- #1
Sekonda
- 207
- 0
Hey,
My question is with part (c) of the below:
I wanted to check that I had done this write as I struggle to determine the correct invariants for each frame... despite their invariance. So for the lab frame I had
[tex]\frac{\ E_{lab}^{2}}{c^{2}}-p^{2}=(\frac{E}{c}+m_{p}c)^{2}-p^{2}=2Em_{p}+m_{p}^{2}c^{2}=m^{2}c^{2}[/tex]
(Where E is the energy of the cosmic ray proton)
Where the last step is done by using the relativistic energy-momentum relation and the very last term is the invariant mass. The Centre of mass frame has:
[tex]\frac{E_{CoM}^{2}}{c^{2}}=m^{2}c^{2}[/tex]
Finally we attain:
[tex]2Em_{p}+m_{p}^{2}c^{2}=\frac{E_{CoM}^{2}}{c^{2}}\: ,\: E=\frac{\frac{E_{CoM}^{2}}{c^{2}}-m_{p}^{2}c^{2}}{2m_{p}}[/tex]
I think this is correct but I used 7TeV for the centre of mass energy, should I use 14TeV? It says the 7TeV is the centre of mass energy per collision, so I'm guessing I use E(CoM)=7TeV and find E(lab) which was about 2.5*10^4 TeV.
Thanks if anyone can tell me if this is correct!
sk
My question is with part (c) of the below:
I wanted to check that I had done this write as I struggle to determine the correct invariants for each frame... despite their invariance. So for the lab frame I had
[tex]\frac{\ E_{lab}^{2}}{c^{2}}-p^{2}=(\frac{E}{c}+m_{p}c)^{2}-p^{2}=2Em_{p}+m_{p}^{2}c^{2}=m^{2}c^{2}[/tex]
(Where E is the energy of the cosmic ray proton)
Where the last step is done by using the relativistic energy-momentum relation and the very last term is the invariant mass. The Centre of mass frame has:
[tex]\frac{E_{CoM}^{2}}{c^{2}}=m^{2}c^{2}[/tex]
Finally we attain:
[tex]2Em_{p}+m_{p}^{2}c^{2}=\frac{E_{CoM}^{2}}{c^{2}}\: ,\: E=\frac{\frac{E_{CoM}^{2}}{c^{2}}-m_{p}^{2}c^{2}}{2m_{p}}[/tex]
I think this is correct but I used 7TeV for the centre of mass energy, should I use 14TeV? It says the 7TeV is the centre of mass energy per collision, so I'm guessing I use E(CoM)=7TeV and find E(lab) which was about 2.5*10^4 TeV.
Thanks if anyone can tell me if this is correct!
sk