Oscillating Nuclear Charge Radii as Sensors for Ultralight Dark Matter
Bibliographic record
Abstract
We show that coupling of ultralight dark matter (UDM) to quarks and gluons would lead to an oscillation of the nuclear charge radius for both the quantum chromodynamic (QCD) axion and scalar dark matter, an effect which is of particular importance for heavy elements. Consequently, the resulting oscillation of electronic energy levels could be resolved with optical atomic clocks, and their comparisons can be used to investigate UDM nuclear couplings, which were previously only accessible with other platforms. We demonstrate this idea using the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msub> <a:mrow> <a:mmultiscripts> <a:mrow> <a:mi>S</a:mi> </a:mrow> <a:mprescripts/> <a:none/> <a:mrow> <a:mn>2</a:mn> </a:mrow> </a:mmultiscripts> </a:mrow> <a:mrow> <a:mn>1</a:mn> <a:mo>/</a:mo> <a:mn>2</a:mn> </a:mrow> </a:msub> <a:mo stretchy="false">(</a:mo> <a:mi>F</a:mi> <a:mo>=</a:mo> <a:mn>0</a:mn> <a:mo stretchy="false">)</a:mo> <a:mo stretchy="false">↔</a:mo> <a:msub> <a:mrow> <a:mmultiscripts> <a:mrow> <a:mi>F</a:mi> </a:mrow> <a:mprescripts/> <a:none/> <a:mrow> <a:mn>2</a:mn> </a:mrow> </a:mmultiscripts> </a:mrow> <a:mrow> <a:mn>7</a:mn> <a:mo>/</a:mo> <a:mn>2</a:mn> </a:mrow> </a:msub> <a:mo stretchy="false">(</a:mo> <a:mi>F</a:mi> <a:mo>=</a:mo> <a:mn>3</a:mn> <a:mo stretchy="false">)</a:mo> </a:mrow> </a:math> electric octupole and <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mrow> <h:msub> <h:mrow> <h:mmultiscripts> <h:mrow> <h:mi>S</h:mi> </h:mrow> <h:mprescripts/> <h:none/> <h:mrow> <h:mn>2</h:mn> </h:mrow> </h:mmultiscripts> </h:mrow> <h:mrow> <h:mn>1</h:mn> <h:mo>/</h:mo> <h:mn>2</h:mn> </h:mrow> </h:msub> <h:mo stretchy="false">(</h:mo> <h:mi>F</h:mi> <h:mo>=</h:mo> <h:mn>0</h:mn> <h:mo stretchy="false">)</h:mo> <h:mo stretchy="false">↔</h:mo> <h:msub> <h:mrow> <h:mmultiscripts> <h:mrow> <h:mi>D</h:mi> </h:mrow> <h:mprescripts/> <h:none/> <h:mrow> <h:mn>2</h:mn> </h:mrow> </h:mmultiscripts> </h:mrow> <h:mrow> <h:mn>3</h:mn> <h:mo>/</h:mo> <h:mn>2</h:mn> </h:mrow> </h:msub> <h:mo stretchy="false">(</h:mo> <h:mi>F</h:mi> <h:mo>=</h:mo> <h:mn>2</h:mn> <h:mo stretchy="false">)</h:mo> </h:mrow> </h:math> electric quadrupole transitions in <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:mrow> <o:mmultiscripts> <o:mrow> <o:msup> <o:mrow> <o:mi>Yb</o:mi> </o:mrow> <o:mrow> <o:mo>+</o:mo> </o:mrow> </o:msup> </o:mrow> <o:mprescripts/> <o:none/> <o:mrow> <o:mn>171</o:mn> </o:mrow> </o:mmultiscripts> </o:mrow> </o:math> . Based on the derived sensitivity coefficients for these two transitions and a long-term comparison of their frequencies using a single trapped <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mrow> <q:mmultiscripts> <q:mrow> <q:msup> <q:mrow> <q:mi>Yb</q:mi> </q:mrow> <q:mrow> <q:mo>+</q:mo> </q:mrow> </q:msup> </q:mrow> <q:mprescripts/> <q:none/> <q:mrow> <q:mn>171</q:mn> </q:mrow> </q:mmultiscripts> </q:mrow> </q:math> ion, we find bounds on the scalar UDM-nuclear couplings and the QCD axion decay constant. These results are at a similar level compared to the tightest spectroscopic limits, and future investigations, also with other optical clocks, promise significant improvements.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".