Roadmap¶

The physics of an isolated atom is one engine with several exits. Everything below is a choice of two independent things: the operator that couples the initial and final state, and the exit — what you integrate over and what you report. Layers L0–L4 are shared by all of them; see Architecture.

Already computed and thrown away¶

These quantities exist inside the current call graph and are discarded before returning. Exposing them is output plumbing, not physics — which is why they come first.

Quantity	Where it already is	Status
EELS core-loss dσ/dΔE	The `diag.dNde` matrix (ε node × K node). Its K = 0 column, times \(4\gamma^2 a_0^2\), is the parallel-illumination dσ/dε.	done — `edge` subcommand
Inner-shell stopping power	One contraction of `diag.dNde` with the ε quadrature weights.	done — reported by `edge`
Elastic phase shifts \(\delta_l\)	The continuum solver least-squares fits the tail to \(u \approx a F_l + b G_l\). Then \(\delta_l = \mathrm{atan2}(b, a)\).	done — `phase` subcommand, validated against the Born approximation to 3 % at high \(l\)

Small to medium effort¶

Quantity	Effort	Why it is cheap here
Generalized oscillator strength (GOS) / Bethe surface	done	The `gos` subcommand. The E₀ dimension is gone: one run per channel instead of one per (channel, E₀), a factor of ~22 against the shipped grids. Validated against the Bethe sum rule at large Q and, at Q → 0, against the exact hydrogen continuum dipole strength.
Double-differential d²σ/dΩdΔE	small	The K = 0 branch of the angular integral already evaluates \(S/Q^4\) on a θ grid — and that grid is built by a transform that flattens the forward \(1/Q^4\) peak, so nodes automatically cluster where EELS collection angles are.
Partial cross sections σ(β, Δ)	medium	The EELS quantification k-factor itself. Broadest reach of anything on this list. The real work is designing ε nodes for the energy window.
X-ray scattering factors \(f_x(s)\), Mott–Bethe, \(f_e(s)\)	done	The `fx` subcommand — straight from the SCF charge density. Verified against the closed form for hydrogen 1s to 8×10⁻¹⁴. Against published parameterizations it agrees to 1–3 % for light and medium Z, drifting to ~7 % for Au at high \(s\) where the non-relativistic density costs the most. Beyond \(s \approx 3\) Å⁻¹ the Gaussian fits die exponentially while \(f_e\) genuinely falls as \(s^{-2}\), so there Temari is the correct one.
Mott elastic dσ/dΩ, σ_el, σ_tr	done	The `mott` subcommand. Spin is in: the κ-resolved Dirac continuum gives \(\delta_\kappa\), hence both the direct amplitude \(f(\theta)\) and the spin-flip amplitude \(g(\theta)\), the Sherman function \(S(\theta)\), and \(\sigma_\text{el}\), \(\sigma_\text{tr}\). Against NIST SRD 64 the ratio sits at 0.90–0.94 above 1 keV. ⚠ The scattering potential must stay purely electrostatic — adding the target's own Xα exchange is not a field the incoming electron feels, and it inflates \(\sigma_\text{el}\) to 1.6–4.9× NIST.
Photoionization σ_nl(ω) and asymmetry β_nl	medium	Swap the fast-electron operator for the photon dipole operator. The energy normalization is already the one photoionization requires.
M shell (M1–M5)	done	All five subshells ship in dataset v5 (525 channels against v3's 246). It cost five rows in the channel table plus a \([3j]^2\) table extended to \(l_\text{init} = 2\).
ΔSCF binding and relaxation energies	medium	Both the neutral and the relaxed-ion SCF are already solved and cached.
Compton scattering function S(q)	medium	Bound–bound multipole matrix elements are the same integral as the radial table.
TDS absorptive form factor	medium	Same shape of problem: an integrand with two forward peaks.

Larger¶

Delocalized STEM-EELS ionization form factor \(F(s; \beta, \Delta)\) — a circular aperture breaks the separable Gauss–Legendre quadrature, because θ is measured from \(\hat{k}_+\)
Anomalous dispersion \(f'\), \(f''\) (Cromer–Liberman class)
Central-atom phase and backscattering amplitude for EXAFS
Bound–bound transitions (white lines)

Deliberately out of scope¶

Fluorescence yields, Auger and Coster–Kronig rates. Multi-electron transition probabilities are a different problem; use the tabulated literature values.
Quantitative white lines. An isolated atom in a mean field cannot produce multiplets or a solid-state DOS. The planned route is indirect: the low-\(Q\) deficit in the GOS sum rule \(\int \mathrm{d}f/\mathrm{d}\Delta E \, \mathrm{d}\Delta E \to\) occupancy is the missing white-line strength, so measure it before deciding anything.

Phases¶

Phase	Content	Status
P0	Repository, design principles, layer declaration	done
P1	Vectorization across radial points	done — 11.7× over the dataset-generation code, all bit-identical
P2	Split into the L0–L5 layer files; verification in CI	done — bit-identical; the operator/exit seam waits for a second exit to define it
P3	The discarded exits: GOS, dσ/dΔE, δ_l, stopping power	done
P4	Elastic side: \(f_x(s)\), Mott–Bethe, Mott DCS; add the sum-rule check	done
P5	EELS quantification σ(β, Δ); systematic comparison against Egerton SIGMAK/SIGMAL and Hartree–Slater GOS
P6	Photon side: σ_nl, β_nl; comparison against xraylib
P7	M shell, full Dirac continuum	done — M1–M5 and the κ-resolved two-component continuum ship in dataset v5

P2 was deliberately unglamorous: pure code movement, so bit identity was a hard requirement — verified with selftest, refcheck (unchanged at 9.044×10⁻⁸) and the kernel bit-identity checks. What it did not do is make the operator and the exit injectable: L5 still calls the L4 routines by name. That seam gets defined by the first quantity that needs it, which is P3 — and P3 is where Temari first becomes useful for something other than EDX.

The gap worth aiming at¶

The strongest scientific argument in the list is the GOS: the standard EELS tables date from the 1980s (Egerton's SIGMAK/SIGMAL, Leapman's Hartree–Slater tables), and a modern, open, relativistic GOS table effectively does not exist. The engine already computes what is needed and throws it away, and the exit costs a factor of 22 less than the tables already being generated.