EPR energy difference

[JRomans]

gj = 1; B0 = 2 T, uB = 5.788E-5 eV/T
No HFS
E = -gJ*uB*B0*mJ
a) mJ = -3/2 -> -1/2
b) mJ = -1/2 -> +1/2

dEa = (-1*5.788E-5 eV/T * 2 T *(-3/2) – (-1*5.788E-5 eV/T * 2 T *(-1/2))) = 5.788E-5 eV/T * 2 T * (3/2-1/2) = 5.788E-5 eV/T * 2 T = 115.76E-6 eV = 2.799 GHz

dEb = (-1*5.788E-5 eV/T * 2 T *(-1/2) – (-1*5.788E-5 eV/T * 2 T * 1/2)) = 5.788E-5 eV/T * 2 T * (1/2+1/2) = 5.788E-5 eV/T * 2 T = 115.76E-6 eV = 2.799 GHz

with HFS
Bhf = 10 T, I = 1/2, J = 3/2
A = uBhf/IJ
u = gJuN*I
uI/uN = 2.7832 -> uI = 2.7832*uN = 8.773E-8 eV/T
E = -gJ*uB*B0*mJ – uIB0 + AmImJ

I) mI = +1/2
II) mI = -1/2

aI) dEa = -gJ*uB*B0*mJ – uIB0 + AmImJ = 115.76E-6 eV – (8.773E-8 eV/T * 2 T) + [((1*3.152E-8 eV/T * 1/2)*10 T)/(1/2*3/2)]*(-3/2+1/2)*1/2

dEaI = 115.76E-6 eV – 17.545E-8 eV – 10.5063E-8 eV = 115.479487 eV

aII) dEa = -gJ*uB*B0*mJ – uIB0 + AmImJ = 115.76E-6 eV – (8.773E-8 eV/T * 2 T) + [((1*3.152E-8 eV/T * 1/2)*10 T)/(1/2*3/2)]*(-3/2+1/2)*(-1/2)

dEaII = 115.76E-6 eV – 17.545E-8 eV + 10.5063E-8 eV = 115.68961 eV

bI) dEb = -gJ*uB*B0*mJ – uIB0 + AmImJ = 115.76E-6 eV – (8.773E-8 eV/T * 2 T) + [((1*3.152E-8 eV/T * 1/2)*10 T)/(1/2*3/2)]*(-1/2-1/2)*1/2

dEbI = dEaI ?

bII) dEb = -gJ*uB*B0*mJ – uIB0 + AmImJ = 115.76E-6 eV – (8.773E-8 eV/T * 2 T) + [((1*3.152E-8 eV/T * 1/2)*10 T)/(1/2*3/2)]*(-1/2-1/2)*-1/2

dEbII = dEaII ?

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