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

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

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

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

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

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

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

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

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

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

Carbon Dating UI Colloq. 26-Jan-2009 “Shroud of Turin” Is this the shroud in which Jesus Christ was wrapped after his crucifixion? Radiocarbon dating: 1260-1390 after Christ R. Machleidt Carbon Dating UI Colloq. 26-Jan-2009

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

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

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

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Carbon Dating UI Colloq. 26-Jan-2009 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

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

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 2 CNS Summer School 2005

Carbon Dating UI Colloq. 26-Jan-2009 … 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

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

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 2 CNS Summer School 2005

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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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

Carbon Dating UI Colloq. 26-Jan-2009 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

Carbon Dating UI Colloq. 26-Jan-2009 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

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

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Carbon Dating UI Colloq. 26-Jan-2009 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

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

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

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