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Orthopositronium-Lifetime Problem

Orthopositronium-Lifetime Problem. By: Charles Fang Physics 138 Presentation. Outline. Introduction/Story History Experiment Setup Analysis Conclusion. Story Time…. Characters: Eric, the Electron e - Patricia, the Positron e + Physics 138 Class, the Assassins.

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Orthopositronium-Lifetime Problem

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  1. Orthopositronium-Lifetime Problem By: Charles Fang Physics 138 Presentation

  2. Outline • Introduction/Story • History • Experiment Setup • Analysis • Conclusion

  3. Story Time… • Characters: • Eric, the Electron e- • Patricia, the Positron e+ • Physics 138 Class, the Assassins

  4. How Long Before Eric and Patricia Break-up? • Once upon a time, there was a guy (Eric) who liked to go out to clubs. He was the type of person who would always approach girls and one of two things would happen. • First, the girl (Patricia) thinks he is rude, and a fight erupts. They annihilate each other and produce two or three photons.

  5. Story (continue) • The second possibility is that Patricia and Eric get married and form a positronium family. Once they are married, two more outcomes still could occur inside the club. • First, assassins try to stab Eric. As a result, two photons are emitted. • Another possibility is that Eric and Patricia get into a fight and annihilate each other and produce 3 photons. • THE END!

  6. Introduction • The orthopositronium(oPs) lifetime problem has been a long standing problem. • It is very interesting to study because the QED calculation by theorist is different from experimentalist’s. There has been many explanation for the discrepancy such as mirror matter. • Finally in 2003, two groups(Tokyo and Ann Arbor) finally got data that are close to the QED calculation.

  7. So What Is Positronium? • Positron(e+) + Electron(e-) = Positronium • Two Types of System In Ground State • Singlet-State - “Parapositronium” • Triplet-State - “Orthopositronium” • Lifetime of pPs is very small compared to oPs. This is significant because when we go measure the lifetime of oPs, the pPs will become negligible in the experiment.

  8. Parapositronium(Singlet State) • Stot = 0, L = 0 • Spin part of the wave-function is ANTI-SYMMETRIC: • (e p - e p) / 2

  9. Orthopositronium(Triplet State) • Stot = 1, L = 0 • Spin part of the wave-function is SYMMETRIC: • e p (MsTot = +1) • (e p +e p) / 2 (MsTot = 0) • e p (MsTot = -1)

  10. Wave-function for Positronium • pos must be have an overall “anti-symmetric” wave-function • pos = (spin part) (spatial part) • oPs = S * A • pPs = A * S

  11. So What Are We Trying To Find? • Solve the orthopositronium-lifetime (the amount of time it takes for the oPs to decay into 3 emitting photons) • Understand the experiment and analysis (Tokyo group which used powder).

  12. Main Equation • obs(t) = 3 + pick(t) (Eq. 1) • obs(t): observed oPs decay rate • 3:decay rate of oPs in vacuum into 3 (what the theorist calculated) • pick(t):pick-off annihilation rate into 2 • In the experiment, we will calculate the ratio of pick(t) / 3 that will help us eventually find the theoretical value of3

  13. Outline • Introduction/Story • History • Experiment Setup • Analysis • Conclusion

  14. History of Experimental Data

  15. Outline • Introduction/Story • History • Experiment Setup • Analysis • Conclusion

  16. Schematic Diagram of Experimental Setup

  17. Life As An Orthopositronium

  18. Life As An Orthopositronium (Case 1)

  19. Life As An Orthopositronium (Case 2)

  20. Variables In the Experiment • pick(t) • Density of sand • Temperature of sand • 3 • Depends only on the e+, e-

  21. Outline • Introduction/Story • History • Experiment Setup • Analysis • Conclusion

  22. Analysis • Ratio of pick(t) / 3 is determined by the energy spectrum measured by the Ge detectors. • For a time-varing rate (t):

  23. Energy Spectrum of oPs decay

  24. Pick-off Spectrum

  25. Ratio of pick(t) / 3 for 2 Runs

  26. Nobs(t) Graph

  27. Next… • Plug the ratio pick(t) / 3 into:

  28. Finally! • Fit the equations and data collected • Only free fit variables • Rstop • C • 3  What we want to find!!

  29. Decay Rates as a Function of Fitting Start Time

  30. Orthopositronium-Lifetime Is… • 3 = 7.0396 + 0.0012 (stat.) + 0.0011(sys.) s-1 • Agrees with NRQED prediction corrected up to a O(2) term. • Agrees with the Ann Arbor group after they realized that oPs thermalized.

  31. Outline • Introduction/Story • History • Experiment Setup • Analysis • Conclusion

  32. Conclusion • Two groups with two different methods obtained results similar to the QED calculation. Problem is solved!

  33. Acknowledgements • Material from this presentation adapted from • Asai, S., Jinnouchi, O., Kobayashi, T., “Solution of Orthopositronium lifetime Puzzle.” • Westbrook, C.I., Gidley, D.W., Conti, R.S., and Rich, A., Phys. Rev. Lett. 58 1338 (1987)

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