Nuclear magnetic resonance (NMR) experiments at fields up to 58T in pulsed magnets at the Dresden High Magnetic Field Laboratory are reported. The challenge to resolve NMR shifts in these time-dependent fields is addressed for the first time, and it is shown that this can indeed be accomplished with high precision with an internal reference. As a result, signal averaging is possible during a single magnetic field pulse, but also for multiple pulses. Thus, even very weak signals can in principle be recorded and their shifts can be determined. In a second set of experiments, the measurement of nuclear relaxation is investigated. Using adiabatic inversion with the inherent time dependence of the magnetic field and small-angle inspection, it is shown that relaxation measurements are possible, as well. The shift experiments were performed with 27Al NMR on a mixture of aluminum metal and a Linde type A zeolite. For the relaxation studies, 27Al NMR and 69Ga NMR on the metals aluminum and gallium were preformed, respectively.
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