Proton and Electron Collision

  • Thread starter hesus
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  • #1
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Hi,

i have the following exercise:
At the HERA acceleratro of DESY in Hamburg electrons and protons were accelerated to E_e=27.5 GeV and E_p = 920GeV and brought to collision.

A)How large is the reaction energy in the centre-of-mass system?
B) What is the velocity of the HERA centre-of-mass System in the lab system?

A) I think the CMS is defined by[tex]\vec{p}[/tex]_e +[tex]\vec{p}[/tex]_p=0, am i right? ([tex]\vec{p}[/tex] is the three-momentum.

Therefore, i can calculated the sum of the two four-momentum.
[tex]s=(p_p+p_e)^2= (E_p+E_e)^2 [/tex]
Reaction energy ist then sqrt(E).

B) How can i solve this?
Thank you.
 

Answers and Replies

  • #2
213
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the centre of mass equation is [tex]p^{2} = (E_{p}+E_{e})^{2} - (p_{p}+p_{e})^{2}[/tex] and you have to keep in mind direction for momenta
 
  • #3
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Well, this was my question.
Isn't the CMS defined by [tex] \vec{p}_p+\vec{p}_e=0[/tex]?
 
  • #4
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no that's not how its defined its [tex]p_{cms} = 0[/tex] but that dosen't mean [tex]p_{e} + p_{p} = 0[/tex] it just means that we transport ourselves in the frame of the collision which is stationary and all the energy of the system is expressed as a mass.
 
  • #5
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Well, if you have just two particles..shouldn't it just be [tex]P_{CMS}=P_E+P_P[/tex]? how do you define P_CMS?
 
  • #6
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[tex]p_{cms}[/tex] is the three momentum in the centre of mass frame and it is always 0. now the invariant quantity in any frame is the rest mass i.e. [tex](m_{cms})^{2} = (m_{lab})^2[/tex]. The rest mass in the lab frame is given by [tex] (m_{lab})^2 = (E_{p}+E_{e})^{2} - (\overline{p}_{p}+\overline{p}_{e})^{2}[/tex] and that is the origin of that formula. In one word [tex]\overline{p}_{cms} \neq \overline{p}_{p}+\overline{p}_{e}[/tex]
 
  • #7
4,239
1
Backing up a little...

Well, this was my question.
Isn't the CMS defined by [tex] \vec{p}_p+\vec{p}_e=0[/tex]?

it might clarify things to know that

[tex] \vec{p}_{p\ lab} +\vec{p}_{e\ lab} \neq 0 \ ,[/tex]

but in the center of mass frame,

[tex] \vec{p}_{p\ cm} +\vec{p}_{e\ cm} =0 \ .[/tex]
 

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