pub fn theta_quadrature_n(s: Screening, eps: f64, beta: f64, n: usize) -> f64Expand description
Centre-of-mass scattering angle (radians, in [0, pi]) by Gauss-Mehler
quadrature with n nodes (Mendenhall and Weller, Nucl. Instrum. Methods B 58
(1991) 11; Gauss-Chebyshev rule of the first kind).
With u = x0/x the integral becomes Int_0^1 du / sqrt(F(u)) where
F(u) = (1 - u^2) H(u) vanishes at the turning point. Writing
u = cos t removes the inverse-square-root endpoint singularity, leaving
Int_0^{pi/2} dt / sqrt(H(cos t)), which the midpoint rule in t (the
Gauss-Mehler nodes) integrates with exponential convergence. H is
evaluated from the cancellation-free form
H(u) = beta^2/x0^2 + [phi(x0) - u phi(x0/u)] / (eps x0 (1 - u^2)).