Is the Angle Between Scattered Neutron and Recoiling Proton Always 90 Degrees?

[dRic2]

Homework Statement

Show that when a neutron is scattered from hydrogen, the angle between the laboratory velocities of the scattered neutron and the recoiling proton is always 90°.

Homework Equations

Conservation of momentum
(Conservation of Energy)

The Attempt at a Solution

This isn't a difficult exercise if the collision is assumed to be elastic. In that case straight classical mechanics equations lead to the result. But is this kind of collision always elastic? I mean a neutron hits a proton... It should be elastic after all if you do not go into sub-nuclear physics... If the collision were not to be considered elastic, could I still show the thesis ? I don't think so, but I'm not 100% sure...

Thanks
Ric

 

[mfb]

If the collision is not elastic it is not true any more - but then you produce new particles or the proton or neutron become something else and asking for the angle becomes meaningless.

 

[dRic2]

As I thought, thanks for confirming.

Anyway I know nothing about "sub"-nuclear physics, but I recall that a neutron and a proton are made of quarks. Is it possible that some of the energy of the collision is lost to "excite" a quark above its ground state? (I don't even know if quarks have energy states so... This is just for fun). If such a thing is possible then I would still have the same two particles, but an inelastic scattering may occur.

 

[mfb]

If you excite one of the particles it is an inelastic process and you get different hadrons. They have different names, although that is just a convention. PDG has a list (not a full list, these are just hadrons with up and down quarks only).

 

[dRic2]

Good to know. Thank you! :)