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.

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).