Centre of mass energy

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1. I have to work out the centre of mass energy of a beam collider of e-e+ each beam having an energy of 45.6Gev, That was no problem, i used the formula below and got The centre of mass = (2E)^2 = 91.2Gev. My problem arises when i apply this to a beam hitting a fixed target. The question states " What energy beam is required to get the same centre of mass"

The same formula should apply and the solution iv attempted is below. I end up having to know the rest mass of the target which i wasnt given. Im working in natural units where c=1




2. Two beams ( E, Px, 0, 0 ) (E, -Px, 0, 0)
Beam and target ( E, Px, 0, 0 ) (Mt, 0, 0, 0)

Formula used -> Ecm^2 = (∑E)^2 - (∑p)^2




3. Two beams

Ecm^2 = (2E)^2 = (91.2)^2 Therefore Ecm = 91.2Gev

Fixed targert

Ecm = (E + Mt)^2 - P^2 = 2Mt(E+Mt)

Therefore = Ecm^2 = 2Mt(E+Mt)



Any help would be appriciated, cheers.
 

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