Module urr 

Unresolved Resonance Region (LRU=2) cross-section calculation.

Computes average cross-sections via the Hauser-Feshbach formula using the average level-spacing and partial widths stored in UrrData.

Hauser-Feshbach Formula

For each (L, J) combination at energy E:

g_J = (2J+1) / ((2I+1) · (2s+1))

LRF=1: Γ_n(E) = 2 · P_L(ρ(E)) · GNO    [GNO = reduced neutron width]
LRF=2: Γ_n(E) from tabulated energy grid using INT interpolation
        INT=1 histogram, INT=2 lin-lin, INT=3 log-x/lin-y,
        INT=4 lin-x/log-y, INT=5 log-log (all 5 ENDF codes supported)

Γ_tot = Γ_n + GG + GF + GX

σ_γ  += (π/k²) · g_J · (2π · Γ_n · GG) / (D · Γ_tot)
σ_f  += (π/k²) · g_J · (2π · Γ_n · GF) / (D · Γ_tot)
σ_cn += (π/k²) · g_J · (2π · Γ_n · Γ_n) / (D · Γ_tot)    [neutron-out]

σ_cn is the compound-elastic contribution; the competitive (GX) channel contributes to total but not elastic. Potential scattering σ_pot = 4π·AP²/100 (AP in fm, result in barns) is included in the returned total and elastic so that the URR band produces a physically consistent cross-section without requiring special handling at the call site.

Width-Fluctuation Correction — not yet implemented

The kernel above is the energy-averaged Hauser-Feshbach expression in the W = 1 limit: no width-fluctuation (Porter-Thomas / Moldauer / Dresner) factor is applied. The χ² degrees of freedom AMUN / AMUF are parsed from ENDF File 2 and stored on UrrJGroup (within UrrData), but are not yet consumed here. SAMMY’s URR treatment (FITACS, manual Section VIII) includes the fluctuation integrals, so NEREIDS URR cross-sections will differ from SAMMY’s where fluctuation effects are significant.

Units

All energies in eV, all lengths (AP, channel radii) in fm (true physics femtometers, 10⁻¹⁵ m), cross-sections in barns.

ENDF stores radii in 10⁻¹² cm (= 10 fm); the parser converts to fm at parse time by multiplying by 10 (see ENDF_RADIUS_TO_FM in parser.rs), matching SAMMY’s FillSammyRmatrixFromRMat.cpp line 422.

SAMMY Reference

• SAMMY manual Section VIII.A (equations for the Unresolved Resonance Region)
• SAMMY’s URR analysis code is FITACS (acs/ in the SAMMY source tree), which includes the width-fluctuation corrections this module omits

References

• ENDF-6 Formats Manual §2.2.2
• W. Hauser, H. Feshbach, Phys. Rev. 87 (1952) 366

Functions

urr_cross_sections

Compute energy-averaged Hauser-Feshbach cross-sections in the Unresolved Resonance Region (width-fluctuation correction not yet applied; see the module docs).