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ADC: Improving fitting

This meeting on 09/11/2016 discusses the limitations of the Landau distribution in energy loss calculation and explores the potential of using the Vavilov distribution as a more general alternative. Parameters like κ, ξ, and Emax are considered to determine when to use each distribution based on material thickness. The fitting with Vavilov distribution shows significant improvements in accuracy, as demonstrated by lower chi^2 values. Implementation of Vavilov distribution may provide better energy resolution compared to the current Landau plots. Future work includes waveform spectra analysis for further enhancements.

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ADC: Improving fitting

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  1. ADC: Improving fitting Meeting 09/11/2016 – Andreas Christou

  2. Limitations of the Landau distribution: • Valid if maximum energy loss in 1 collision >> typical energy loss. In the formal definition of the distribution the maximum energy loss is infinite. • Assumes typical energy loss is >> binding energy of innermost electron. • Assumes particle velocity is constant. • Energy loss computed dependant on step size.

  3. Potential alternative distribution: Vavilov distribution. Seen as a more general form of the Landau distribution • A thick material modelled by the Landau distribution will tend towards the Vavilov distribution. • Issue with Vavilov distribution is it has a complex analytic form, therefore takes a long time to compute results. • A relevant parameter to consider is κ – the significance parameter. • ξ – related to Rutherford scattering cross section, mean energy loss • Emax – maximum allowed energy transfer in a single collision with an atomic electron • For large thicknesses κ tends to be large and vice versa for small thicknesses. • For κ <0.01 the distribution used should be the Landau, 0.01<κ<10 should be Vavilov distribution. • Vavilov distribution does not have same restriction on maximum transferable energy. • May be relevant to attempt to calculate κ and determine if the Vavilov distribution should be used.

  4. ADC fits with higher range • Have fitted the majority of the ADC spectra with both the original fit and the higher step fit for comparison. • The chi^2 of the fits demonstrate a significant improvement. However visibly the fits still do not as closely match the distribution as they should. • Energy resolution =40.294% Energy resolution = 42.769%

  5. To do: Potentially implement the Vavilov distribution and compare to current Landau plots. May also begin working on the waveform spectra. Energy resolution = 13.845% Energy resolution = 14.292%

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