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without HI: E = 0.09261 meV
with HI:
A = 0.2101 micro eV
The levels will split with 3/4*A and 1/2*A for mJ = 3/2 and 1/2 levels respectfully.
For transition from mJ = -3/2 to -1/2 we get +/- (3/4-1/4) A so 1/2 A energy differences in the transition energy. For mJ = -1/2 to +1/2, we get (1/4 + 1/4) A so also 1/2 A shifts. We can conclude that the photon energies will be altered by an amount equal to +/- 0.105 micro eV so E will be 0.09156 meV and 0.09366meV.
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