Function br_emission_coefficient

pub fn br_emission_coefficient(
    x: f64,
    theta_e: f64,
    theta_z: f64,
    n_h: f64,
    n_he: f64,
    n_e: f64,
    x_e_frac: f64,
    cosmo: &Cosmology,
) -> f64

BR emission coefficient K_BR at frequency x.

K_BR(x) = (α λ_e³/(2π√(6π))) θ_e^{-7/2} × (e^{-xφ}/φ³) × Σ_i Z_i² N_i g_ff

This is the coefficient such that: dn/dτ|_BR = (K_BR / x³) [n_eq − n]

where n_eq is the Planck distribution at T_e. The rate per unit volume is ∝ N_e × N_i (two-body process). Converting to per Thomson time (÷ N_e σ_T c) cancels one N_e, leaving N_i × λ_e³ (dimensionless) in the coefficient.

Arguments

• x - dimensionless frequency hν/(kT_z)
• theta_e - electron temperature kT_e/(m_e c²)
• theta_z - reference temperature kT_z/(m_e c²)
• n_h - hydrogen number density [1/m³]
• n_he - helium number density [1/m³]
• n_e - electron number density [1/m³]
• x_e_frac - ionization fraction X_e = N_e/N_H