Function mlbw_cross_sections_for_range 

pub fn mlbw_cross_sections_for_range(
    range: &ResonanceRange,
    energy_ev: f64,
    awr: f64,
    target_spin: f64,
) -> (f64, f64, f64, f64)

Compute true MLBW cross-sections for a single resolved resonance range.

MLBW differs from SLBW only in the elastic cross-section: it includes resonance-resonance interference (coherent sum over resonances in the collision matrix, instead of SLBW’s incoherent sum).

Capture and fission are identical to SLBW (incoherent per-resonance sums).

SAMMY Reference

• mlb/mmlb4.f90 Abpart_Mlb
• mlb/mmlb3.f90 Elastc_Mlb

Physics

The collision matrix element for a single neutron channel in MLBW is:

U_nn = e^{-2iφ} · [1 + i · Σ_r Γ_n^r / (E_r - E - iΓ_tot^r/2)]

where the sum is the coherent sum over all resonances in the spin group.

Then: σ_elastic = (π/k²) · g_J · |1 - U_nn|² σ_total = (2π/k²) · g_J · (1 - Re(U_nn))

For SLBW, |1-U|² is computed per-resonance and summed (incoherent). For MLBW, U is the coherent sum, then |1-U|² is computed once.