How do I calculate the beam energy for fixed target experiments?

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SUMMARY

The discussion centers on calculating beam energy and momentum for fixed target experiments within the STAR experiment framework. Key calculations include determining the beam energy and momentum in the laboratory frame, rapidity differences, center-of-mass rapidity, and velocities in both laboratory and center-of-mass frames. The relevant expressions involve the rest mass of protons (0.938272 GeV) and kinetic energies ranging from 10 MeV to 200 GeV. The participant initially struggled with these calculations but later resolved their confusion.

PREREQUISITES
  • Understanding of kinematics in particle physics
  • Familiarity with the concepts of rapidity and center-of-mass energy
  • Knowledge of relativistic energy-momentum relations
  • Basic proficiency in using the book "Ultrarelativistic Heavy-Ion Collisions"
NEXT STEPS
  • Study the relationship between total energy, rest mass, and kinetic energy in relativistic contexts
  • Learn how to calculate rapidity and its significance in particle collisions
  • Explore the derivation of center-of-mass energy (√S) for proton-proton interactions
  • Review examples of fixed target experiments and their energy calculations
USEFUL FOR

Undergraduate students in physics, particularly those involved in experimental particle physics, researchers in high-energy physics, and anyone seeking to understand the calculations involved in fixed target experiments.

colin.mcenroe
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Hello all,

I apologize if this is posted in the incorrect forum. I started working on a summer research project today and it is a part of the STAR experiment. Well, I am a fourth year undergrad (though I am slow by one year) and I am really in over my head here. The professor gave me an another fellow undergrad a text called Ultrarelativistic Heavy-Ion Collisions and set us loose with it. He wants us to use it to learn all about kinematics and such, and I am totally lost because this book seems aimed at graduate level students. He gave us three exercises to work out, but neither my associate nor I were able to complete them. I hope this doesn't violate any rules, but I would like your advice on how to tackle the following problem:

For fixed target experiments, given a kinetic energy of the beam, calculate the beam energy and momentum in the laboratory frame, the rapidity covered in the lab, yproj − ytarg, the center-of-mass rapidity, the velocity of the beam in the laboratory frame, √ S, Ecm, pcm, and the velocity of the beam in the center-of-mass frame. Write the expression used to calculate each quantity. Assume pp interactions with a proton mass of 0.938272 GeV. The velocities should be in c = 1 units so that v ≡ β. The values of Eare 10, 100 and 500 MeV, 1, 2, 10, 14, 60, 160 and 200 GeV.

Now I am stuck on the very first calculation, the beam energy and momentum but I am too embarrassed to ask my professor for help on this stuff because he said it would be really easy. Thanks for your advice!

Colin
 
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You know the rest mass of the proton, How are Total energy, rest mass and Kinetic Energy related?

This is really elementary stuff and should have been covered in your Modern Physics class... I think you might be over thinking things here.
 
Yeah, sorry about that, figured it out the next morning when I went back. :blushing:
 

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