How to calculate thickness of the wall in a wire chamber

In summary, the question is asking for the thickness of a wall in a wire chamber if 68% of particles are scattered less than the wire resolution. To find this, the formula for deflection angle is used, with given values for momentum, wire resolution, distance from wall to wire, radiation length of wall material, mass of charged particle, and charge. The goal is to find x, but it is unclear how the 120 microns and 68% play a role. A possible approach is to use a gaussian distribution table to find the angle that corresponds to 68% of particles being below the resolution, and then use this angle to find x/x0.
  • #1
Kyrios
28
0

Homework Statement


This is a question on multiple coulomb scattering in a wire chamber

momentum p = 500MeV/c
wire resolution = 120 microns
distance from wall to wire = 0.01m
radiation length of wall material X_0 = 2E-3 m
mass of charged particle [itex]m_{\pi} [/itex] = 139.6 MeV/c^2
charge z = 1

How thick is the wall if 68% of the particles are scattered less than the wire resolution?

Homework Equations



[tex] \theta = \frac{13.6}{\beta p} z \sqrt{\frac{x}{x_0}} [/tex]

The Attempt at a Solution



What I am trying to find is x, but am uncertain of where exactly the 120 microns and 68% comes in.
I looked up a distribution table and for z=0.68, the area below z = 0.7517. (I think this is what you have to do for 68% scatter less than the resolution?)
The gaussian distribution forms a triangle to work out theta, with the side opposite to the angle. I assume the mean would be zero, so would this side just be 0.7517x120microns?
 
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  • #2
I don't understand your attempt.

The formula gives the average deflection angle.

I would first see which angle gives the "maximal" scattering (a deviation by one times the wire resolution within the wire chamber). Then you can find x/x0 to have 68% of the particles below this angle.
 

1. How is the thickness of the wall in a wire chamber calculated?

The thickness of the wall in a wire chamber is typically calculated using the formula: t = p * V / (E * N), where t is the thickness of the wall, p is the gas pressure inside the chamber, V is the average particle velocity, E is the electric field strength, and N is the number of electrons per unit length created by the gas ionization.

2. What is the purpose of calculating the thickness of the wall in a wire chamber?

The thickness of the wall in a wire chamber is an important factor in determining the efficiency and performance of the chamber. It helps to ensure that the chamber is capable of accurately detecting and measuring particles passing through it.

3. How does the gas pressure affect the thickness of the wall in a wire chamber?

The gas pressure inside the chamber directly affects the thickness of the wall. As the pressure increases, the thickness of the wall must also increase in order to maintain the same electric field strength and number of electrons per unit length. This is because a higher pressure results in more gas molecules, which in turn leads to a higher chance of particle interactions and ionization.

4. Can the thickness of the wall in a wire chamber be adjusted?

Yes, the thickness of the wall in a wire chamber can be adjusted by changing the gas pressure, electric field strength, or number of electrons per unit length. However, these adjustments must be made carefully to ensure the chamber maintains its efficiency and accuracy.

5. Are there any other factors that need to be considered when calculating the thickness of the wall in a wire chamber?

Yes, in addition to the gas pressure, electric field strength, and number of electrons per unit length, other factors such as the type and composition of the gas, the size and shape of the chamber, and the type of particles being detected should also be taken into account when calculating the thickness of the wall in a wire chamber.

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