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Solving a Half-Century-Old Mystery: Why is There Carbon Dating?

Solving a Half-Century-Old Mystery: Why is There Carbon Dating?. R. Machleidt University of Idaho. A plain paper …. and a lot of fuss …. Outline. What is C-14 dating? What’s the “mystery”? Beta-decay of a nucleus Calculating the transition C-14  N-14

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Solving a Half-Century-Old Mystery: Why is There Carbon Dating?

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

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

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

  4. Carbon Dating UI Colloq. 26-Jan-2009

  5. Carbon Dating UI Colloq. 26-Jan-2009

  6. Carbon Dating UI Colloq. 26-Jan-2009

  7. Carbon Dating UI Colloq. 26-Jan-2009

  8. 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 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). Carbon Dating UI Colloq. 26-Jan-2009

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

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

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

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

  14. Carbon Dating UI Colloq. 26-Jan-2009

  15. Carbon Dating UI Colloq. 26-Jan-2009

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

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

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

  19. Carbon Dating UI Colloq. 26-Jan-2009

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

  21. The bottom line is, it all depends on nuclear forces; so, what are they like? 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 2 CNS Summer School 2005

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

  24. The analogy Atom: Coulomb force Nucleus: Nuclear forces γ γ n p + - γ mesons 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: Carbon Dating UI Colloq. 26-Jan-2009 Carbon Dating UI Colloq. 26-Jan-2009 Nuclear Forces - Lecture 2 CNS Summer School 2005

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

  27. Carbon Dating UI Colloq. 26-Jan-2009

  28. Consequences of Brown-Rho scalingfor 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? Carbon Dating UI Colloq. 26-Jan-2009

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

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

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

  32. Carbon Dating UI Colloq. 26-Jan-2009

  33. 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. 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! Carbon Dating UI Colloq. 26-Jan-2009

  35. The End 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 Carbon Dating UI Colloq. 26-Jan-2009

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