Vector model spin 1 dynamics

Contents 1. Introduction 176 2. Static NMR Spectra and the Description of Dynamic Exchange Processes 178 2.1. Simulation of static NMR spectra 178 2.2. Simulation of DNMR spectra with average density matrix method 180 3. Calculation of DNMR Spectra with the Kinetic Monte Carlo Method 182 3.1. Kinetic description of the exchange processes 183 3.2. Kinetic Monte Carlo simulation of DNMR spectra for uncoupled spin systems 188 3.3. Kinetic Monte Carlo simulation of coupled spin systems 196 3.4. The individual density matrix 198 3.5. Calculating the FID of a coupled spin system 200 3.6. Vector model and density matrix in case of dynamic processes 205 4. Summary 211 Acknowledgements 212 References 212... 

Key Words Dynamic NMR, Kinetic Monte Carlo, Chemical exchange, Spin system, Spin set, Individual density matrix, Trajectory, Eigencoherence, Vector model, Mutual exchange, Nonmutual exchange. 

The frequencies assigned to the individual coherences are different for any two conformers present in dynamic spin systems. The product functions, that is, the states the terms were assigned to, are identical. The single spin vector model of the previous section can be extended to weakly coupled systems by changing the precession frequencies of the single quantum coherences during the exchanges of the nuclei instead of... 

The spin dynamics of the deuteron (spin /= 1) are more complex than those of the spin 1/2 nuclei, and the simple vector model used in other chapters, derived from the Bloch equations, provides no particular insight into deuteron spin dynamics. However, some of the geometric simplicity of the Bloch equations is present in a product-operator formalism, used to describe spin 1 NMR [117]. This formalism can provide a visual understanding of the deuteron pulse sequences in terms of simple precession and pulse rotations, albeit among a greater number of coordinate axes. The formalism can be used to understand the production of quadrupole order and the T q relaxation time (Figure 8.2(b)) and the two-dimensional deuteron exchange experiment (section 8.5). 

Efforts to use relativistic dynamics to describe nuclear phenomena began in the 1950s with application to infinite nuclear matter. Johnson and Teller [Jo 55] developed a nonrelativistic field theory for interacting nucleons and neutral, scalar mesons which served as a catalyst for Duerr, who, in a landmark paper [Du 56], developed a relativistic invariant version of the Johnson and Teller model which included both scalar and vector meson fields. He showed that nuclear saturation and the strong spin-orbit potential of the shell model could be readily understood. He also predicted a single particle potential which qualitatively reproduced the real part of the central optical potential well depth and its energy dependence for incident kinetic energies up to 200 MeV. 

F.6.4.2. Lineshape Models. The Mossbauer lineshape can be influenced by all relaxation modes of the Fokker-Planck equation (see Section D.3). Because the relative importance of these modes depends on their population, it should be necessary to know both the eigenvalues of Brown s equation and the amplitudes of the associated modes. In fact, to determine the lineshape, it is necessary to connect the dynamics of the stochastic vector m given by Brown s equation with the quantum dynamics of the nuclear spin. This necessitates the use of superoperator Fokker-Planck equations and, to our knowledge, the problem has not yet been completely solved. 

Normal modes may be used to estimate the effect of including zero point energy in the model. The second moments of the amplitude distribution of are a factor in the calculation of the thermal fluctuations of the intemuclear vector of a given. spin pair v = (i, j), which itself appears in the calculation of the dynamic scaling factor y in equation (37). 

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