- #1
Kyrios
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Homework Statement
I am trying to find the minimum energy for a proton beam to make pions that have 100Gev of momentum. The proton beam is hitting a fixed target.
Homework Equations
p + n -> n + n + ##π^{+}##
The Attempt at a Solution
In the centre of mass frame, there is zero initial momentum. But the pion has 100GeV of momentum on the other side, so I gave the neutrons the same amount in the opposite direction to cancel it out.
Then I used E=2m##c^2## for the initial energy and got the relativistic mass. (I wasn't sure about this)
The velocity was very close to the speed of light, and I then used relativistic velocity addition to find gamma. (this is for the proton colliding with the neutron)
I had gamma ~ 9000
In the end I had an answer of ##E_{proton beam}## ~ 8.5 TeV
Is this the right sort of value to be looking at? If necessary I can write up all my working.