Relative difference between the parameters ν_TA and ν_NTA corresponding to the cases with and without traditional approximation respectively, as a function of the ratio N/σ (horizontal axis) and 2Ω /σ (vertical axis) in logarithmic scales, and for various values of the ratios σ₀/σ and γ = τ/k. From left to right, log (γ) = {−2,2}. From bottom to top, . The normalized relative difference between ν_TA and ν_NTA is given by ς = |ν_TA−ν_NTA|/|ν_TA + ν_NTA|. Blue (red) areas designate regions where the traditional approximation is (not) appropriate. Parameters: θ = π/ 4 and α = π/ 2.