homework3

# A calculate the natural and doppler broadening of the

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Unformatted text preview: cal for moderate Galactic latitude) in our own Galaxy. You may assume the gas to have a turbulent velocity dispersion σv = 20 km/s and negligible thermal velocities. (a) Calculate the natural and Doppler broadening of the Lyman ­α line. (b) Make a plot of the optical depth τν due to absorption in the Lyman ­α line and the observed spectrum Sν in the relevant part of the spectrum. (c) How wide is the range of frequencies Δν that is more than 50% absorbed? What is Δν/νLyα? #3. Resonances in the Electric Susceptibility. [14 points] Consider a material with a number density n of oscillators. Each oscillator is taken to be an electron with charge −e, mass me, and sits in a potential of spring 2 constant m e ω 0 . Additionally it feels a damping force Fdamp = −meγv (of unspecified origin), with γ<<ω0. (a) Derive the electric susceptibility and dielectric constant of the material as a € function of frequency. (b) Taking Im χ(ω) from (a), use the Kramers ­Kronig relations to derive Re χ(ω). Show that this agrees with your result from (a)....
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