Physics:Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy

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The nonlinear King plot anomaly in calcium isotope spectroscopy is when isotope shift measurements of calcium atoms deviate from linearity. This effect was reported in 2025 by Wilzewski et al. in Physical Review Letters.[1]

The anomaly may originate from nuclear effects within the Standard Model, but it could also indicate previously unknown interactions. One hypothesis is the existence of a fifth force mediated by a new boson.

This result is part of ongoing research in precision spectroscopy, which uses atomic systems to probe physics beyond current theoretical models.

Calcium-48 atom, includes 20 protons, 20 electrons, and 28 neutrons
Atomic transitions in calcium ions used in high-precision spectroscopy experiments.

Background

Isotope shifts

In atomic physics, an isotope shift is the difference in spectral line frequencies between isotopes of the same element. These shifts arise primarily from:

  • The mass shift, due to differences in nuclear mass
  • The field shift, due to differences in nuclear charge distribution

The isotope shift between isotopes A and A′ for a given transition is:

δνA,A′=K⋅μA,A′+F⋅δ⟨r2⟩A,A′

where μA,A′ is the inverse mass factor, δ⟨r2⟩A,A′ is the change in mean-square nuclear charge radius, and K and F are electronic coefficients.[2]

King plots

Schematic example of a King plot showing expected linear behavior and possible nonlinear deviation.
Kings plot B_L versus E_ν data visualisation

A King plot compares isotope shifts from two different electronic transitions. Under standard assumptions, the relationship is linear:

δν1=a⋅δν2+b

Linearity holds if only mass and field shifts contribute. Deviations may indicate:

  • Higher-order nuclear structure effects
  • Many-body electronic correlations
  • Physics beyond the Standard Model

Experiment

Methodology

Wilzewski et al. performed high-precision spectroscopy on five stable calcium isotopes:

  • 40Ca
  • 42Ca
  • 44Ca
  • 46Ca
  • 48Ca

Two electronic transitions were measured using trapped ions and laser spectroscopy with sub-Hz precision.[1]

The experiment combined singly ionized calcium (Ca+) with highly charged ions to probe both electronic and nuclear contributions.

Results

The resulting King plot showed a statistically significant deviation from linearity. The magnitude of the deviation exceeded experimental uncertainties, indicating a genuine physical effect rather than measurement noise.[1]

Interpretation

Standard Model explanations

Possible Standard Model sources of nonlinearity include:

  • Higher-order mass shift corrections
  • Nuclear polarization effects
  • Nuclear deformation and many-body structure

These contributions are difficult to calculate precisely and may explain the observed anomaly.[3]

New physics hypotheses

An alternative explanation is a new interaction between electrons and neutrons mediated by an unknown boson.

Yukawa interaction

This interaction can be modeled by a Yukawa potential:

V(r)=gegne−mϕrr

where ge and gn are coupling constants and mϕ is the boson mass.[4]

This interaction would introduce additional isotope-dependent shifts, producing nonlinearities in King plots.

Constraints on new bosons

The experiment constrains properties of hypothetical new particles, including:

  • Electron–neutron coupling strength
  • Boson mass in the approximate range:

10 eV≲mϕ≲107 eV

These constraints narrow the parameter space for new forces accessible via atomic spectroscopy.[1]

Relation to fundamental physics

The Standard Model includes four fundamental interactions:

  1. Gravitation
  2. Electromagnetism
  3. Weak interaction
  4. Strong interaction

A new Yukawa-mediated interaction would represent a fifth force, with implications for:

  • Dark matter
  • Matter–antimatter asymmetry
  • Hidden sector physics

However, current evidence remains inconclusive.

Comparison with other experiments

Similar nonlinear King plot effects have been studied in:

Some experiments report comparable deviations, though interpretations remain debated.[5]

Future research

Further work is needed to distinguish between nuclear and new-physics explanations:

  • Multi-transition (higher-dimensional) King plots
  • Improved nuclear theory calculations
  • Studies of additional elements
  • Increased experimental precision

References

  1. ↑ 1.0 1.1 1.2 1.3 Wilzewski, A. et al. (2025). "Nonlinear Calcium King Plot Constrains New Bosons and Nuclear Properties". Physical Review Letters 134 (23), 233002. DOI
  2. ↑ King, W. H. (1963). "Comments on the Article 'Peculiarities of the Isotope Shift in the Samarium Spectrum'". Journal of the Optical Society of America. DOI
  3. ↑ Flambaum, V. V. et al. (2018). "Isotope shift, nonlinearity of King plots, and the search for new particles". Physical Review A. DOI
  4. ↑ Delaunay, C. et al. (2017). "Probing atomic Higgs-like forces at the precision frontier". Physical Review D. DOI
  5. ↑ Counts, I. et al. (2020). "Evidence for nonlinear isotope shift in ytterbium". Physical Review Letters. DOI

See also

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Index

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Conceptual illustration of plasma physics in a fusion context, showing magnetically confined ionized gas in a tokamak and the collective behavior governed by electromagnetic fields and transport processes.
Conceptual illustration of plasma physics in a fusion context, showing magnetically confined ionized gas in a tokamak and the collective behavior governed by electromagnetic fields and transport processes.


Author: Harold Foppele

Source attribution: Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy

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