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The Zeeman Effect: Mercury Fine Structure and Determination of e / m - - PowerPoint PPT Presentation
The Zeeman Effect: Mercury Fine Structure and Determination of e / m - - PowerPoint PPT Presentation
The Zeeman Effect: Mercury Fine Structure and Determination of e / m Edwin Ng | 14 March 2012 Theory of the Zeeman Effect Relating FP Spectrum to Energy Governing equation for Fabry-Perot Relate this to the energy of a splitting
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Relating FP Spectrum to Energy
Governing equation for Fabry-Perot Relate this to the energy of a splitting
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Governing Equation for e/m
From theory of the Zeeman effect, Solve for e/m in the Bohr magneton
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Zeeman Splitting: Pictures
Unpolarized σ Polarized π Polarized
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Zeeman Splitting: Interferograms
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Zeeman Splitting: Interferograms
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Zeeman Splitting: Interferograms
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Zeeman Splitting: Interferograms
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Zeeman Splitting: Interferograms
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Zeeman Splitting: Interferograms
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Fitting Procedure: Overview
Fit selected regions of interferogram with a sum
- f Gaussians on top of a background
Interested in nj which give peak positions
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Fitting Procedure: Method I
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Fitting Procedure: Method I Summary
δn is the average of consecutive peaks
Uncertainties on δn:
Statistical uncertainty: Uncertainty of splitting nj – nj-1 Systematic uncertainty: S.D. of all such splittings
divided by square root of (peaks-1)
Δn is the FSR (diff. between two reference peaks) The ratio R = δn/Δn propagates all uncertainties
Finally, extract R/δg (δg = ½ for green)
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Fitting Procedure: Method II
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Fitting Procedure: Method II Summary
δn is splitting of two representative lines Uncertainty on δn is just uncertainty of nj – nj-1 Δn is the FSR (diff. between two reference peaks) Calculate the ratio R = δn/Δn (small uncertainty) δg is now between the two representative lines
δg = 3 for σ-σ green; δg = 14/6 for σ-σ 5770 yellow
Uncertainty on δg: neighboring (unresolved) lines
±½ for green line and ±1/6 for 5770 yellow
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e/m From Green Line
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e/m From Yellow Line (5770 Å)
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Conclusions
Observed splitting of energy degeneracy by
Zeeman effect
Observed polarization of emitted photons Final determination of e/m
(1.813 ± 0.130rand. ± 0.076syst.) x 1010 kG-1s-1 Correct value: 1.759 x 1010 kG-1s-1 Result: (1.031 ± 0.074rand. ± 0.043syst.) e/m
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