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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...
Nuclear Stability03:18

Nuclear Stability

Protons and neutrons, collectively called nucleons, are packed together tightly in a nucleus. With a radius of about 10−15 meters, a nucleus is quite small compared to the radius of the entire atom, which is about 10−10 meters. Nuclei are extremely dense compared to bulk matter, averaging 1.8 × 1014 grams per cubic centimeter. If the earth’s density were equal to the average nuclear density, the earth’s radius would be only about 200 meters.
To hold positively charged protons together in the...
Other Nuclides: 31P, 19F, 15N NMR01:16

Other Nuclides: 31P, 19F, 15N NMR

Many organic, inorganic, and biological molecules contain spin-half nuclei such as nitrogen-15, fluorine-19, and phosphorus-31. As a result, NMR studies of these nuclei have found extensive applications in chemical and biological research.
While fluorine-19 and phosphorous-31 have high natural abundances (100%) and positive gyromagnetic ratios, nitrogen-15 has a low natural abundance and a negative gyromagnetic ratio. However, nitrogen-15 is still preferred over nitrogen-14 (which has a high...
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.
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...
¹H NMR: Pople Notation01:09

¹H NMR: Pople Notation

The Pople nomenclature system classifies spin systems based on the difference between their chemical shifts. Coupled spins are denoted by capital letters with subscripts indicating the number of equivalent nuclei. When the coupled nuclei have well-separated chemical shifts, they are assigned letters that are far apart in the alphabet, such as A and X. When the difference in chemical shifts is small, coupled nuclei are named using adjacent letters of the alphabet (AB, MN, or XY).
A proton...

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Related Experiment Video

Updated: May 18, 2026

Line Shape Analysis of Dynamic NMR Spectra for Characterizing Coordination Sphere Rearrangements at a Chiral Rhenium Polyhydride Complex
10:52

Line Shape Analysis of Dynamic NMR Spectra for Characterizing Coordination Sphere Rearrangements at a Chiral Rhenium Polyhydride Complex

Published on: July 27, 2022

Medium-mass nuclei with normal-ordered chiral NN+3N interactions.

Robert Roth1, Sven Binder, Klaus Vobig

  • 1Institut für Kernphysik, Technische Universität Darmstadt, Germany. robert.roth@physik.tu-darmstadt.de

Physical Review Letters
|September 26, 2012
PubMed
Summary

Normal-ordered three-nucleon interactions simplify nuclear structure calculations. This approximation is validated for medium-mass nuclei, enabling studies with chiral interactions.

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Atomic Scale Structural Studies of Macromolecular Assemblies by Solid-state Nuclear Magnetic Resonance Spectroscopy
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Atomic Scale Structural Studies of Macromolecular Assemblies by Solid-state Nuclear Magnetic Resonance Spectroscopy

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Thermochemical Studies of Ni(II) and Zn(II) Ternary Complexes Using Ion Mobility-Mass Spectrometry
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Thermochemical Studies of Ni(II) and Zn(II) Ternary Complexes Using Ion Mobility-Mass Spectrometry

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Last Updated: May 18, 2026

Line Shape Analysis of Dynamic NMR Spectra for Characterizing Coordination Sphere Rearrangements at a Chiral Rhenium Polyhydride Complex
10:52

Line Shape Analysis of Dynamic NMR Spectra for Characterizing Coordination Sphere Rearrangements at a Chiral Rhenium Polyhydride Complex

Published on: July 27, 2022

Atomic Scale Structural Studies of Macromolecular Assemblies by Solid-state Nuclear Magnetic Resonance Spectroscopy
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Atomic Scale Structural Studies of Macromolecular Assemblies by Solid-state Nuclear Magnetic Resonance Spectroscopy

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Thermochemical Studies of Ni(II) and Zn(II) Ternary Complexes Using Ion Mobility-Mass Spectrometry
16:11

Thermochemical Studies of Ni(II) and Zn(II) Ternary Complexes Using Ion Mobility-Mass Spectrometry

Published on: June 8, 2022

Area of Science:

  • Nuclear Physics
  • Quantum Many-Body Theory
  • Computational Physics

Background:

  • Nuclear structure calculations require accurate descriptions of nucleon-nucleon and three-nucleon forces.
  • Chiral effective field theory provides a systematic framework for constructing these forces.
  • Computational limitations often necessitate approximations for complex nuclei.

Purpose of the Study:

  • To rigorously benchmark the normal-ordering approximation for three-nucleon interactions in nuclear structure.
  • To assess the applicability of this approximation in importance-truncated no-core shell model and coupled-cluster calculations.
  • To enable ab initio calculations for medium-mass and heavy nuclei using chiral Hamiltonians.

Main Methods:

  • Similarity Renormalization Group (SRG) evolution of chiral two- and three-nucleon interactions.
  • Importance-truncated no-core shell model (IT-NCSM) calculations.
  • Coupled-cluster (CC) calculations, including singles and doubles (SD) excitations.
  • Benchmarking normal-ordering approximation for light and medium-mass nuclei (He, O, Ca isotopes).

Main Results:

  • The normal-ordering approximation for three-nucleon interactions is validated for nuclei beyond the lightest isotopes.
  • IT-NCSM results show good agreement with coupled-cluster calculations for oxygen isotopes.
  • Successful application of SRG-evolved chiral Hamiltonians in CC calculations for medium-mass nuclei.

Conclusions:

  • The normal-ordered two-body approximation is a reliable method for nuclear structure calculations with chiral interactions.
  • This approach facilitates the study of medium-mass and heavy nuclei.
  • Chiral Hamiltonians demonstrate significant predictive power in nuclear structure calculations.