# Probability of scattering is uniform in all directions

• venomxx
In summary, the probability of scattering refers to the likelihood of particles being scattered in different directions when they interact with each other. It is important to understand the uniformity of scattering in all directions for various fields such as physics, chemistry, and engineering. The probability of scattering is determined through experiments and mathematical models, and can be affected by factors such as particle properties, medium, and external influences. The uniformity of scattering is also related to principles of energy and momentum conservation in physics.
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

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!

## 1. What is the "probability of scattering is uniform in all directions"?

The probability of scattering refers to the likelihood that particles will be scattered in different directions when they interact with each other. When it is said that the probability of scattering is uniform in all directions, it means that the likelihood of particles being scattered in any particular direction is equal.

## 2. Why is it important to understand the uniformity of scattering in all directions?

Understanding the uniformity of scattering in all directions is crucial in various fields such as physics, chemistry, and engineering. This knowledge helps scientists predict the behavior of particles in different environments and design experiments or technologies accordingly.

## 3. How is the probability of scattering determined to be uniform in all directions?

The probability of scattering is determined by conducting experiments and analyzing the data. Scientists use mathematical models and theories, such as the scattering cross section formula, to calculate the probability of scattering in different directions and determine if it is uniform.

## 4. Are there any factors that can affect the uniformity of scattering in all directions?

Yes, there are various factors that can affect the uniformity of scattering in all directions. These include the properties of the particles, the medium in which they are scattered, and the energy of the particles. Other external factors, such as magnetic or electric fields, can also influence scattering behavior.

## 5. How does the uniformity of scattering in all directions relate to other principles in physics?

The uniformity of scattering in all directions is closely related to principles such as conservation of energy and momentum. These principles dictate that the total energy and momentum of a system remain constant during scattering interactions, which can affect the probability of particles being scattered in different directions.

Replies
1
Views
1K
Replies
1
Views
2K
Replies
1
Views
1K
Replies
5
Views
1K
Replies
0
Views
849
Replies
1
Views
2K
Replies
1
Views
1K
Replies
8
Views
2K
• Optics
Replies
6
Views
3K