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Related Concept Videos

Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

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NMR-active nuclei have energy levels called 'spin states' that are associated with the orientations of their nuclear magnetic moments. In the absence of a magnetic field, the nuclear magnetic moments are randomly oriented, and the spin states are degenerate. When an external magnetic field is applied, the spin states have only 2 + 1 orientations available to them. A proton with = ½ has two available orientations. Similarly, for a quadrupolar nucleus with a nuclear spin value of...
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Atomic Nuclei: Nuclear Spin State Population Distribution01:14

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Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
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Atomic Nuclei: Nuclear Relaxation Processes01:23

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.
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Spin–Spin Coupling Constant: Overview01:08

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In bromoethane, the three methyl protons are coupled to the two methylene protons that are three bonds away. In accordance with the n+1 rule, the signal from the methyl protons is split into three peaks with 1:2:1 relative intensities. The methylene protons appear as a quartet, with the relative intensities of 1:3:3:1.
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The Pauli Exclusion Principle03:06

The Pauli Exclusion Principle

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The arrangement of electrons in the orbitals of an atom is called its electron configuration. We describe an electron configuration with a symbol that contains three pieces of information:
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Atomic Nuclei: Nuclear Spin01:08

Atomic Nuclei: Nuclear Spin

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All atomic particles possess an intrinsic angular momentum, or 'spin'. Electrons, protons, and neutrons each have a spin value of ½, although protons and neutrons in nuclei may have higher half-integer spins owing to energetic factors.
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Related Experiment Video

Updated: Oct 29, 2025

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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Centralizer theory for long-lived spin states.

Christian Bengs1

  • 1School of Chemistry, School of Chemistry, University of Southampton, University Road, Southampton, SO17 1BJ United Kingdom.

The Journal of Chemical Physics
|July 9, 2021
PubMed
Summary

Nuclear Magnetic Resonance (NMR) researchers can now more easily identify long-lived spin states. A new method uses Lie algebraic techniques on the relaxation algebra, simplifying calculations for various spin systems.

Area of Science:

  • Nuclear Magnetic Resonance (NMR) Spectroscopy
  • Quantum Information Science
  • Chemical Physics

Background:

  • Nuclear long-lived spin states are crucial in Nuclear Magnetic Resonance (NMR) techniques due to their resistance to relaxation.
  • Current methods for identifying these states often rely on complex group theoretical arguments and have seen limited innovation.
  • The increasing importance of long-lived spin states necessitates more efficient and accessible identification strategies.

Purpose of the Study:

  • To present a streamlined and more accessible method for calculating nuclear long-lived spin states.
  • To replace traditional group theoretical approaches with Lie algebraic methods for analyzing relaxation properties.
  • To provide a practical algorithm for identifying long-lived spin states in various spin systems.

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Related Experiment Videos

Last Updated: Oct 29, 2025

Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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Main Methods:

  • Focusing on the relaxation algebra instead of the relaxation superoperator's symmetry properties.
  • Utilizing Lie algebraic methods to analyze the centralizer of the relaxation algebra.
  • Developing a straightforward algorithm for calculating the centralizer, which forms a basis for long-lived spin states.

Main Results:

  • Demonstrated that the centralizer of the relaxation algebra directly yields the set of long-lived spin states.
  • Showcased a method that bypasses the need for complex symmetry arguments.
  • Successfully applied the method to identify long-lived spin states in spin-1/2 pairs and rapidly rotating methyl groups.

Conclusions:

  • The proposed Lie algebraic approach offers a significant simplification for calculating nuclear long-lived spin states.
  • This method provides a more straightforward and computationally efficient alternative to existing group theoretical strategies.
  • The developed algorithm is broadly applicable to various spin systems, enhancing NMR methodology.