# UMD ASTR 601 - Line Broadening (4 pages)

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## Line Broadening

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- Pages:
- 4
- School:
- University of Maryland, College Park
- Course:
- Astr 601 - Radiative Processes

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Line Broadening Initial questions What processes can change the profile of an atomic line What about in the practical case where we have a finite signal to noise Spectral lines are not arbitrarily sharp There are a variety of mechanisms that give them finite width and some of those mechanisms contain significant information We ll consider a few of these in turn then have a detailed discussion about how line shapes and profiles have given information about rapidly rotating accretion disks around black holes First Ask class why can t a spectral line be arbitrarily sharp Ultimately it comes from the uncertainty principle in the form E t h 2 If a line were arbitrarily sharp this would imply perfect knowledge of E which can t happen unless the atom spends an infinite amount of time before decaying into a lower state If instead the decay time is finite say decay then the approximate width of the line is E h decay This is called natural broadening and represents the limit on how sharp a line can be If one has an atom in state n and the spontaneous decay rate to a lower energy state n is Ann then the spontaneous decay proceeds at a rate X Ann 1 n Ask class Is this the only contribution to the decay No there are also induced decay processes stimulated emission These should be added to the spontaneous rates The energy decays at a rate exp t The energy is proportional to the square of the coefficient of the wave function so that coefficient decays at a rate exp t 2 The decaying sinusoid that is obtained for the electric field then gives a line profile of the Lorentz form as we saw in the semiclassical picture 4 2 0 2 4 2 2 Ask class from the above discussion can they name a state that will have zero breadth because it can persist indefinitely The ground state is stable so its energy can be defined with in principle arbitrary sharpness If instead the level n is itself an excited level that energy level has breadth as well Then approximately the effective width of the transition

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