Illustration of the procedure used to modify the Ni II/Ni III ratio in CMFGEN. In this example we wish to scale the Ni II/Ni III ratio of the M_Ch model DDC25 at 203 d past explosion by ℛ₂₃ = 0.1. The upper panel shows the original and scaled Ni II/Ni III ratios (Eq. C.2). The middle and bottom panels show the scaling coefficients (a₁, a₂) applied to the population densities of Ni II and Ni III, respectively (Eqs. C.8 and C.7). We note that a₁/a₂ = ℛ₂₃ = 0.1 at all depths by definition (Eq. C.5). When the original Ni II/Ni III ratio becomes small enough (≲10⁻¹ beyond ∼4000 km s⁻¹), a₁ ≈ 0.1 ( = ℛ₂₃) and a₂ ≈ 1, as expected (see text for details).