Project: Photoemission using synchrotron radiation at MAX Lab

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# Project: Photoemission using synchrotron radiation at MAX Lab - PowerPoint PPT Presentation

Project: Photoemission using synchrotron radiation at MAX Lab. A virtual lab project. Goals. Learn about photoelectron spectra Extract the bond distance for different states of CO+ from PES (Franck-Condon analysis) Extract the life time of valence and core electronic states

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### Project: Photoemission using synchrotron radiation at MAX Lab

A virtual lab project

Goals
• Extract the bond distance for different states of CO+ from PES (Franck-Condon analysis)
• Extract the life time of valence and core electronic states
• Learn about fitting in MATLAB
Photoelectron spectroscopy
• Ionization
• Electron kinetic energy is measured
• Data presented on a binding-energy scale
• Electronic states
• Vibrational states
Vibrational progressions
• Real-life spectra: anharmonic model

Harmonic term

Anharmonic term

Line shapes
• Lorentzian
• The quantum mechanical result using Fermi’s Golden Rule for photoionization produces a similar equation, also described using a Lorentzian distribution about the nominal energy, 0. The width of the peak at half of the peak maximum (FWHM) is defined as 
Gaussian
• Photon BW
• Electron analyzer resol
• The half width of the ‘Gaussian’ function at a value of 1/e is standard deviation), the FWHM is then 2.354 
Data treatment
• Fit the data to a function

Peak energies (vibrational progression)

Line shapes:

• Lorentzian natural line shape
• Gaussian profile ‘measurement’
• Mathematically speaking
• Measurement: convolution of Gauss + Lorentz
Pre-lab exercise
• Plot Lorentzian
• Plot Gaussian profiles
• Convolute these profiles
• Study the result…
Analysis
• Develop a model function for fit profile
• Line shape: convolution
• Peak energies: vibrational progression
• Least-squares fit: minimize difference between model and measurement, adjust model parameters
• Use peak intensities in Franck-Condon analysis to get bond-distance change
Least-squares fit
• Funct(E,,exe,n,,I1..In)
• N,  are known
• E, ,I1..In we can guess (initial)
• MATLAB

optimization = fminsearch('difpart1',initial,options);

fitdata2 = ourfit(modelfunct,datax,datay);

d=conv(gaussian,spectrum1);

initial = [14.34,0.27,12500,680,0.010,0.02];