Solid Effect is a name for a method, or theory description of dynamic polarization transfer from electron spin to nuclear spin due to the hyperfine splitting.

The Hamiltonian for the system on 1 electron and 1 nucleus is:

H = (A+B) S \cdot I

where A and B are scalar coupling and dipolar coupling.

when an external H-field applied. the spin will precess and split in energy according their spin direction. since electron has negative gyromagnetic ratio, it like to align along with the field.  the Hamiltonian is:

H = -\omega_s S_z + \omega_I I_z + (A+B) S_z I_z

the energy diagram is:

if we apply a field with suitable frequency on the transverse direction of the external field, we can excite the transition. in fact for electron only, the transition is called ESR ( electron spin resonance ) or EPR ( electron paramagnetics resonance ).

since the transition:

\left| - , + \right> \leftrightarrow \left| + , - \right>

does not change the total magnetic number, this is called allowed transition or Zero quantum transition. on the other hand, the transition:

\left| - , - \right> \leftrightarrow \left| + , +\right>

change the total magnetic number by 2, which is forbidden in nature according to the selection rule. Thus it is called forbidden transition or Double quantum transition.

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