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This chapter addresses some of the basic concepts of spin exchange optical pumping (SEOP) and starts with a short review of units that may be helpful for scientists working with hyperpolarised (hp) noble gases. A general definition for spin polarization that goes beyond spin I=1/2 systems is provided. SEOP of 129Xe (spin I=1/2) is presented and compared to SEOP of 83Kr (I=9/2) to illustrate the underlying physics of hp noble gas production. The dependence of the spin polarization, P, and the apparent polarization, Papp, on the SEOP pressure, noble gas concentration, laser power, and laser linewidth are presented and experimental examples are provided. A practical gas transfer and compression system that enables almost complete extraction of the hp noble gases from the SEOP cell, even if operating at SEOP pressures below ambient, is described. The presented hp noble gas production concepts should be of interest for pre-clinical and clinical MRI application in biomedical research. However, many of the presented aspects are also relevant for materials science and engineering-related MRI applications. In particular, SEOP experiments with xenon–methane mixtures are described to illustrate the usage of non-inert buffer gases for SEOP.

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