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VMI images – fitting

VMI images – fitting. Helgi Rafn Hróðmarsson. The purpose of this fitting procedure is to check whether the assumption that the angular distribution data can be fitted with an expression of both the two-photon excitation transition as well as the ionization pathway.

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VMI images – fitting

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  1. VMI images –fitting Helgi Rafn Hróðmarsson

  2. The purpose of this fitting procedure is to check whether the assumption that the angular distribution data can be fitted with an expression of both the two-photon excitation transition as well as the ionization pathway. (seeslides9 – 21 in https://notendur.hi.is/~agust/rannsoknir/Crete/PPT-131219.pptx )

  3. -for redcoloured parameters unknown => deriveb(ph) i.e. somethinglike: (1) + A ~ Experiment ph f b(ph) f i 0 180 q

  4. Previous fit functional form usedbyDimitrisZaouris was I(q)= A(1 + b2*(1.5*cos2(q)-0.5) The new fit equation (named „Ice fit“) is basedon a two-stepexcitationscheme as formulated in slides 9 – 21 in https://notendur.hi.is/~agust/rannsoknir/Crete/PPT-131219.pptx : • I(q)=A*(1+b2(f)*(1.5*cos2(q)-0.5))*(1+b2(ph) *(1.5*cos2(q)-0.5)) • where • A is a normalizing constant. • b2(f) = -0.62215, obtained from REMPI data. (seeslide 17 in https://notendur.hi.is/~agust/rannsoknir/Crete/PPT-131219.pptx) • b2(ph) is the “beta-factor” for the ionization pathway.

  5. E(v=0,J=1) – peak A – Ice fit 1

  6. E(v=0,J=1) – peak B – Ice fit 1

  7. E(v=0,J=2) – peak A – Ice Fit 1

  8. E(v=0,J=2) – peak B – Ice fit 1

  9. E(v=0,J=3) – peak A – Ice fit 1

  10. E(v=0,J=3) – peak B – Ice fit 1

  11. E(v=0,J=4) – peak A – Ice fit 1

  12. E(v=0,J=4) – peak B – Ice fit 1

  13. E(v=0,J=5) – peak A – Ice fit 1

  14. E(v=0,J=5) – peak B – Ice fit 1

  15. E(v=0,J=6) – peak A – Ice fit 1

  16. E(v=0,J=5) – peak B – Ice fit 1

  17. E(v=0,J=7) – peak A – Ice fit 1

  18. E(v=0,J=7) – peak B – Ice fit 1

  19. E(v=0,J=8) – peak A – Ice fit 1

  20. E(v=0,J=8) – peak B – Ice fit 1

  21. E(v=0,J=9) – peak A- Ice fit 1

  22. E(v=0,J=9) – peak B- Ice fit 1

  23. The Greek fit

  24. The Icelandic fit b2(ph)

  25. Peak A angular distributions„Ice fit“:

  26. Peak A – Intensity contour

  27. Peak B angular distributions

  28. Peak B – Intensity contour

  29. Now to test another fit equation namely... • I(q)=A*(1+b2(f)*P2(cos(q))+b4(f)*P4(cos(q)))*(1+b2(ph)*P2(cos(q))+b4(ph)*P4(cos(q))) • I(q)=A*(1 + b2(f) * (1.5 * cos2(q) - 0.5) + b4(f) * (1/8) * (35 * cos4(q) – 30 * cos2(q) + 3)) * (1 + b2(ph) * (1.5 * cos2(q) - 0.5) + b4(ph) * (1/8) * (35 * cos4(q) – 30 * cos2(q) + 3))) • ...to try to get a better fit to the curves. • Let’s try this fit of peak A and peak B. • Again, as before, we keep b2(ph) constant and we’ll be observant whether the b2(f) constant stays about the same or it changes dramatically.

  30. J=1 – Peak A

  31. And comparison with theprevious “Ice fit”.

  32. E(v=0,J=1) – peak A – Ice fit 1

  33. 1) We get a better fit than before with more points from the edges of the scattering. • 2) The b2(f) constantchanges from 1.15 to 1.28, i.e. not a gargantuan increase. • 3) Wealso get values for the b4(f) constant as well as b4(ph) constant.

  34. J=1 – Peak B

  35. J=2 – Peak A

  36. J=2 – Peak B

  37. J=3 – Peak A

  38. J=3 – Peak B

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