pub fn gaunt_ff_nr(x: f64, theta_e: f64, z_charge: f64) -> f64Expand description
Non-relativistic thermally-averaged free-free Gaunt factor.
Uses a softplus interpolation that smoothly approaches the classical Born limit at low frequencies while remaining ≥ 1 at high frequencies: g_ff = 1 + softplus((√3/π)(ln(2.25/(x Z)) + 0.5 ln(θ_e)) + 1.425)
The argument uses Z (nuclear charge, linear) not Z², following the Coulomb parameter convention where η_Z = Z e²/(ℏv) enters linearly inside the logarithm. The 0.5×ln(θ_e) is an empirical interpolation between the Born and classical regimes.
This approximation is from CosmoTherm (private communication, J. Chluba), calibrated against the exact Karzas & Latter (1961) Gaunt factor tabulations and the BRpack library (Chluba, Ravenni & Bolliet 2020, MNRAS 492, 177). The offset constant 1.425 improves agreement in the transition region.