# When 2 particle beams meet head on

When 2 particle beams meet head on, more energy is avaliable than when the particle beam is directed at a fixed target. Why is this?

My textbook gives an explanation which I dont understand, involving rest mass energy. Any alternate explanation or explaining the one given will be great.

Thank you

## Answers and Replies

mathman
Science Advisor
To understand it, first look at the low speed case. When two things going at speed x, the relative speed is 2x, so the energy involved is larger than an object hitting a fixed target at speed x.
In particle accelerators, the particles are going close to the speed of light, so the relationship between the particles involves adding energy by adding mass using the Lorentz transformation.

Look at Eq 38.3 in
http://pdg.lbl.gov/2009/reviews/rpp2009-rev-kinematics.pdf
This equation converts energy in the center of mass system (colliding beams) to fixed target beams. This equation can be derived from either Eq 38.1 or 38.2.

Bob S