Without hyperfine interaction, the levels are all equidistant such that for both transitions,
∆E_0 = g µ_B B_0 = 0.11576764 meV.
For the case with HFF, we need to add the perturbations. Because EPR selection rules tell us that ∆m_J=1 and ∆m_I=0, such that in our case
∆E_pert = ±A/2, where the ± results from the different sign in the m_I’s.
A = g µ_N B_HF / J = 2.1016342×10^-7 eV, so we have energy differences of ∆E_0 ± |∆_pert| = 0.1159778 meV or 0.1155575 meV.