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Related Concept Videos

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...
Spin–Spin Coupling: One-Bond Coupling01:17

Spin–Spin Coupling: One-Bond Coupling

Coupling interactions are strongest between NMR-active nuclei bonded to each other, where spin information can be transmitted directly through the pair of bonding electrons. While nuclei polarize their electrons to the opposite spins, the bonding electron pair has opposite spins. Configurations with antiparallel nuclear spins are expected to be lower in energy. When coupling makes antiparallel states more favorable, J is considered to have a positive value. The one-bond coupling constant, 1J,...
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...
NMR Spectroscopy: Spin–Spin Coupling01:08

NMR Spectroscopy: Spin–Spin Coupling

The spin state of an NMR-active nucleus can have a slight effect on its immediate electronic environment. This effect propagates through the intervening bonds and affects the electronic environments of NMR-active nuclei up to three bonds away; occasionally, even farther. This phenomenon is called spin–spin coupling or J-coupling. Coupling interactions are mutual and result in small changes in the absorption frequencies of both nuclei involved. While nuclei of the same element are involved in...
Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)01:20

Spin–Spin Coupling: Two-Bond Coupling (Geminal Coupling)

Two NMR-active nuclei bonded to a central atom can be involved in geminal or two-bond coupling. Geminal coupling is commonly seen between diastereotopic protons in chiral molecules and unsymmetrical alkenes, among others.
The central atom need not be NMR-active because its electrons are affected by the electron polarization of the spin-active atoms. However, spin information is transmitted less effectively than in one-bond coupling, and 2J values are usually weaker than 1J values. The energy of...
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...

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Experimental Methods for Spin- and Angle-Resolved Photoemission Spectroscopy Combined with Polarization-Variable Laser
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Spin-isospin resonances: a self-consistent covariant description.

Haozhao Liang1, Nguyen Van Giai, Jie Meng

  • 1State Key Lab Nucl. Phys. & Tech., School of Physics, Peking University, Beijing, China.

Physical Review Letters
|October 15, 2008
PubMed
Summary

A new self-consistent charge-exchange relativistic random phase approximation (RPA) accurately models nuclear excitations. This method successfully reproduces Gamow-Teller resonance and spin-dipole resonance properties in key nuclei.

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Area of Science:

  • Nuclear Physics
  • Quantum Chemistry
  • Theoretical Physics

Background:

  • Relativistic Hartree-Fock (RHF) methods are crucial for describing nuclear structure.
  • Charge-exchange excitations, like Gamow-Teller resonance (GTR) and spin-dipole resonance (SDR), provide insights into nuclear dynamics.
  • Previous models often required readjustment of interaction parameters.

Purpose of the Study:

  • To establish a fully self-consistent charge-exchange relativistic random phase approximation (RPA) based on the RHF approach.
  • To verify the self-consistency using the isobaric analog state (IAS) check.
  • To accurately reproduce excitation properties and sum rules for GTR and SDR without parameter readjustment.

Main Methods:

  • Development of a fully self-consistent charge-exchange relativistic RPA framework.
  • Utilizing the relativistic Hartree-Fock (RHF) approach as the foundation.
  • Performing calculations for doubly magic nuclei: 48Ca, 90Zr, and 208Pb.

Main Results:

  • The established method demonstrates full self-consistency, verified by the IAS check.
  • Excitation properties and nonenergy weighted sum rules for GTR and SDR are well reproduced.
  • The calculations were performed for 48Ca, 90Zr, and 208Pb without readjusting the particle-hole residual interaction.

Conclusions:

  • The developed charge-exchange relativistic RPA provides a robust and self-consistent theoretical framework.
  • The model accurately predicts key nuclear excitation modes, validating its predictive power.
  • The dominant contribution of exchange diagrams in these processes is confirmed.