# Homework Help: Relativistic collision of Au nuclei - why is this wrong?

1. Sep 28, 2009

### bcjochim07

1. The problem statement, all variables and given/known data
The RHIC at Brookhaven is colliding fully ionized gold nuclei accelerated to an energy of 200 GeV per nucleon. Each Au nucleus contains 197 nucleons. a) what is the speed of each Au nucleus just before collision? b) What is the momentum of each at that instant in time? c) What energy and momentum would be measured for one of the Au nuclei by and observer in the rest system of the other Au nucleus?

2. Relevant equations

3. The attempt at a solution
Got part a and b, no problem a) 0.999989134 c b) 3.9399e4 GeV/c

But I can't seem to get the answer to part c correct. Here's what I did:

The energy of each Au ion is 179 * 200 GeV = 39400 GeV

What we need for part c is the velocity of one Au ion as seen by another. We can't just jump to using the equation E'=gamma*(E-v*px) because the momentum and energy in part a are in the frame of the Au ion, not the laboratory. The laboratory would measure different values for a and b.

So lets use the velocity addition formula

ux' = [(0.999989134 c) - (-0.999989134c)]/(1-(-0.999989134c*0.999989134c)/c^2)

ux' = 0.9999999999c , gamma = 1/sqrt(1-.9999999999^2) = 22360.68

so now we can use E' = gamma*(E-v*px)
E' = 22360.68 * (39400GeV-(-0.9999999999c)*39399.578GeV/c)
E' = 1.762 x 10 ^ 9 GeV

but the answer given is 3.310 x 10 ^ 9 GeV.

Where did I go wrong?