Transition Energies

[ajsheffler]

Without Hyperfine Interaction, the difference in energy between two levels =-g_J*mu_B*B_0
So the difference is -2*mu_B, -2 times the Bohr magneton

With Hyperfine Interaction, there is a correction to the energy of each level = A*m_I*m_J where A =(g * mu_N * B_hf)/J
so for the transition from -3/2 to -1/2, assuming m_I = 1/2,
A = (20/3)*mu_N
The difference is (-1/2)*A = (-20/6)*mu_N, (-20/6) times the Nuclear magneton. For m_I=-1/2, the sign would change…

for the transition from -1/2 to 1/2, assuming m_I = 1/2,
the difference is (1/2)*A = (-20/6)*mu_N. For m_I = -1/2, the sign would change…

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