Solid Angle Rutherford Scattering

In summary, the equation for solid angle for a Rutherford scattering detector is given by d\Omega =2\pi sin\phi d\phi, where A is the detector window area and D is the distance to the detector. This can be integrated to get \Omega =\frac{2\pi A}{D}\int sin\phi d\phi, taking into consideration the correct bounds for ϕ. The negative value obtained from the integral of sine is resolved when using the correct bounds.
  • #1
Purple Baron
9
0

Homework Statement


derive an equation for the solid angle for a Rutherford scattering detector given a detcor window area of [itex]A[/itex] and a distance to the detector of [itex]D[/itex] for some scattering angle [itex]\phi[/itex] given that [itex]d\Omega =2\pi sin\phi d\phi[/itex]

Homework Equations


[itex]d\Omega =2\pi sin\phi d\phi[/itex]
[itex]A=Dd\phi [/itex]

The Attempt at a Solution


integrating [itex]d\Omega =2\pi sin\phi d\phi[/itex] to get solid angle gives [itex]\Omega =\frac{2\pi A}{D}\int sin\phi d\phi[/itex] howver this gives a negative value due to the integral of sine and shouldn't soild angle be positive? Is this correct or am i missing a step? Thank You
 
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  • #2
You sure this gives a negative value ? Can you show how you get it ? Bounds, primitive ?
 
  • #3
Purple Baron said:
A=Ddϕ
That's dimensionally incorrect. You have an area on the left and a distance on the right. And the dϕ looks wrong.
Shouldn't it be ##A = D^2d\Omega##?
As BvU posted, your problem with the negative sign will resolve itself when you put in the bounds on ϕ.
 

Related to Solid Angle Rutherford Scattering

What is solid angle in Rutherford scattering?

Solid angle is a measure of the amount of space covered by a particular object or region in three-dimensional space. In Rutherford scattering, it refers to the angle at which a charged particle is deflected after passing through a target material.

How is solid angle related to Rutherford scattering cross section?

The Rutherford scattering cross section is proportional to the solid angle of deflection. This means that as the solid angle increases, the cross section also increases, indicating a higher likelihood of the particle being deflected.

What is the significance of solid angle in the study of Rutherford scattering?

Solid angle is important in Rutherford scattering because it helps us understand the probability of a charged particle being deflected at a particular angle. By calculating the solid angle, we can determine the likelihood of a particle being deflected in a certain direction, which is crucial in understanding the structure of atoms and nuclei.

How is solid angle calculated in Rutherford scattering experiments?

In Rutherford scattering experiments, solid angle is typically calculated using the formula Ω = 2π(1-cosθ), where θ is the angle of deflection. This formula takes into account the spherical nature of solid angle and is commonly used in calculations involving Rutherford scattering.

Can solid angle be measured in other types of scattering experiments?

Yes, solid angle can be measured in other types of scattering experiments, such as Compton scattering and Thomson scattering. In these cases, the formula for calculating solid angle may differ depending on the specific experiment, but the concept remains the same.

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