Module urr

nereids_physics

Module urr 

Source
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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-lin,
        INT=4 lin-log, 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.

§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

  • unr/munr03.f90 Csig3 subroutine
  • SAMMY manual Section 4 (URR treatment)

§References

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

Functions§

urr_cross_sections
Compute Hauser-Feshbach average cross-sections in the Unresolved Resonance Region.