Non-perturbative treatment of the solid effect of dynamic nuclear polarization
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Published:2023-06-05
Issue:1
Volume:4
Page:129-152
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ISSN:2699-0016
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Container-title:Magnetic Resonance
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language:en
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Short-container-title:Magn. Reson.
Abstract
Abstract. In the solid effect of dynamic nuclear polarization (DNP), the concerted flips of the electronic and nuclear
spins, which are needed for polarization transfer, are induced by the microwaves. Commonly, the effect
of the microwaves is modeled by a rate process whose rate constant is determined perturbatively.
According to quantum mechanics, however, the coherent microwave excitation leads to Rabi nutation,
which corresponds to a rotation rather than a rate process. Here we reconcile the coherent effect of
the microwaves with the description by rate equations by focusing only on the steady state of the spin
dynamics. We show that the phenomenological
rate constants describing the synchronous excitation of the electronic and nuclear spins can be selected
such that the description by rate equations yields the same steady state as the exact quantum-mechanical treatment. The resulting non-perturbative rates differ from the classical, perturbative ones
and remain valid also at the high microwave powers used in modern-day DNP. Our treatment of
the solid effect highlights the role of the coherences in the mechanistic steps of polarization transfer
and reveals the importance of the dispersive (i.e., out-of-phase) component of the EPR line. Interestingly,
the multiplicative dependence of the DNP enhancement on the dispersive EPR component was intuited in
the very first report of the solid effect in liquids (Erb et al., 1958a). The time-domain description of the solid effect developed
here is extendable to liquids, where the dipolar interaction changes randomly in time due
to molecular diffusion.
Funder
Deutsche Forschungsgemeinschaft
Publisher
Copernicus GmbH
Subject
Atomic and Molecular Physics, and Optics,Condensed Matter Physics,Analytical Chemistry
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