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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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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...
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Atomic Nuclei: Nuclear Relaxation Processes01:23

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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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Atomic Nuclei: Nuclear Magnetic Moment00:59

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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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Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
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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.
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Evidence for partial dynamical symmetries in atomic nuclei.

R F Casten1, R B Cakirli2, K Blaum3

  • 1Wright Nuclear Structure Laboratory, Yale University, New Haven, Connecticut 06520-8124, USA.

Physical Review Letters
|September 27, 2014
PubMed
Summary
This summary is machine-generated.

This study extensively tests Partial Dynamical Symmetries (PDS) in atomic nuclei. The SU(3) PDS model shows success, revealing pervasive symmetry remnants and offering new insights into nuclear collective models.

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Area of Science:

  • Nuclear Physics
  • Quantum Mechanics
  • Atomic Structure

Background:

  • Symmetries provide simplified descriptions for complex natural systems.
  • Partial Dynamical Symmetries (PDS) offer a way to broaden the applicability of symmetry principles.
  • Understanding nuclear structure relies on models that capture complex interactions.

Purpose of the Study:

  • To conduct the first extensive experimental test of a Partial Dynamical Symmetry (PDS) in atomic nuclei.
  • To compare the predictions of an SU(3) PDS model with experimental data for deformed nuclei.
  • To investigate the implications of PDS for collective nuclear models.

Main Methods:

  • Comparison of an SU(3) Partial Dynamical Symmetry (PDS) model with experimental B(E2) values.
  • Analysis of gamma to ground band transitions for 47 deformed nuclei.
  • A parameter-free PDS model was utilized for direct comparison.

Main Results:

  • The parameter-free SU(3) PDS model demonstrated significant success in describing B(E2) values for deformed nuclei.
  • Characteristic discrepancies were observed, suggesting that remnants of symmetry are more widespread than previously assumed.
  • The SU(3) PDS provides novel perspectives on collective models, including the interacting boson approximation.

Conclusions:

  • Partial Dynamical Symmetries, specifically the SU(3) model, are a valuable tool for understanding nuclear structure.
  • Observed deviations from the PDS model highlight the importance of finite size effects and SU(3) configuration mixing in nuclei.
  • The study indicates that symmetry principles play a more fundamental and pervasive role in nuclear physics than previously recognized.