# EPR resonance energies

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AndreasCeulemans
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Without hyperfine interactions, the energy shift is given by E=-g_j*µ_B*B_0*m_j, where the bohr magneton µ_b=9.274*10^(-24)J/T

So the energy difference between two adjacent levels is E=1*2T*µ_b*(delta m_j)=1.8548*10^(-23)J because delta m_j is 1 do to selection rules.

With hyperfine turned on, the +- 3/2 levels are split into two with change of 0.5 µ_n*B_hf, where the nuclear magneton µ_n=5.05*10^(-27)J/T. And the +- 1/2 levels are split with 1/6 µ_n*B_hf.

µ_n*B_hf=5.05*10^(-26)J~5*10^(-26)J
This means the -1/2 to -3/2 transition is split into 2 (since delta m_I=0) with energies:

E1 = 1.85647E-23 J
E2 = 1.85313E-23 J

Similar for the 1/2 to -1/2

E1 = 1.85647E-23 J
E2 = 1.85313E-23 J

,where the same energies are found as in the -1/2 to -3/2 transition.

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