the Overhauser effect/method was posposed by Albert W. Overhauser on 1953, that, it can polarizing nuclei. or later called Dynamic Nuclear polarization.
the spin Hamiltonian is
where S is the electron spin, I is nuclear spin, B is external field strength and A is hyperfine structure coupling tensor. is a constant such that:
it related to the Larmor (angular ) frequency, which is in radius by :
it is same for proton with a corresponding g-factor and mass, or other nuclei with g-factor and charge and mass. for example, proton Larmor frequency is:
the Hamiltonian commute for both spin eigenstate. thus, we can write the energy as:
where m is the eigenvalue of and M is the eigenvalue for . For spin-half electron and nuclei, there will be 4 levels by . the selection rule is:
this is called the Overhauser Effect.
The Jeffries-Abragam Effect occur when a pumping radiation induced a “forbidden” transition”: