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I'm trying to solve the following problem for a course in radiation physics.

A thin ray of intensity $I_0$ and energy $E_0$ impacts in a material. What is the intensity and the energy of the photons after having travelled a distance d?

I know that the intensity decreases as a negative exponential, but I was wondering how to calculate the change in the energy.

The only process relevant for this I think that must be incoherent scattering (because in both pair production and photoelectric effect the photon is absorbed) so I thought about calculating the energy transferred by the photons and subtracting it from the initial energy.

I also thought about calculating the energy transfer coefficient but I think that I lack information to do it this way.

How can I calculate the energy after having travelled a distance d?

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Typically, this sort of problem is solved by an MCNP simulation

If you assume that all the photons that collide with an atom are absorbed, then the energy is jsut E_0.

With charged particles, there is the phenomenon of energy strangling.

other then that, I can think of the following: You might be able to some how average the compton-scattering equation to get some sort of mean energy for photons that undergo compton scattering, but you'd need to know material information. There's also the klien-neshina formula that you might be able to parameterize your answer in terms of.

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  • $\begingroup$ Looking at this question again, your professor probably wants the answer "The intensity is reduced by a factor mu*dx and the energy stays the same." It's a trivial answer but correct to a first order. $\endgroup$ – Terry Price Jul 9 '18 at 17:48

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