# Coherent neutron scattering

• I
kelly0303
Hello! I am not sure I understand how neutron coherent scattering takes place. The case I am particularly talking about is neutron scattering off a hydrogen molecule. When thinking of Coulomb interaction, I would imagine this as if the incident particle (not a neutron, as the neutron doesn't have electric charge) sees the molecule as a point particle of charge 2e (is this right?). But in the case of the neutron, we have nuclear force (I ignore the weak force here), which is short range (~##10^{-15}m##) while the distance between the 2 protons in the molecule is around ##10^{-10}m##. How can the neutron see both protons at the same time i.e. as a point particle, given that the distance between them is so much bigger than the range of the force acting between the proton and the neutron?

Mentor
Where would an electric charge see anything as a point particle with charge 2e?
How can the neutron see both protons at the same time i.e. as a point particle, given that the distance between them is so much bigger than the range of the force acting between the proton and the neutron?
Consider a modified double slit experiment with light: Have light shining on a black surface with two parallel reflecting narrow strips. You'll get an interference pattern from the strips, even though the two strips are independent of each other.

DEvens
kelly0303
Where would an electric charge see anything as a point particle with charge 2e?
Consider a modified double slit experiment with light: Have light shining on a black surface with two parallel reflecting narrow strips. You'll get an interference pattern from the strips, even though the two strips are independent of each other.
I am not sure I understand what you mean.

Mentor
Interference doesn't need the potentials of the two nuclei to overlap, just like the slits in the double-slit experiment don't overlap. The neutron can be scattered at either nucleus, you add the complex amplitudes, which means you get interference effects.

kelly0303
Interference doesn't need the potentials of the two nuclei to overlap, just like the slits in the double-slit experiment don't overlap. The neutron can be scattered at either nucleus, you add the complex amplitudes, which means you get interference effects.
So do I think of the hydrogen molecule as a single object with which the neutron interacts as a whole?

Mentor
No, it's important that it has two nuclei inside.

DEvens
kelly0303
No, it's important that it has two nuclei inside.
So what is the difference between coherent and incoherent neutron scattering? From what I read online, in coherent scattering, the neutron interacts with the whole object as a whole (for example if it interacts with a crystal as a whole, you get Bragg peaks, as the spacing between crystal latices creates diffraction). In an incoherent scattering, you have interaction with individual constituents of that object (individual crystal nodes for example, so you get some random pattern, as the neutron doesn't see the regular spacing of the crystal anymore). But you are saying basically the opposite i.e. that the neutron in coherent scattering sees every individual object i.e. proton in the case of the molecule. What am I missing here? Thank you!

Mentor
The neutron still interacts with nuclei, but the coherence between these interactions (a fixed phase relation) makes the result differ from many isolated interactions.