1. Solving a Half-Century-Old Mystery: Why is There Carbon Dating?
R. Machleidt
University of Idaho

2. Carbon Dating UI Colloq. 26-Jan-2009
A plain paper …
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

3. Carbon Dating UI Colloq. 26-Jan-2009
and a lot of fuss …
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Carbon Dating UI Colloq. 26-Jan-2009

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Carbon Dating UI Colloq. 26-Jan-2009

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R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

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R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

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R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

8. Carbon Dating UI Colloq. 26-Jan-2009
Outline
What is C-14 dating?
What’s the “mystery”?
Beta-decay of a nucleus
Calculating the transition C-14  N-14
Brown-Rho scaling of meson masses and the resolution of the mystery
Conclusions
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

9. Some facts about C-14 dating
Discovered in 1949 by Willard Libby, Professor at U. Chicago; Chemistry Nobel Prize 1960.
The carbon in the atmosphere (contained in carbon dioxide) includes a small fraction of C-14 (1 part per trillion) which is created in the upper atmosphere by the nuclear reaction
n + N-14  p + C-14
where the incident neutron results from cosmic ray interactions.
The half-life of C-14 is 5730 years.
Organisms, while alive, constantly take up atmospheric carbon dioxide through photosynthesis:
6 CO2 + 6 H2O + Energy  C6H12O6(Glucose) + 6 O2
and, thus, replenish C-14, keeping it at the level of the atmosphere.
As soon as the organism is dead, the ratio C-14/C-12 drops because C-14 decays while C-12 is stable. From the ratio, the age of organic remains can be determined: “Carbon dating”
Because of the long half-life of C-14, the method is good for dating over archaeological times (up to about 60,000 years).
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

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Caves of Lascaux, Southwestern France; about 15,000 B.C.
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

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“Kennewick Man”, Kennewick, WA; about 9,000 years old
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

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“Shroud of Turin”
Is this the shroud in which Jesus Christ was wrapped after his crucifixion?
Radiocarbon dating: after Christ
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

13. Carbon Dating UI Colloq. 26-Jan-2009
What’s the “mystery”?
Half-lives
of allowed
beta-decays
of some
light nuclei
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

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Carbon Dating UI Colloq. 26-Jan-2009

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Carbon Dating UI Colloq. 26-Jan-2009

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How to calculate this?
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

17. The transition matrix element
Fermi
Gamow-Teller
(GT)
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Carbon Dating UI Colloq. 26-Jan-2009

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Conclusion –
We have to calculate:
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Carbon Dating UI Colloq. 26-Jan-2009

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R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

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All depends on the structure of these two nuclei which, in turn, depends on the forces between the nucleons (“nuclear forces”).
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

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The bottom line is, it all depends on nuclear forces; so, what are they like?
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

22. Summary: Most important parts of the nuclear force
Central force
Tensor force:
Spin-orbit force:
Carbon Dating UI Colloq. 26-Jan-2009
Nuclear Forces - Lecture CNS Summer School 2005

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… and how are those forces made? Let’s understand this by analogy to the Coulomb force
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

24. Nucleus: Nuclear forces
The analogy
Atom: Coulomb force
Nucleus: Nuclear forces γ + - γ p n
mesons
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

25. Summary: Most important parts of the nuclear force
Short
Inter-
mediate
Long range
Central force
Tensor force:
Spin-orbit force:
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009
Carbon Dating UI Colloq. 26-Jan-2009
Nuclear Forces - Lecture CNS Summer School 2005

26. Carbon Dating UI Colloq. 26-Jan-2009
This was the picture in free space. But what happens when two nucleons interact inside a nucleus, surrounded by other nucleons? γ p n γ p n ≅ γ p n
lighter mesons
and nucleons γ p n
mesons ≅
“Brown-Rho Scaling”
with lighter masses ≅
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

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R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

28. Consequences of Brown-Rho scaling for the nuclear force
When the mesons change their mass in the nuclear medium (inside nuclei), then the force changes.
One important meson is the rho-meson which is involved in the tensor force: how does its mass-change affect the tensor force?
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

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Tensor forces
created by
rho and pi
The medium effect from BRS:
tensor force gets weaker
with increasing density.
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

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Back to the C-14 beta decay
How does the weakening
of the tensor force affect
the Gamow-Teller matrix
Element?
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

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Increasing density
Increasing density
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Carbon Dating UI Colloq. 26-Jan-2009

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Carbon Dating UI Colloq. 26-Jan-2009

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Summary
The C-14  N-14 transition depends most sensitively on the structure of the N-14 nucleus which, in turn, depends most sensitively on the strength of the nuclear tensor force.
In the nuclear medium, the masses of the mesons that “make” nuclear forces change as compared to free space.
This “Brown-Rho scaling” of, particularly, the rho-meson mass weakens the tensor force inside the nucleus.
This change of the tensor force reduces the GT matrix element and, by that, increases the predicted half-life of C-14 to the experimental value.
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

34. The more general relevance of all this
This is just one example for the fact that, during the past decade, nuclear theory has made great advances and is now able to produce precise and reliable predictions for even very complicated nuclear structure problems.
Thus, in the future, one doesn’t have to do “dirty” and expensive experiments, instead one can use the predictions of a reliable theory.
This will have great spin-off, e.g., for the development of the “Fourth Generation of Nuclear Reactors”: Instead of building expensive and potentially dangerous prototypes, one can design the reactor “on the computer” by calculating all the reactions that take place inside the reactor. This is now in reach!
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Carbon Dating UI Colloq. 26-Jan-2009

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The End
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009

36. The reasoning underlying Brown-Rho scaling
At low energy, the chiral symmetry of QCD (in the u/d quark sector) is spontaneously broken.
One signature for this is the existence of a quark condensate, which is density dependent and disappears at sufficiently high density (and temperature).
By QCD sum rules, the masses of the low-lying hadrons (except the pion) are related to the quark condensate.
Consequently, hadron masses may depend on the density of the nuclear medium and decrease with increasing density.
For vector meson masses, the following simple density dependence is assumed
R. Machleidt
Carbon Dating UI Colloq. 26-Jan-2009