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

H = \gamma S\cdot B + \gamma_n I \cdot B + I\cdot A \cdot S

where S is the electron spin, I is nuclear spin, B is external field strength and A is hyperfine structure coupling tensor. \gamma is a constant such that:

\gamma = g \frac{e \hbar}{2 m_e}

it related to the Larmor (angular ) frequency, which is in radius by :

\omega_0 = \gamma/\hbar

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:

\omega_0(p)/ (2 \pi) = 42.5775 MHz T^{-1}

\omega_0(e)/ (2 \pi) = - 28.025 GHzT^{-1}

\omega_0(n)/ (2 \pi) = 0

the Hamiltonian commute for both spin eigenstate. thus, we can write the energy as:

E(m,M) = \gamma B_0 m + \gamma_n B_0 M + A m M

where m is the eigenvalue of  S_z and M is the eigenvalue for I_z . For spin-half electron and nuclei, there will be  4 levels by m \times M = 4 . the selection rule is:

\Delta m = \pm1, \Delta M = 0

this is called the Overhauser Effect.

The Jeffries-Abragam Effect occur when a pumping radiation induced a “forbidden” transition”:

\Delta m = \pm 1 , \Delta M = \pm 1

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