View source for Physics:Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy

{{Short description|Anomalous nonlinearity in calcium isotope spectroscopy potentially indicating new physics}}

{{Quantum book backlink|Quantum optics and experiments}}
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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''.<ref name="Wilzewski2025">
Wilzewski, A. ''et al.'' (2025). "Nonlinear Calcium King Plot Constrains New Bosons and Nuclear Properties". ''Physical Review Letters'' '''134''' (23), 233002. [https://doi.org/10.1103/PhysRevLett.134.233002 DOI]
</ref>

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 [[Wikipedia:Dihydrogen_cation#Precision_spectroscopy|precision spectroscopy]], which uses atomic systems to probe physics beyond current theoretical models.

[[File:Calcium-482.svg|thumb|Calcium-48 atom, includes 20 protons, 20 electrons, and 28 neutrons]]
[[File:Calcium Spectrum.png|thumb|300px|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 <math>A</math> and <math>A'</math> for a given transition is:

<math>\delta \nu^{A,A'} = K \cdot \mu^{A,A'} + F \cdot \delta \langle r^2 \rangle^{A,A'}</math>

where <math>\mu^{A,A'}</math> is the inverse mass factor, <math>\delta \langle r^2 \rangle^{A,A'}</math> is the change in mean-square nuclear charge radius, and <math>K</math> and <math>F</math> are electronic coefficients.<ref name="King1963">King, W. H. (1963). "Comments on the Article 'Peculiarities of the Isotope Shift in the Samarium Spectrum'". ''Journal of the Optical Society of America''. [https://doi.org/10.1364/JOSA.53.000638 DOI]</ref>

=== King plots ===
[[File:King Plot.png|thumb|300px|Schematic example of a King plot showing expected linear behavior and possible nonlinear deviation.]]

[[File:Kings plot B_L versus E_ν data visualisatie.png|thumb|300px|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:

<math>\delta \nu_1 = a \cdot \delta \nu_2 + b</math>

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:

* <math>^{40}\text{Ca}</math>  
* <math>^{42}\text{Ca}</math>  
* <math>^{44}\text{Ca}</math>  
* <math>^{46}\text{Ca}</math>  
* <math>^{48}\text{Ca}</math>  

Two electronic transitions were measured using trapped ions and laser spectroscopy with sub-Hz precision.<ref name="Wilzewski2025" />

The experiment combined singly ionized calcium (Ca<sup>+</sup>) 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.<ref name="Wilzewski2025" />

== 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.<ref name="Flambaum2018">Flambaum, V. V. ''et al.'' (2018). "Isotope shift, nonlinearity of King plots, and the search for new particles". ''Physical Review A''. [https://doi.org/10.1103/PhysRevA.97.032510 DOI]</ref>

=== 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:

<math>V(r) = g_e g_n \frac{e^{-m_\phi r}}{r}</math>

where <math>g_e</math> and <math>g_n</math> are coupling constants and <math>m_\phi</math> is the boson mass.<ref name="Delaunay2017">Delaunay, C. ''et al.'' (2017). "Probing atomic Higgs-like forces at the precision frontier". ''Physical Review D''. [https://doi.org/10.1103/PhysRevD.96.093001 DOI]</ref>

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:

<math>10 \ \text{eV} \lesssim m_\phi \lesssim 10^7 \ \text{eV}</math>

These constraints narrow the parameter space for new forces accessible via atomic spectroscopy.<ref name="Wilzewski2025" />

== Relation to fundamental physics ==

The Standard Model includes four fundamental interactions:

# [[Gravitation]]  
# [[Electromagnetism]]  
# [[Wikipedia:Weak interaction|Weak interaction]]  
# [[Wikipedia:Strong interaction|Strong interaction]]  

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

* [[Wikipedia:Dark matter|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:

* [[Wikipedia:Ytterbium|Ytterbium]] spectroscopy  
* [[Wikipedia:Strontium|Strontium]] optical clock transitions  

Some experiments report comparable deviations, though interpretations remain debated.<ref name="Counts2020">Counts, I. ''et al.'' (2020). "Evidence for nonlinear isotope shift in ytterbium". ''Physical Review Letters''. [https://doi.org/10.1103/PhysRevLett.125.123002 DOI]</ref>

== 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 ==
<references responsive="1" />

=See also=
{{#invoke:PhysicsQC|tocHeadingAndList|Physics:Quantum basics/See also}}
* [[Physics:Isotopic shift|Isotopic shift]]  
* [[Physics:Quantum logic spectroscopy|Precision spectroscopy]]  
* [[Wikipedia:Standard Model|Standard Model]]  
* [[Wikipedia:Fifth force|Fifth force]]  
* [[Physics:Yukawa potential|Yukawa potential]]


{{Author|Harold Foppele}}

{{Sourceattribution|Quantum Nonlinear King plot anomaly in calcium isotope spectroscopy|1}}