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59:21 Valence EELS, High Energy Resolution Valence EELS, High Energy Resolution	Valence EELS, High Energy Resolution 2017 PARADIM SUMMER SCHOOL Low loss EELS David Muller optical spectroscopy formal sciences concepts in physics silicon rich silicon dioxide chemical elements band gap scattering electron density lowest energy feature reducing agents valence electrons quick rule pyrotechnic fuels electron microscope waveguide mode nuclear physics percent radius electron real trouble dielectric boundary conditions nice big factorial and binomial topics tightly bound electric field spatial resolution single scattering optics sample thickness interface plasma nano particles optical gap direct bandgap phosphates particle physics fluid dynamics high energy electron atomic physics dielectric responses biology and pharmacology of chemical elements liquid cell multiple scattering electron beam energy resolution tiny signal single particle transition cherenkov radiation electron gas free electron gas optical transition energy loss energy lost characteristic angle free electronic energy filter low energy charge oscillations valence region surface plasma toxicology free path silicon oxide optical spectra bulk material exit haitian call auspex fourier analysis quantum mechanics big background image charge electrostatics lastic scattering nice thing interesting standing wave bessel function boundary conditions ion image single particle standing wave modes funny feature electron states scattering event direct gap good free electron physical quantities energy loss function vector calculus dietary minerals absorption and radiative transfer (optics) electrical engineering thick sample field lines length scale electronics terminology electrodynamics phoria transform radiation sensitive caption complete hof plasma frequency log scale experimental particle physics hof epsilon semiconductor materials higher energy high frequency atomic resolution interface mode good news harmonic oscillator special relativity dielectric function diverges logarithmically shine light couple 100 volt t.m. incredibly complicated bad news electromagnetism energy range cherenkov modes 100 volt spherical modes linear operators in calculus chemistry bulk plasma From James Overhiser 87 plays