinear LS fit; wavelet transform; learned (XANES-Net, EXAFS-CNN)
Convergence rate q:: 2
Complexity:: FEFF O(N_path * N_energy); Artemis fit O(iter * N_param * N_E)

Specs (0)

No L2 specs registered yet for this principle.