Module slbw 

Single-Level Breit-Wigner (SLBW) cross-section calculation.

SLBW is the simplest resonance formalism. It treats each resonance independently (no interference between resonances). It is useful as:

• A validation check against the more complex Reich-Moore calculation
• A quick approximation for isolated resonances
• An educational/debugging tool

For isolated, well-separated resonances, SLBW and Reich-Moore should give nearly identical results.

This module also provides true MLBW (Multi-Level Breit-Wigner) via mlbw_cross_sections_for_range, which includes resonance-resonance interference in the elastic channel (see SAMMY mlb/mmlb3.f90).

SAMMY Reference

• mlb/mmlb4.f90 Abpart_Mlb subroutine
• SAMMY manual Section 2.1.1

Formulas

For each resonance at energy E_r with total J:

σ_capture(E) = g_J × π/k² × Γ_n(E)·Γ_γ / ((E-E_r)² + (Γ/2)²)

σ_elastic(E) = g_J × π/k² × [Γ_n(E)² / ((E-E_r)² + (Γ/2)²) + 2·sin(φ)·(Γ_n(E)·(E-E_r)·cos(φ) + Γ_n(E)·Γ/2·sin(φ)) / ((E-E_r)² + (Γ/2)²) + sin²(φ)]

where Γ_n(E) = Γ_n(E_r) × √(E/E_r) × P_l(E)/P_l(E_r) and Γ = Γ_n(E) + Γ_γ + Γ_f

Functions

mlbw_cross_sections_for_range

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

slbw_cross_sections

Compute SLBW cross-sections at a single energy.

slbw_cross_sections_for_range

Compute SLBW cross-sections for a single resolved resonance range.