Magnetic Field Gradients in High Resolution NMR; Magnetic Resonance, Historical Perspective; NMR Data Processing; NMR Principles; NMR Pulse Sequences; NMR Spectrometers; Nonuniform Sampling Methods in NMR Data Acquisition; Product Operator Formalism in NMR; Statistical Tools for Molecular Covariance Spectro...
The effects of pulses of variable flip angle can be conveniently described by products of polarization operators (instead of Cartesian product operators) [101]. A single spin is described by the four polarization operators (also called single spin operators) I+, I−, Iα and Iβ. Decoupling...
These calculations entailed taking the formalism derived in the previous Section, and replacing the position independent spatial translation operator T (Eqs. (7, 8)) with radially-dependent TðyÞ operators accounting for the flow velocities predicted by Fluent®. The resulting simu- lations ...
Solid-state nuclear magnetic resonance and nuclear quadrupole resonance as complementary tools to study quadrupolar nuclei in solids, Concepts Magn. Reson. 45A, 1-11 (2017). Free access David J. Siminovitch Spin precession: A spin-1 case study using irreducible tensor operators, Concepts Magn. Re...
(2007) Overview • Larmor Precession • Bulk Magnetization • Rotating Frame • RF Pulse in Rotating Frame • FID • Product Operators – Foundation for Future Lectures • pw calibration, pw calibration by Nutation • Simple 1D • Spin Echo • T2 – Relaxation • T1 - ...
Such a rotation is identical in nature to that due to evolution under an offset, and using product operators it can be written exp −iφI I exp iφI = cosφ I + sinφ I ( z ) x ( z ) x y [3] The right hand sides of Eqs. [2] and [3] are not immediately comparable,...
directproductΓ R ⊗Γ S oftwoabstracttwo-dimensionalstatespacesofvirtualspinsequal to1/2.SoeveryoperatorPbeingdeterminedinfour-dimensionalbasisΓ I canbeexpressed asalinearcombinationofproductsR⊗Sofspinvectorcomponentoperators,determined inΓ R andΓ S spaces.Inotherwords,itisproposedtoexperimentallyin...
This holds both for liquid-state NMR pulse sequences, where the product-operator formalism is very effective [2], for solids where anisotropic interactions need be considered [3], and for relaxation in liquids [4], [5]. In many cases, it is not possible to derive analytical solutions, in...
pulse of 1H flip angle 90° excites in-phase magnetization along the x direction and a subsequent delay of τhet=1/|2J| allows these to evolve completely into heteronuclear two-spin order (i.e., 2IxSz for a spin pair I=1/2 [1H] and S=1/2) as labeled by the product operators....
ω is the Larmor angular frequency. The net magnetization at the cessation of the RF signal pulse, is computed for arbitrary RF pulse and gradient field waveforms, by numerical integration of equation (1) using rotation operators to accommodate the vector product and iterating its differential ...