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Related Concept Videos

Atomic Nuclei: Nuclear Spin01:08

Atomic Nuclei: Nuclear Spin

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.
Atomic nuclei have a net nuclear spin, , which can have an integer or half-integer value. In atomic nuclei, the spins of protons are paired against each other but not with neutrons, and vice versa. Consequently, an even number of protons does not contribute to...
Atomic Nuclei: Nuclear Spin State Overview01:03

Atomic Nuclei: Nuclear Spin State Overview

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 one, the...
Atomic Nuclei: Nuclear Spin State Population Distribution01:14

Atomic Nuclei: Nuclear Spin State Population Distribution

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.
Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule01:10

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1  triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the others.
Spin–Spin Coupling Constant: Overview01:08

Spin–Spin Coupling Constant: Overview

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.
Qualitatively, any spin plus-half nucleus polarizes the spins of its electrons to the minus-half state. Consequently, the paired electron in the hydrogen–carbon bond must have a...
Atomic Nuclei: Nuclear Magnetic Moment00:59

Atomic Nuclei: Nuclear Magnetic Moment

All atomic nuclei are positively charged. When they have a nonzero spin, they behave like rotating charges. As a consequence of their charge and spin, these nuclei generate a magnetic field (B). This, in turn, gives rise to a magnetic moment (μ), which is randomly oriented in the absence of an external magnetic field. When an external magnetic field (B0) is applied, the magnetic moment vectors can align with the field or against it in 2 + 1 orientations. A hydrogen nucleus, which is just a...

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Related Experiment Video

Updated: May 17, 2026

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Proton spin structure from measurable parton distributions.

Xiangdong Ji1, Xiaonu Xiong, Feng Yuan

  • 1Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China.

Physical Review Letters
|October 30, 2012
PubMed
Summary

We explored proton spin structure using measurable parton distributions. A new polarization sum rule was derived for transversely polarized protons, linking to generalized parton distributions.

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Setting Limits on Supersymmetry Using Simplified Models
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Area of Science:

  • Nuclear Physics
  • Particle Physics
  • Quantum Chromodynamics

Background:

  • Proton spin structure is fundamental to understanding nucleon properties.
  • Parton distributions offer a framework to describe internal proton structure.
  • Generalized Parton Distributions (GPDs) provide a more complete picture beyond traditional distributions.

Purpose of the Study:

  • To systematically study the proton spin structure.
  • To derive a polarization sum rule for transversely polarized protons.
  • To decompose the spin of longitudinally polarized protons.

Main Methods:

  • Derivation of a polarization sum rule using leading GPDs in hard exclusive processes.
  • Helicity decomposition for longitudinally polarized protons.
  • Analysis of quark and gluon helicity distributions and orbital angular momentum contributions.

Main Results:

  • A novel polarization sum rule for transversely polarized protons was established.
  • The helicity decomposition reveals contributions from quark/gluon helicities and orbital angular momentum.
  • Subleading GPDs and Wigner distributions are linked to orbital angular momentum.

Conclusions:

  • The study provides a comprehensive framework for understanding proton spin.
  • Measurable parton distributions offer a path to experimentally probe spin components.
  • Connections between GPDs, Wigner distributions, and orbital angular momentum are highlighted.