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¹H NMR: Complex Splitting

¹H NMR: Complex Splitting

A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied...

¹³C NMR: ¹H–¹³C Decoupling

¹³C NMR: ¹H–¹³C Decoupling

The probability of having two carbon-13 atoms next to each other is negligible because of the low natural abundance of carbon-13. Consequently, peak splitting due to carbon-carbon spin-spin coupling is not observed in spectra. However, protons up to three sigma bonds away split the carbon signal according to the n+1 rule, resulting in complicated spectra.
A broadband decoupling technique is used to simplify these complex, sometimes overlapping, signals. Broadband decoupling relies on a...

¹H NMR: Interpreting Distorted and Overlapping Signals

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are...

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule

In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1 triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...

Spin–Spin Coupling Constant: Overview

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...

Molecular Orbital Theory II

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Related Experiment Video

Updated: Apr 5, 2026

Setting Limits on Supersymmetry Using Simplified Models

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Stringent Constraints on New Pseudoscalar and Vector Bosons from Precision Hyperfine Splitting Measurements.

Cedric Quint¹, Fabian Heiße¹, Joerg Jaeckel²

¹Max Planck Institute for Nuclear Physics, Saupfercheckweg 1, 69117 Heidelberg, Germany.

Physical Review Letters

|April 3, 2026

Summary

New pseudoscalar and vector bosons can cause spin-dependent forces. Hyperfine structure measurements in atoms offer a sensitive probe, with existing Be data yielding competitive limits for axionlike particles (ALPs) and future Cs measurements promising enhanced discovery potential.

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Area of Science:

Atomic Physics
Particle Physics
Quantum Electrodynamics (QED)

Background:

Axionlike particles (ALPs) and new bosons can mediate novel spin-dependent forces.
These forces affect atomic and ionic systems, particularly their hyperfine structure.
Understanding these interactions is crucial for probing physics beyond the Standard Model.

Purpose of the Study:

To investigate the sensitivity of hyperfine structure measurements to axionlike particles and new bosons.
To establish constraints on pseudoscalar and vector couplings using atomic spectroscopy data.
To assess the future discovery potential of these measurements for new fundamental forces.

Main Methods:

Analysis of hyperfine structure splittings in hydrogenlike and lithiumlike ions.
Utilizing differences in splittings to mitigate nuclear uncertainties in calculations and measurements.
Comparison of experimental data with theoretical predictions for various coupling scenarios.

Main Results:

Existing measurements on Beryllium (Be) ions provide competitive limits for pseudoscalar couplings around m_ϕ ≳ 100 keV.
These limits confirm or improve existing constraints by up to a factor of 2, depending on nuclear models.
Future measurements on Cesium (Cs) show potential for 2-2.5 times improved discovery of pseudoscalars and an order of magnitude for vector bosons.

Conclusions:

Hyperfine structure measurements in specific atomic charge states serve as a powerful probe for new spin-dependent forces.
Atomic spectroscopy experiments, like those on Be, already place stringent limits on ALPs and related new bosons.
Upcoming experiments, particularly on Cs, offer significant prospects for discovering new fundamental particles and interactions.