Without hyperfine splitting:
The energy levels are calculated as follows:
E = -gm_Bm_JB_0 with B_0 = 2T, g = 1, m_B = 5.7883818012(26)×10^−5 eV·T^−1. We only have transitions if the m_j difference is 1, so we have:
deltaEwithout = abs(-gm_Bdeltam_JB_0)=m_B B_0 = 11.57676*10^-5 eV=115.768 µeV.
If a hyperfine interaction is applied with a Bhf of 10 T, we have an extra energy splitting:
between m_J=-3/2 and -1/2:
Here A = µBhf/IJ = gµ_NBhf/J = µ_N10/3/2=20µ_N/3 T=3.1524512550*10^-8eV*20/3 = 0.21 µeV.