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Atomic Nuclei: Nuclear Spin State Population Distribution

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 Spin State Overview

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 Relaxation Processes

Atomic Nuclei: Nuclear Relaxation Processes

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. This...

Atomic Nuclei: Nuclear Magnetic Moment

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...

Atomic Nuclei: Magnetic Resonance

Atomic Nuclei: Magnetic Resonance

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...

NMR Spectroscopy: Spin–Spin Coupling

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...

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Related Experiment Video

Updated: Jun 14, 2026

High-Temperature and High-Pressure In situ Magic Angle Spinning Nuclear Magnetic Resonance Spectroscopy

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Limits on new long range nuclear spin-dependent forces set with a K-3He comagnetometer.

G Vasilakis¹, J M Brown, T W Kornack

¹Department of Physics, Princeton University, Princeton, New Jersey 08544, USA.

Physical Review Letters

|April 7, 2010

Summary

Researchers used a novel magnetometer to search for new forces acting on neutrons. This experiment sets new limits on neutron interactions, constraining theories beyond the Standard Model.

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Last Updated: Jun 14, 2026

High-Temperature and High-Pressure In situ Magic Angle Spinning Nuclear Magnetic Resonance Spectroscopy

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Quantification of Hydrogen Concentrations in Surface and Interface Layers and Bulk Materials through Depth Profiling with Nuclear Reaction Analysis

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Published on: March 29, 2016

Area of Science:

Nuclear physics
Particle physics
Atomic physics

Background:

The Standard Model of particle physics does not account for all observed phenomena.
Searches for new fundamental forces and particles are crucial for advancing physics.
Spin-polarized atoms offer high sensitivity for detecting subtle interactions.

Purpose of the Study:

To search for anomalous nuclear spin-dependent forces.
To constrain neutron coupling to new light particles.
To test theories beyond the Standard Model, such as unparticles and Lorentz symmetry violation.

Main Methods:

Utilized a magnetometer with co-located spin-polarized Potassium (K) and Helium-3 (3He) atoms.
Employed a separate 3He spin source to generate potential anomalous forces.
Measured changes in 3He spin precession frequency with high precision (18 pHz).

Main Results:

Constrained anomalous spin forces between neutrons to <2x10^-8 of magnetic interactions.
Constrained anomalous spin forces between neutrons to <2x10^-3 of gravitational interactions.
Established new limits on neutron coupling to light pseudoscalar and vector particles at a 50 cm length scale.

Conclusions:

The experiment provides stringent constraints on new physics models.
The results exclude certain parameter spaces for unparticles and spontaneous Lorentz symmetry breaking.
The high-precision magnetometer demonstrates a powerful tool for fundamental physics searches.