Results from LOC runs with homogeneous spherical models and the N₂H⁺ molecule. Frames a and b show, respectively, the mean T_ex(1 − 0) values when the J = 1 − 0 hyperfine structure is ignored or is taken into account. Frame c shows their ratio and is analogous to the PEP results in Fig. A.1. The axes are the mean values of the model cloud density n(H₂) and N₂H⁺ column density. The gas kinetic temperature is T_kin = 20 K.