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Atomic Nuclei: Nuclear Relaxation Processes

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In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis, the precessing magnetic moments are randomly oriented around the z-axis. This...

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The earth's gravitational field produces a 'twisting force' perpendicular to the angular momentum of a spinning mass (such as a spinning top) that causes the mass to 'wobble' around the gravitational field axis in a phenomenon called precession. Similarly, the magnetic moment (μ) of a spinning nucleus precesses due to an external magnetic field directed along the z-axis. The precession of the magnetic moment vector about the magnetic field is called Larmor precession, and the angular frequency...

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Related Experiment Video

Updated: May 22, 2026

Hyperpolarized Xenon for NMR and MRI Applications

Hyperpolarized Xenon for NMR and MRI Applications

Published on: September 6, 2012

A comment on the pseudo-nuclear Zeeman effect.

Silvia Sottini¹, Edgar J J Groenen

¹Department of Molecular Physics, Huygens Laboratory, Leiden University, The Netherlands.

Journal of Magnetic Resonance (San Diego, Calif. : 1997)

|May 15, 2012

Summary

This study presents a new method for describing electron-nuclear double resonance (ENDOR) spectra in high-spin systems. The approach simplifies calculations by using the expectation value of electron spin, offering a more logical alternative to conventional methods.

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Area of Science:

Solid State Physics
Quantum Chemistry
Spectroscopy

Background:

Electron Paramagnetic Resonance (EPR) and Electron-Nuclear Double Resonance (ENDOR) are key techniques for studying magnetic properties of materials.
High-spin systems with zero-field doublets are often analyzed using effective spin Hamiltonians.
Conventional ENDOR analysis can involve complex cross-terms like the pseudo-nuclear Zeeman effect.

Purpose of the Study:

To develop a more straightforward and logically consistent method for describing ENDOR spectra in high-spin systems.
To demonstrate the validity of this new approach using theoretical calculations and experimental data.
To offer an alternative to the conventional pseudo-nuclear Zeeman effect in ENDOR analysis.

Main Methods:

Utilizing a nuclear spin Hamiltonian where the electron spin operator is replaced by its expectation value.
Obtaining the expectation value from a first-order wave function in the electron Zeeman interaction.
Applying perturbation theory for a more logical description compared to second-order cross-terms.

Main Results:

A simplified yet accurate description of ENDOR spectra is achieved by using the expectation value of the electron spin angular momentum.
This method provides a more coherent theoretical framework than the conventional pseudo-nuclear Zeeman effect.
Calculations for a high-spin cobalt complex validated the approach for determining electron spin expectation values and hyperfine level energies.

Conclusions:

The proposed method offers a more intuitive and theoretically sound approach to ENDOR spectroscopy for high-spin systems.
It simplifies spectral analysis by avoiding complex second-order interactions.
This work provides a valuable tool for researchers utilizing EPR and ENDOR techniques.