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Error Analysis

Error Analysis. Analytical 02 October 2013. Penfold-Leiss Cross Section Unfolding. Measure Yields at: where, The solution can be written in two forms:. Or, Matrix form:. Statistical Errors. Statistical Error Propagation (1).

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Error Analysis

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  1. Error Analysis Analytical 02 October 2013

  2. Penfold-Leiss Cross Section Unfolding • Measure Yields at: where, • The solution can be written in two forms:

  3. Or, Matrix form:

  4. Statistical Errors

  5. Statistical Error Propagation (1) • Note: • With: In case of background Subtraction • Then:

  6. Where:

  7. Statistical Error Propagation (2) Although, For mono-chromatic beam

  8. Statistical Error Propagation (Wrong) • Then: Wrong • This is equivalent to: Wrong

  9. Absolute Systematic Errors

  10. Systematic Error Propagation (1) • For absolute beam energy uncertainty of δE (= 0.1%): This is the cross section dependence on energy • Accounted for dNij due to energy error when calculating dyi

  11. With: • Then:

  12. Where:

  13. Systematic Error Propagation (2)

  14. Other Absolute Systematic Errors Simulation • Then:

  15. Results Radiator Thickness = 0.02 mm Bubble Chamber Thickness = 3.0 cm Number of 16O nuclei = 3.474e22 /cm2 Background subtraction of 18O(γ,α)14C 17O(γ,n)16O: Still to do

  16. 12C(α, γ)16O S-Factor • Statistical Error: dominated by background subtraction from18O(γ,α)14C (depletion = 5,000) • Systematic Error: dominated by absolute beam energy (δE= 0.1%) SE1(300 keV) = 74±21 keV b

  17. Relative Systematic Errors

  18. Systematic Error Propagation (1) • For absolute beam energy uncertainty of δE (= 0.1%) and zero relative beam energy uncertainty: This is the cross section dependence on energy • Accounted for dNij due to energy error when calculating dyi

  19. With: • Then:

  20. Where: Note: Correlation Coefficient =1

  21. Systematic Error Propagation (2)

  22. Other Relative Systematic Errors Simulation • Then:

  23. Relative Systematic Errors Results Note: Relative systematic errors do not get amplified in PL Unfolding

  24. 12C(α, γ)16O S-Factor • Statistical Error: dominated by background subtraction from18O(γ,α)14C (depletion = 5,000) • Relative Systematic Errors SE1(300 keV) = 74±21 keV b

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