Probability of scattering is uniform in all directions

[venomxx]

Homework Statement

Its not really a question, more something I am 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 there's 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

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 I am 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

 

[Jhero]

Thank you for bringing up this question. I can understand your confusion regarding the probability being zero in the book's answer. However, I believe that the book is referring to the overall probability of the interaction, not just the probability of a single beam hitting the detector.

In the scattering experiment, the overall probability of the interaction is calculated by taking the square of the sum of all possible amplitudes. In this case, since there are only two possible amplitudes (f and g), the overall probability would be (f + g)^2. And since the amplitudes for spin flip (g) are interfering with a minus, the overall probability would be (f - g)^2, which is equal to 0.

Regarding your question about isotropy, the experiment is considered isotropic when the probability of scattering is uniform in all directions. This means that regardless of the angle at which the particles are scattered, the probability of the interaction occurring is the same. In this case, it is not related to the number of detectors, but rather the symmetry of the experiment.

I hope this helps to clarify your confusion. Keep up the good work in your studies!