Relativistic Decay: Calculating Pion Momentum

In summary, a Sigma^+ decays into a neutron and a pion^+ meson at rest, with a kinetic energy of 92 MeV. Using the equation for relative kinetic energy and the fact that $m_\sigma$ = $m_\pi$ + $m_n$, the momentum of the pion can be calculated without involving gamma factors or velocity.
  • #1
FilipLand
52
3

Homework Statement


A Sigma^+ decays at rest into a neutron and a pion^+ meson, i.e. according to the reaction

$$\Sigma \rightarrow n + \pi$$
The n and π masses are assumed known. The kinetic energy of the π + is measured to be 92 MeV.

Determine the momentum of the pion.

Homework Equations



The Attempt at a Solution



I have tried to use four-momentum and that $m_\sigma$ = $m_\pi$ + $m_n$ but can't just use these relation to solve the problem. I think its really easy once one just know how to do it...
 
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  • #2
Hint: There is a lot of superfluous information.
 
  • #3
Orodruin said:
Hint: There is a lot of superfluous information.

Yes well of course?
I tried solve for v in the formula for rel. Kinetic energy and plug into p=\gamma m*v but don’t get the right answer..
 
  • #4
Hint: Kinetic energy is total energy minus rest energy. There is no need to start involving gamma factors or the velocity.
 

1. What is relativistic decay?

Relativistic decay is a process in which a particle, such as a pion, decays into smaller particles at speeds close to the speed of light. This process is described by the theory of relativity and takes into account the effects of time dilation and length contraction.

2. How is pion momentum calculated in relativistic decay?

The momentum of a pion in relativistic decay is calculated using the equation p = E/c, where p is the momentum, E is the energy, and c is the speed of light. This equation takes into account the relativistic effects of time dilation and length contraction on the momentum of the pion.

3. What is the significance of calculating pion momentum in relativistic decay?

Calculating the pion momentum in relativistic decay allows us to understand the behavior and characteristics of particles at high speeds. It also helps us to make accurate predictions about the decay process and the resulting particles.

4. What factors affect the calculation of pion momentum in relativistic decay?

The calculation of pion momentum in relativistic decay is affected by factors such as the mass of the pion, the speed at which it is traveling, and the energy of the decay process. These factors all contribute to the relativistic effects on the pion's momentum.

5. Can we use classical mechanics to calculate pion momentum in relativistic decay?

No, classical mechanics cannot accurately calculate pion momentum in relativistic decay. This is because classical mechanics does not take into account the relativistic effects of time dilation and length contraction, which are essential in understanding the behavior of particles at high speeds.

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