Comparison of the results calculated from the improved new model with or without the second simplification described in Section 2.5. The solid red and yellow lines show the results calculated without the simplification for T_e = 10 000 K, n_e = 10⁶ cm^–3, and EM=10¹⁰ cm^–6 pc and T_e = 10 000 K, n_e = 10⁷ cm^–3, and EM=10¹¹ cm^–6 pc, respectively. The dashed and dash-dotted black lines are those calculated with the simplification for the corresponding cases. In the top panel, we plot b_n at the center of uniform spherical H II regions. β_n,n+1 is presented in the bottom panel.