Electron-nuclear spin system

Jeschke G, Schweiger A. 1996. Generation and transfer of coherence in electron-nuclear spin systems by non-ideal microwave pulses. Mol Phys 88 355-383. 

The overall Hamiltonian of an electron-nuclear spin system in a magnetic field is given by ... 

We now come back to the simplest possible nuclear spin system, containing only one kind of nuclei 7, hyperfine-coupled to electron spin S. In the Solomon-Bloembergen-Morgan theory, both spins constitute the spin system with the unperturbed Hamiltonian containing the two Zeeman interactions. The dipole-dipole interaction and the interactions leading to the electron spin relaxation constitute the perturbation, treated by means of the Redfield theory. In this section, we deal with a situation where the electron spin is allowed to be so strongly coupled to the other degrees of freedom that the Redfield treatment of the combined IS spin system is not possible. In Section V, we will be faced with a situation where the electron spin is in... 

In previous chapters we have seen that the Hamiltonian describing a nuclear spin system is considerably simplified when molecules tumble rapidly and randomly, as in the liquid state. However, that simplicity masks some fundamental properties of spins that help us to understand their behavior and that can be applied to problems of chemical interest. We turn now to the solid state, where these properties often dominate the appearance of the spectra. Our treatment is limited to substances such as molecular crystals, polymers, and glasses, that is, solids in which there are well-defined individual molecules. We do not treat metals, ionic crystals, semiconductors, superconductors, or other systems in which delocalization of electrons is of critical importance. 

Nuclear spin dependent neutron scattering relies on polarisation variation, i.e. on a change of the order of the nuclear spin system. Resonant (or anomalous) X-ray scattering is a concomitant feature of core electron ionisation (Eq. (2)). The dispersion of the resonant coherent scattering is very small compared to the rise of absorption (and fluorescence) due to electronic excitation. It typically amounts to... 

The general form of the spin Hamiltonian for a nuclear-electron two spin system is—... 

In adiabatic demagnetization experiments, Suzuki et al. (1983) observed antiferromagnetic ordering of the enhanced nuclear spin system of Ho in CsaNaHoCle with the ground nonmagnetic doublet at 1.5 mK. Murao (1988) considered the coupled equations of motion of the electron and nuclear magnetic moments in this crystal with reference... 

To proceed, it is necessary to consider the straightforward perturbation treatment of two weakly interacting subsystems, in our case the nuclear moment on the one hand and the electrons around fixed nuclei of the molecule on the other. Whereas our treatment is focused on a nuclear spin system and an electronic system, the approach is general. Suppose the Hamiltonian of the combined system is given by... 

Initially, we neglect tenns depending on the electron spin and the nuclear spin / in the molecular Hamiltonian //. In this approximation, we can take the total angular momentum to be N(see (equation Al.4.1)) which results from the rotational motion of the nuclei and the orbital motion of the electrons. The components of. m the (X, Y, Z) axis system are given by ... 

ENDOR transitions can be easily understood in temis of a simple system consisting of a single unpaired electron spin (S=2) coupled to a single nuclear spin (1=2). The interactions responsible for the various... 

IT. Total Molecular Wave Functdon TIT. Group Theoretical Considerations TV. Permutational Symmetry of Total Wave Function V. Permutational Symmetry of Nuclear Spin Function VT. Permutational Symmetry of Electronic Wave Function VIT. Permutational Symmetry of Rovibronic and Vibronic Wave Functions VIIT. Permutational Symmetry of Rotational Wave Function IX. Permutational Symmetry of Vibrational Wave Function X. Case Studies Lis and Other Systems... 

As was shown in the preceding discussion (see also Sections Vin and IX), the rovibronic wave functions for a homonuclear diatomic molecule under the permutation of identical nuclei are symmetric for even J rotational quantum numbers in and E electronic states antisymmeUic for odd J values in and E elecbonic states symmetric for odd J values in E and E electronic states and antisymmeteic for even J values in Ej and E+ electeonic states. Note that the vibrational ground state is symmetric under pemrutation of the two nuclei. The most restrictive result arises therefore when the nuclear spin quantum number of the individual nuclei is 0. In this case, the nuclear spin function is always symmetric with respect to interchange of the identical nuclei, and hence only totally symmeUic rovibronic states are allowed since the total wave function must be symmetric for bosonic systems. For example, the nucleus has zero nuclear spin, and hence the rotational levels with odd values of J do not exist for the ground electronic state f EJ") of Cr. 

In this section, we extend the above discussion to the isotopomers of X3 systems, where X stands for an alkali metal atom. For the lowest two electronic states, the permutational properties of the electronic wave functions are similar to those of Lij. Their potential energy surfaces show that the baniers for pseudorotation are very low [80], and we must regard the concerned particles as identical. The Na atom has a nuclear spin " K, and K have nuclear... 

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