Classical Electrodynamics · Problem 16.12

Radiating Systems, Multipole Fields and Radiation — John David Jackson

Physics — E&M · radiation-damping-classical-models-charged-particles

Problem

A classical model for the description of collision broadening of spectral lines is that the oscillator is interrupted by a collision after oscillating for a time TT so that the coherence of the wave train is lost. (a) Taking the oscillator used in Section 16.7 and assuming that the probability that a collision will occur between time TT and (T+dT)(T + dT) is (νe−νT dT)(\nu e^{-\nu T}\,dT), where ν\nu is the mean collision frequency, show that the averaged spectral distribution is dI(ω)dω=I02πΓ+2ν(ω−ω0)2+(Γ2+ν)2\frac{dI(\omega)}{d\omega} = \frac{I_0}{2\pi}\frac{\Gamma + 2\nu}{(\omega - \omega_0)^2 + \left(\dfrac{\Gamma}{2} + \nu\right)^2} so that the breadth of the line is (2ν+Γ)(2\nu + \Gamma). (b) For the sodium doublet at 5893 \AA\ the oscillator strength is f=0.975f = 0.975, so that the natural width is essentially the classical value, Δλ=1.2×10−4\Delta\lambda = 1.2 \times 10^{-4} \AA. Estimate the Doppler width of the line, assuming the sodium atoms are in thermal equilibrium at a temperature of 500K, and compare it with the natural width. Assuming a collision cross section of 10−1610^{-16} cm2^2, determine the collision breadth of the sodium doublet as a function of the pressure of the sodium vapor. For what pressure is the collision breadth equal to the natural breadth? The Doppler breadth?

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