Pierrelatte, June 1972 / Oklo, Gabon

The Uranium That Had Already Burned

A 1972 uranium assay was low by only 0.0031 percentage points. Follow that tiny deficit into Gabon, run the isotope clock backward, and make neodymium and ruthenium reveal the fission that uranium alone could not prove.

The first object is almost nothing: two mass-spectrometer readings separated in the fourth decimal place. Put them on the bench. The page will not ask the anomaly to carry more than it can.

Place the readings together

The accepted comparison at Pierrelatte was 0.7202 atom percent uranium-235. Material later traced to Gabon returned 0.7171. Press the balance to perform the subtraction from the source values.

Layer 1 / live arithmetic

One difference. Two honest ways to name its size.

atom % U-235
reference
Historical comparison
0.7202
atom percent uranium-235
Pierrelatte accepted value
Gabon ore
Measured assay
0.7171
atom percent uranium-235
Pierrelatte mass spectrometry

The source values are waiting on the balance.

What the first object settles: the assay was low at the published precision. It does not settle why. Analytical error, contamination, provenance, and chemical processing still had to be checked. The truthful first verdict is anomaly detected, not reactor proved.

Turn the isotope ratio backward

Uranium-235 decays faster than uranium-238. Choose which 1972 value starts the clock, then choose which published age you mean. Ore formation and reactor criticality are different dated targets.

Plausibility check

The output is computed from two published half-life central values.

R = U-235 / U-238
Start from
Run back to
3.08% uranium-235 of the U-235 plus U-238 pair

Rpast = Rnow exp[(λ235 - λ238)t]

fpast = Rpast / (1 + Rpast)

Computing...

This is a two-isotope clock using 703.81 million years and 4.4683 billion years as published central half-lives. It omits uranium-234 and does not model geometry, water moderation, neutron poisons, or leakage. An ancient abundance near 3 percent is not, by definition, proof of criticality.

Let one isotope remove the ordinary rock

Raw Oklo neodymium is a mixture. Fission does not produce neodymium-142, so that one column fixes the scale of the natural component. It is the fitted point and is not allowed to score its own fit. The other six columns are the test.

Layer 2 / held-out isotope test

Natural admixture is fitted once. Neutron-capture pairs are then preserved by summing.

Neuilly et al. Table I
Bench view
Values behind the bars

Raw Oklo M is not a pure fission spectrum. Select the subtraction.

mixture visible

The single-isotope view after subtraction still misses by as much as 6.22 percentage points. That is not a failed fission fingerprint. Neutron capture moves 143Nd into 144Nd and 145Nd into 146Nd. Preserve those pairs, and the four held-out groups read 54.96, 33.65, 8.12, 3.27 percent against 55.31, 33.31, 8.26, 3.12. The largest mismatch is 0.35 percentage points.

Ask another element

Neodymium could be accused of having been corrected into agreement. Ruthenium is a separate holdout from a later paper. Choose either Oklo sample. Every bar is observed yield divided by calculated fission yield.

Independent elemental holdout

The ratios come from Table 7 numerators and denominators, divided live.

Hidaka et al. 1992
Oklo sample
Ru-96not detected
Ru-98not detected
Ru-100not detected
Published inputs, live division
masscalculatedobservedobserved / calculated

SF-29 ratios: 0.82, 0.97, 1.01, 1.00

The 99Ru deficit is not hidden. The paper connects it to partial loss of long-lived precursor 99Tc. Ruthenium is well retained here, not perfectly frozen, and other fission products were remobilized more strongly.

What the rock does not read directly

Oklo isotope data have been used to constrain change in the fine-structure constant. These are model outputs, not a raw rock measurement. Switch between two peer-reviewed analyses and keep their assumptions attached.

Published conditional result

This control selects a paper. It does not re-run a reactor model.

95 percent confidence
Analysis
Damour and Dyson, 1996
-0.9 × 10-7 < Δα/α < 1.2 × 10-7

What the number depends on

    The tighter published card is |Δα|/α < 1.1 × 10-8, subject to a stated restriction involving change in mq/Λ. The change in scale between papers is evidence of model dependence, not evidence that the rock changed.

    The moat

    The check

    The ledger below is rebuilt in your browser from the published inputs embedded at the foot of this page. The dependency-free verifier carries a separate copy of those source-table anchors, derives every displayed result, and fails if the page inputs drift.

    assay 0.0031 percentage points; 0.4304% relative
    clock from 0.7202 3.08% at 1.78 Ga; 3.58% at 1.968 Ga; 3.44 to 3.73%
    Nd held-out groups 54.96, 33.65, 8.12, 3.27 versus 55.31, 33.31, 8.26, 3.12
    SF-29 Ru divisions 0.82, 0.97, 1.01, 1.00

    Uncertainties and limits

    • 0.7202 is the historical comparison used in 1972, not a universal natural-uranium constant. Later high-precision work found natural fractionation.
    • The assay was a clue. Analytical error, contamination, provenance, and processing had to be excluded before fission products carried the diagnosis.
    • 1.78 Ga dates ore formation. 1.968 +/- 0.050 Ga estimates criticality. They are different targets and are not averaged here.
    • The clock uses central half-lives only. Their published uncertainties, later enlarged uncertainty budgets, uranium-234, and reactor physics are not propagated.
    • The 1972 neodymium table is rounded. Its analytical errors and covariance are unavailable here. Natural subtraction assumes 142Nd is non-fissiogenic, and the pairing only protects the named capture transfers.
    • Ruthenium yields depend on the paper's calculated fission curve. The 99Ru deficit records precursor mobility, and retention differs by element and sample.
    • Neither fine-structure bound was re-derived from raw reactor data here. Both depend on temperature, neutron spectrum, resonance sensitivity, and nuclear modeling. The 2015 value also restricts relative change in mq/Λ.
    • The build checked the neodymium numbers through a 2014 verbatim reproduction. It did not independently extract the 1972 Gallica scan.

    Free choices exposed

    • You choose whether the clock starts from the historical 0.7202 reference or the anomalous 0.7171 assay.
    • You choose the 1.78 Ga ore-formation date or the 1.968 Ga criticality estimate. Only the latter carries the displayed +/- 0.050 Ga range.
    • You choose raw, 142Nd-corrected, or capture-paired neodymium. The natural anchor itself is fixed, not tuned.
    • You choose ruthenium sample A or SF-29. The ratios are always observed divided by calculated.
    • You choose which published fine-structure analysis to read. The page does not choose a preferred bound or combine them.
    • Formatting is a free choice: uranium and neodymium results are rounded to the precision printed. The verifier checks before and after rounding.
    Settings that would prove nothing: summing every normalized neodymium isotope always returns 100 percent. Scoring 142Nd after using it to fit the natural fraction would reward a point forced to zero. Treating the backward clock as fission evidence would confuse a decay identity with a reactor observation. Those moves are named and excluded. There is no all-zero comparison setting.

    Run the independent check: node research/oklo-reactor/verify-oklo-reactor.mjs. It starts from published external anchors, including the raw ruthenium Table 7 numerators and denominators, before checking any page result.

    Apparatus

    Sources

    Published inputs remain inputs. Arithmetic derived here remains arithmetic. Full field-by-field checks and unresolved limits are recorded in research/oklo-reactor/README.md.

    Assay. Jean-François Dozol, "From routine sample measurements in CEA to the Oklo phenomenon", Radiation Protection Dosimetry 199 (2023), DOI 10.1093/rpd/ncad014.

    Original diagnosis and neodymium. Neuilly, Bussac, Fréjacques, Nief, Vendryes and Yvon, "Sur l'existence dans un passé reculé d'une réaction en chaîne naturelle...", Comptes Rendus 275 (1972), 1847-1849. Table checked through the reproduction in Davis, Gould and Sharapov.

    Half-lives. Jaffey, Flynn, Glendenin, Bentley and Essling, "Precision Measurement of Half-Lives and Specific Activities of U-235 and U-238", Physical Review C 4 (1971).

    Ages. Lancelot, Vitrac and Allègre, ore formation at 1.78 Ga (1975); Mossman, Nagy, Rigali, Gauthier-Lafaye and Holliger, criticality at 1968 +/- 50 Ma (1993).

    Ruthenium. Hidaka, Konishi and Masuda, "Reconstruction of cumulative fission yield curve and geochemical behaviors...", Geochemical Journal 26 (1992), Table 7.

    Historical reference caveat. Brennecka, Borg, Hutcheon, Sharp and Anbar, "Natural variations in uranium isotope ratios of uranium ore concentrates", Earth and Planetary Science Letters 291 (2010).

    Fine-structure bound, 1996. Damour and Dyson, "The Oklo bound on the time variation of the fine-structure constant revisited", one arXiv version, later Nuclear Physics B 480.

    Fine-structure bound, 2015. Davis and Hamdan, "Reappraisal of the limit on the variation in alpha implied by Oklo", two arXiv versions, later Physical Review C 92.