Question

Why is Thomson scattering independent of the wavelenght of the incident photon? Is it independent of polarizabilty?

Answer 1

wave of Suppose that a plane wave of monochroma monochromatic EN radiation is incident I on a free on a free particle e of particle large of 8 mass m The partule will experience a force from this feald & will accelerate As it accelerate, it will einet radiation in different directions deepersing the incident beam and for a non-relativistie particle acelerated by a force we can see that C dp = e² letul de 1676 (where lê. w l = luksuo for a perperdutar polariuation perpedewlar to the plane of n 8 ) The (leading order) acceleration i due to the plane wave electric field with polarisation & ware vector to 8 Neulon's low ut v e fo to e y the charge moves much less than one wavelength during a cycle ( true for all but the lightest particles & strongest fields) then lulov = 1 he (V. it) avada Then the ang power flox distribution is not IdP) = Collec de av 327 to bare Goce 18.01 me 2 mc2) I 32 t

This u of the same general form as the Scattering expression we described . Some the result contains 6² it makes Bence to divide out the incident extensity 8 this obtain a differential cross bection that works for all but the strongest fields. We this divide out the time - averaged flow of the Poynting veelor of plare ware! 7 = 6c for 2 Th the incident Hire. dr = ( e ) 10 & 12 dr 4A E mo? If we let the plane ware be incident along the z-amis, let û form an angle o with that anis & peek two polarisation directions is x perpendicular to the ( ² ) plane 8 average over polarisations this this det product geelde nett o n a = ( 2 ) + (1008) This i the Thomson formula for scattering of radiation by free charge. It works for x-rays for electrons On s-rays for protons. It dou not work when the photon momentum & the rewil of the charged particle cannot be neglected. The entegral of this

06AS 10 M Thomson It is cross-section. on is for called the electron + GLY the this tel is a ball dus of that ball; The quantity is parentheid has the units of lenger If the total "mass-energy of the electron we to its charge being concentrated in a ball the would be the close order of the rading of that it is called the classual eletron radius . This numo vrops up quite frequently what it tells is is that ever pt particles have a finite scattering cross-section that appears in this limit to be independent of the warlength of the light scattered