Pion decays into gamma rays. Find the energy and angle

In summary, the conversation revolves around finding the angle and energies of two gamma rays emitted from a pion that has a rest energy of 135 MeV and is moving at v = 0.97c. The use of conservation of relativistic energy and momentum is mentioned, as well as the formula E = γmc^2 and P = γmv. The calculations for gamma and energy are given, but there is uncertainty about what to do next. It is suggested to move the post to a different subforum for a simpler exercise in special relativity.
  • #1
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Hi all,

I was having trouble with this problem and hoping that someone could help me with it.

A pion has a rest energy of 135 MeV. It decays into two gamma rays, bursts of electro magnetic radiation that travel at the speed of light. A pion moving through the laboratory at v = 0.97c decays into two gamma rays of equal energies, making equal angles θ with the direction of motion. Find the angle θ and the energies of the two gamma rays. (Hint: gamma rays are electromagnetic radiation with E = pc.)

I am pretty sure I will be using conservation of relativistic energy and momentum but I am still confused.

I know that E=γmc^2 and P=γmv

I find gamma 1/sqrt(1-(0.97c)^2/c^2)≈ 4.11

I know that mc^2= 135MeV

With this I get E=(4.11)(135MeV)≈ 555.32MeV

For P I get (4.11)m(0.97c)=3.99mc≈ 538.66MeV/c

I am a bit unsure what to do next with this.
 
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  • #2
This post should be moved to "Special & General Relativity" subforum. It's a simple exercise in special relativity, and doesn't really require knowledge of particle physics.
 
  • #3
Boost yourself into the pion's rest frame, then back again afterwards?
 

1. What is a pion decay and how does it produce gamma rays?

Pion decay is a process in which a charged pion particle transforms into other particles, including gamma rays. This occurs through the weak interaction, where one of the quarks inside the pion transforms into a different type of quark, emitting a W boson. The W boson then decays into an electron and an electron antineutrino, and the antineutrino interacts with a proton to produce a gamma ray.

2. What factors affect the energy of the gamma rays produced in pion decays?

The energy of the gamma rays produced in pion decays is affected by the mass of the pion, the angle at which it decays, and the energy of the W boson that is produced during the decay process. Additionally, the energy of the gamma ray can also be affected by any interactions or collisions that occur between the gamma ray and other particles in the surrounding environment.

3. How is the energy of gamma rays from pion decays measured?

The energy of gamma rays from pion decays is measured using detectors such as scintillators or calorimeters. These detectors can detect the energy and direction of the gamma ray as it passes through, allowing scientists to determine the energy of the gamma ray. Additionally, the energy can also be calculated by analyzing the energy and momentum of the other particles produced in the decay process.

4. Can the angle of the gamma rays from pion decays be controlled or manipulated?

No, the angle at which gamma rays are produced in pion decays is determined by the conservation of momentum and energy. It is not possible to manipulate or control the angle of the gamma rays produced in this process.

5. Are there any applications for studying pion decays into gamma rays?

Yes, the study of pion decays into gamma rays has several applications in various fields of research. For example, it can be used to study the properties of the weak interaction and test theories in particle physics. It can also be used in medical imaging techniques and in the development of new radiation detection methods.

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