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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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The number of nuclear spins aligned in the lower energy state is slightly greater than those in the higher energy state. In the presence of an external magnetic field, as the spins precess at the Larmor frequency, the excess population results in a net magnetization oriented along the z axis. When a pulse or a short burst of radio waves at the Larmor frequency is applied along the x axis, the coupling of frequencies causes resonance and flips the nuclear spins of the excess population from the...
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Atomic Nuclei: Types of Nuclear Relaxation01:28

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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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The resolution of a mass spectrometer depends on the efficiency of separating ions with different ion masses. The mass of an atom is approximated to the sum of the masses of protons and neutrons inside, considering the masses of protons and neutrons as equal. However, the masses of the proton (1.6726 × 10−24 g) and neutron (1.6749 × 10−24 g) are not truly equal. There is a minor error in the expression of atomic masses relative to the simplest atom of hydrogen. For...
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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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When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
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Related Experiment Video

Updated: Jun 17, 2025

Studying Soft-matter and Biological Systems over a Wide Length-scale from Nanometer and Micrometer Sizes at the Small-angle Neutron Diffractometer KWS-2
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Studying Soft-matter and Biological Systems over a Wide Length-scale from Nanometer and Micrometer Sizes at the Small-angle Neutron Diffractometer KWS-2

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Resonant neutron scattering lengths.

Robert B Von Dreele1

  • 1Advanced Photon Source Argonne National Laboratory 9700 South Cass Avenue Lemont IL60439-4814 USA.

Journal of Applied Crystallography
|August 7, 2024
PubMed
Summary

Rare-earth elements exhibit significant resonant neutron scattering, enabling diffraction studies despite strong absorption. A Breit-Wigner model accurately calculates scattering intensities for these elements using modern neutron sources.

Area of Science:

  • Condensed Matter Physics
  • Materials Science
  • Nuclear Physics

Background:

  • Most elements have predictable neutron scattering, but rare-earths exhibit unique resonant scattering.
  • This resonant scattering is often coupled with high neutron absorption, posing experimental challenges.

Purpose of the Study:

  • To enable neutron diffraction experiments with rare-earth elements.
  • To provide a computational method for accurately determining neutron scattering intensities for rare-earths.

Main Methods:

  • Utilizing high-intensity neutron sources for diffraction experiments.
  • Applying a semi-empirical Breit-Wigner formalism to model resonant scattering lengths (b0, b', b'').
  • Evaluating the model over a typical neutron energy range (10-600 meV) and wavelength range (0.4-2.8 Å).
Keywords:
Breit–Wigner formularare earthsresonant neutron scattering lengths

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Main Results:

  • Demonstrated the feasibility of neutron diffraction experiments with rare-earth elements.
  • Successfully fitted resonant scattering length variations using the Breit-Wigner model.
  • Established a reliable method for calculating scattering intensities applicable to a wide range of neutron energies and wavelengths.

Conclusions:

  • Neutron diffraction is a viable technique for studying rare-earth elements.
  • The Breit-Wigner formalism provides an effective means to quantify resonant neutron scattering in rare-earths.
  • This work facilitates further research into the structural and magnetic properties of rare-earth materials.