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Quantum Mechanics of Alpha Decay

Quantum Mechanics of Alpha Decay. Lulu Liu Partner: Pablo Solis. December 5, 2007. 8.13 Junior Lab Experiment #4. Classical Mechanics: What Do We Expect to See?. What is alpha decay?. V(r) = ZZ  e 2 / r. r 0 ~ fm, V(r 0 ) is energy minimum. We see V(r 0 ) > E . Less than energy min!

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Quantum Mechanics of Alpha Decay

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  1. Quantum Mechanics of Alpha Decay Lulu Liu Partner: Pablo Solis December 5, 2007 8.13 Junior Lab Experiment #4

  2. Classical Mechanics: What Do We Expect to See? • What is alpha decay? V(r) = ZZ e2 / r • r0 ~ fm, V(r0) is energy minimum • We see V(r0) > E • Less than energy min! • It happens at all! image from nu.phys.laurentian.ca

  3. Quantum Tunneling • WKB Approximation T is transmission coefficient, R is radius of nucleus. derived in Yung-Kuo Lim (originally by Gamow) Geiger-Nuttall Law / Gamow Relation: image from hyperphysics.phy-astr.gsu.edu where  = 1/

  4. Verifying the Geiger-Nuttall Law • Measure energy of emitted alphas • Radioactive Series and Bateman Equations • Equipment • Measure half-lives, 1/2 • Plot Ln(1/) vs. Z*E-1/2 (look for linear relation) • Errors • Conclusions

  5. Naturally Occurring Radioactive Series

  6. Bateman Equations • Governs time evolution • for A decays into B: • solve:

  7. Can Detector to MCA Setup ... to MCA Decay chains start with Po

  8. Rn-222 Half-Life Using Scintillator Assumption: Initially Pure Rn-222 Result: Equilibrium established in several hours

  9. Plot of Rn-222 Activity Background ~1/s Accepted Value: 1/2 = 3.84 days Measured Value: 1/2 = 3.99 § 0.36 days

  10. Energy Spectrum from Can Detector Calibrated to Po-212 alpha energy of 8.78 MeV

  11. Evolution of Peaks E

  12. Po-218 Half-Life - Method - Po-218/Bi-212/Rn-220 etc - Halt supply of Po atoms Po-218 - Integrate for 20s every minute • Assume constant background Po-212 • Po-212 (.3 s halflife) • daughter isotope of Bi-212 • Account for Bi-212 activity

  13. Po-218 Half-Life Fit Accepted Value: 1/2 = 3.10 min Measured Value: 1/2 = 3.14 § 0.33 min

  14. Bi-211 and Bi-212 Half-Lives • Initial Conditions: assume equilibrium dA/dt = dB/dt = dC/dt ... A, B, C are amounts of different isotopes in decay chain A/A = B/B = C/C follows from lab guide eq. 4.1 • Obtain ratios of isotope abundance. • Conduct Bateman analysis • decay under no voltage

  15. Bi-212 Fit to Bateman Equations Po-215 -> Pb-211 -> Bi-211 Accepted Value: 1/2 = 1.01 hr Measured Value: 1/2 = 1.13 § 0.13 hr Bi-211

  16. Geiger-Nuttall Fit

  17. Errors • Half-Lives: statistical • Systematic Corrections: • background subtraction, bateman determinations • Additional Effects: • Lack of actual equilibrium in cans • Peak widening (degrading detectors)

  18. Error- Continued Geiger-Nuttall Relation an approximation. Bismuth points Dependence on mass and atomic numbers, atomic radius Can be fit per decay chain, element, etc.

  19. Conclusions • Geiger-Nuttall Law verified • Quantum mechanics offers explanation for alpha decay.

  20. Po-218 Transient Behavior

  21. Geiger-Nuttall Derivation Yung-Kuo Lim, 2000

  22. Lack of Rise Time in Po-218 10 min

  23. Comparing Parameters • m theoretical: -1.3 • m measured: -3.3

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