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A Proton, [tex]m_{1}[/tex] with Kinetic energy T = 200MeV strikes a stationary proton in the lab frame.

p + p -> p + p + X

what is the maximum mass of X, which can be produced.

I think I need to make use of [tex]E^2 - P^2 c^2[/tex] is invariant.

and

In S: [tex]E = (m_{1} + m_{0})c^2 , p = p_{1}[/tex]

In S ' :

[tex]E^2 - P^2 c^2 = E^2_{1}+ 2m_{0}E_{1}c^2 + m^2_{0}c^4 -T^2 (1) where E_{1} = T + m_{0}c^2[/tex]

I'm not sure what is happening in the centre of mass frame, I thought that the particle would have maximum mass when there was zero K.E i.e [tex]E' = (2m_{0} + m_{x})c^2, p' = 0[/tex] in the lab frame but I got lost when I tried to equate this with (1).

p + p -> p + p + X

what is the maximum mass of X, which can be produced.

I think I need to make use of [tex]E^2 - P^2 c^2[/tex] is invariant.

and

In S: [tex]E = (m_{1} + m_{0})c^2 , p = p_{1}[/tex]

In S ' :

[tex]E^2 - P^2 c^2 = E^2_{1}+ 2m_{0}E_{1}c^2 + m^2_{0}c^4 -T^2 (1) where E_{1} = T + m_{0}c^2[/tex]

I'm not sure what is happening in the centre of mass frame, I thought that the particle would have maximum mass when there was zero K.E i.e [tex]E' = (2m_{0} + m_{x})c^2, p' = 0[/tex] in the lab frame but I got lost when I tried to equate this with (1).

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