# Momentum exchange during diffraction

• I
• Swamp Thing
In summary, according to this theory, the change of momentum associated with direction change during a diffraction event is due to quantized momentum transfer to the diffracting object. This theory also applies to diffraction during transmission through a single slit or a double slit.

#### Swamp Thing

I just learned that there is a well established theoretical picture that explains the change of momentum associated with direction change during a diffraction event, in terms of quantized momentum transfer to the diffracting object. For example, https://en.wikipedia.org/wiki/Duane's_hypothesis

This picture is also supposed to be applicable to diffraction during transmission through a single slit or a double slit.

I am just wondering what kind of forces actually mediate the exchange, e.g. in the cases of electron diffraction and photon diffraction. I found hints suggesting that this could be related to phonons within the screen material, but - if so - wouldn't the diffraction then be a function of the solid state physics happening inside the screen?

This leads to my actual question : is it reasonable that the force that "mediates" the deflection and momentum exchange is a kind of Casimir effect occurring within the slit volume, where certain EM modes are suppressed by geometry?

Also, what force would mediate the momentum transfer when a photon is diffracted through a slit?

what kind of forces actually mediate the exchange
You can work it out: there are only four fundamental forces ... list them and see which makes sense. Consider: how do photons normally interact with matter?
The specifics of the interaction are very complicated - it's a bit like how a collision is very complicated but you can do reliable physics on the bits that fly away by using conservation of momentum if we use a "before" and "after" approach.

is it reasonable that the force that "mediates" the deflection and momentum exchange is a kind of Casimir effect occurring within the slit volume, where certain EM modes are suppressed by geometry?
... only by analogy. The possible paths between source and detector are open - the rest supressed. This is not a casimir effect though, just normal absorbtion etc.

Also, what force would mediate the momentum transfer when a photon is diffracted through a slit?
You can work it out: you have a choice of four. List them: which one applies.

http://iopscience.iop.org/article/10.1088/0143-0807/23/6/303/meta
... gives you an idea about what sort of momentum exchange would be present.

Make sure you see the followup though:
http://iopscience.iop.org/article/10.1088/0143-0807/32/1/010/pdf

... full text also available through arxiv.

And just in case:
http://www.vega.org.uk/video/subseries/8
... accessible description of photon-matter interactions.

My understanding is that the phonon model for crystal diffraction constrains the transfer of momentum as energy must also be conserved. It is the lattice spacing that is important.

Thanks. I'll look at those references.