# Probability of scattering is uniform in all directions

1. Dec 7, 2009

### venomxx

1. The problem statement, all variables and given/known data
Its not really a question, more something im confused about i saw in the book.

If you have two beams of neutrons colliding in a scattering experiment, the amplitude of a particle in the incident beam hitting the detector is f, if theres a spin flip its g.

2. Equations :
I was told an experiment like this is isotropic so the probability of scattering is uniform in all directions...

The square of the amplitude gives the probability

Fermions therefore the amplitudes interfer with a minus

3. The attempt at a solution

My answer said that beam 1 had an amplitude ¦f(a) - f(pi-a)¦^2 + ¦g(a) - g(pi - a)¦^2

Where i took the probability of beam 1 or 2 hitting the detector, and the probability of beam 1 or two having a spin flip and hitting the detector. Where (a) is the scattering angle..

The answer given in the book says that its ¦f - f¦^2 + ¦g - g¦^2 = 0

How is the probability zero? Is my thinking completely wrong?

And lastly what im most confuesed about, how can you tell if the interaction is isotropic? Is it if there is one detector it is isotropic and if you have 2 detectors for the two beams it is not?

Cheers in advance...any opinion on this would be appriciated