An Elementary Example of NMR Spectra

Consider two spin one-half nuclei with spins I a and Ib in an applied field B = (0 0 B). The free energy expression 

An oscillating field along the i-axis would induce transitions among these energy levels, the intensities of which would be proportional to j (mj/ x +Ibx ) P Since Iax + Ibx = Ia+ + I a- + Ib+ + Ib-), it means that the states m) and jn) must differ by -fl or —1 in the eigenvalues of Iaz + IBz for an allowed transition. This means that the following transitions are allowed 1 2, 1 — 3, 2 —+ 4, 3 — 4. The eigenvectors are 

When J = 0 (sin 20 = 0), the four lines coalesce into two with equal 

When J nonvanishing and q, there are four lines with almost equal intensity. 

When a a approximately equal to aB(sin20 close to 1), the two outer lines will disappear. 

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