## NMR

The term nuclear magnetic resonance, or NMR for short, is a technique used to study the electronic environment of nuclei.

Crucial for such investigations is that the nuclei have a non-zero nuclear spin. In this case, as already shown in the section "Spin & Polarization", different energy levels result, whose occupation numbers can differ.

In the upper graph, the basic structure of a NMR apparatus can be seen. By applying radio frequency via a RF generator, transitions between the sub-levels can be induced. The absorbed power of the field is proportional to the number of induced transitions. Changing the radio frequency in a sufficient span, one obtains the NMR spectrum, which represents the power absorption at different frequencies for the examined sample.

In this way one obtains, for example, the characteristic spectrum of deuterized butanol.

##### NMR for polarization determination

In the working group "Polarized Target" the NMR principle is mainly used to determine the polarization of the examined samples. With the aid of the NMR spectra obtained and some important principles, it is possible to conclude the polarization.

Thus, the polarization is basically proportional to the area under the NMR signal. Exact values can be determined by performing a TE calibration beforehand. To do this, take the NMR spectrum in **t**hermal **e**quilibrium. The polarization can then be determined from the known values for temperature and magnetic field. This can then be assigned to the determined area. All other polarization values can then be determined with this calibration. The following applies:

\[

P = \begin{cases}

\tanh\left( \frac{ -g \mu_N s B }{ kT} \right) \phantom{ \frac{ P_{TE} }{ A_{TE} } \cdot A }\text{at } TE\\

\frac{ P_{TE} }{ A_{TE} } \cdot A \phantom{ \tanh\left( \frac{ -g \mu_N s B }{ kT} \right) }\text{otherwise}

\end{cases}

\]