English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The explicit criterion is derived in detail for the convergence of the Magnusexpansion and the existence of the Magnus solution in the interaction picture,i.e., the exponential propagator in the weakly coupled spin (I=1/2) systemSnAMX... (n=1,2,3,...) in which only spin group S is subjected to atime-dependent shaped selective radiofrequency pulse. The derivation is builton the same scheme as the Maricq's (J. Chem. Phys. 86 (1987) 5647). It is shownthat the criterion depends only upon amplitude of the time-dependent fieldapplied to the system, and the Magnus expansion converges and the Magnussolution exists when the flip angle of a non-negative-amplitude shaped RF pulseor a weak-amplitude shaped pulse is smaller than 2pi. The exponentialpropagator then can be decomposed into a product of a series of elementarypropagators and can be used to determine time evolution of the spin systemunder the shaped pulse. The linear differential equations to determine theunknown parameters in the Magnus solution are obtained explicitly. Analternative propagator in an expansion form for the Magnus solution is alsoproposed to describe the time evolution when the criterion is not met.

An explicit criterion for existence of the Magnus solution for a coupled spin system under a time-dependent radiofrequency pulse