# Scattering of a Neutron and Proton

• physnut_05
In summary, the conservation of energy and momentum equations state that energy is conserved and momentum is not lost. The angle between the scattered particles is always 90 degrees.
physnut_05
I have a problem here that has me a bit suck:

In scattering between incident neutrons and target protons at rest, show that the angle between the two scattered particles is always 90 degrees.

I have set up the conservation of energy and momentum equations and have:

Energy: Tn=T'n+Tp
Momentum: pn=p'n*cos(X)+pp*cos(Y) AND p'n*sin(X)=pp*sin(Y)

Here X and Y are the angles between the scattered neutron and proton with respect to the horizontal.

I've manipulated these around, found an expression for cos(X), but that doesn't seem to get me much of anywhere. A bump in the correct direction would be appreciated.

This is a classic cute fact about kinematics. You can verify it by making one coin collide with another on a tabletop. Note that it does not claim that the neutron is always scattered at 90 degrees relative to its initial direction of motion; it claims that the final velocity vector of the neutron is at 90 degrees with respect to the final velocity vector of the proton. For that reason, it's not particularly helpful to solve for the angle you're notating X, because what you're really trying to prove is that |X-Y|=90.

The whole thing comes out much more nicely if you do it without imposing a coordinate system at all. Just define notation for three vectors, and write both conservation laws purely in terms of those vectors, with no operations other than vector addition and vector dot products. Use the graphical interpretation of the vector addition as a triangle formed by the vectors.

The reason this problem can be stated in terms of neutron-proton scattering is that the masses are very nearly equal, and there are no internal degrees of freedom that can suck up any energy (assuming that the beam energy is fairly low). It would fail, for example, if you were scattering neutrons off of gold nuclei, since the gold nucleus could be left in an excited state.

Last edited:
Thanks for the help, it does make a lot more sense doing it that way.

## What is the scattering of a neutron and proton?

The scattering of a neutron and proton refers to the interaction between these two particles, where they collide and change direction or momentum. This phenomenon can be observed in various experiments, such as particle accelerators.

## Why do neutrons and protons scatter?

Neutrons and protons scatter due to the strong nuclear force, which is the force that binds these particles together in the nucleus of an atom. When they come close enough to each other, this force causes them to repel or deflect, resulting in scattering.

## What are the factors that affect the scattering of neutrons and protons?

The scattering of neutrons and protons can be affected by various factors such as the energy and angle of the incident particles, the distance between them, and the properties of the target material, such as its density and composition.

## How is the scattering of neutrons and protons studied?

The scattering of neutrons and protons is studied through experiments using particle accelerators or neutron sources. By measuring the energy and angle of the scattered particles, scientists can gather information about the properties of the particles and the forces that govern their interactions.

## What are the applications of studying the scattering of neutrons and protons?

Studying the scattering of neutrons and protons has various applications in nuclear physics, materials science, and other fields. For example, it can help us understand the structure of nuclei, investigate the properties of materials, and develop new technologies such as neutron imaging and neutron therapy for cancer treatment.

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