Function ic_pulse 

pub fn ic_pulse(alpha: f64, beta: f64, r: f64, tau: f64) -> f64

Ikeda–Carpenter moderator emission density I(τ).

τ in µs, rates α,β in 1/µs, mixing r ∈ [0,1]. Returns 0 for τ < 0. Unit-area over τ ∈ [0,∞); first moment 3/α + r/β. NaN-free for all α,β > 0 (including α ≈ β and β ≫ α): the slow/storage term is evaluated from the bounded bracket e^{−βτ} − e^{−ατ}(1+u+½u²) (both exponentials ≤ 1 for τ,α,β > 0, so no e^{|u|} overflow), falling back to a Taylor limit near u = α−β·τ → 0 where that bracket cancels.