Function broadened_cross_sections 

pub fn broadened_cross_sections(
    energies: &[f64],
    resonance_data: &[ResonanceData],
    temperature_k: f64,
    instrument: Option<&InstrumentParams>,
    cancel: Option<&AtomicBool>,
) -> Result<Vec<Vec<f64>>, TransmissionError>

Compute Doppler-broadened cross-sections for each isotope.

Returns Doppler-only cross-sections. Resolution broadening is NOT applied here because it must be applied after Beer-Lambert on the total transmission for physically correct results (issue #442).

When instrument is Some, the auxiliary extended grid is still constructed for Doppler boundary accuracy, but the resolution convolution is not performed.

This is the expensive physics step; cache the result once before fitting many pixels on the same isotopes and energy grid.

Arguments

• energies — Energy grid in eV (sorted ascending).
• resonance_data — Resonance parameters for each isotope.
• temperature_k — Sample temperature for Doppler broadening.
• instrument — Optional instrument resolution parameters. Used only for auxiliary grid construction (Doppler boundary accuracy). Resolution broadening is NOT applied.
• cancel — Optional cancellation token. Cancellation is checked at the start of each isotope’s parallel task; in-flight tasks run to completion (consistent with the rayon pattern in spatial.rs).

Returns

One cross-section vector per isotope on success.

Errors

• TransmissionError::Cancelled — if the cancel flag was observed during parallel execution (either before an isotope started or after all tasks completed).
• TransmissionError::Resolution — if instrument is Some and energies is not sorted ascending.
• TransmissionError::Doppler — if Doppler broadening is enabled (temperature_k > 0.0) and DopplerParams validation fails (e.g., non-positive or non-finite AWR).