# Scattering collisions/lorentz-invariant quantity

1. May 22, 2009

### wyse

hey guys, heres the question.

Physicts probe inside neutrons and protons by scattering electrons off them.
(i) Explain briefly why it is important that the electrons have high energy.

(ii) Assuming that the protons and neutrons were at rest, calculate the minimum momentum to which the electrons should be accelerated, in order to perform such experiments successfully.

(iii) Considering such scattering collisions in the laboratory frame of reference (where the target is stationary), write formulae for the energies of the electrons and target, and evaluate them in GeV (you may ignore the rest-mass of the electron).

(iv) The total energy in the centre-of-mass reference frame in such electron-nucleon collisions corresponds to the maximum possible mass of all particles in the final state and is a Lorentz-invariant quantity. Ignoring the rest-mass of the electron, calculate this quantity.

My workings:

(i) to ensure that they penetrate the protons and neutrons.

(ii) using wavelngth=planck's const/momentum gives 1.2.

(iii) can someone give me a hint for this part please. i don't understand how to get the velocity for the electron (it says ignore rest mass so using this in part (ii) won't help). also how are we supposed to know the final energies, as we're not told velocities etc.

(iv) are we supposed to use the energies calculated for the neutron is (iii) and somehow find the velocity so we can work out the mass?

thanks for any help.

Last edited: May 22, 2009
2. May 22, 2009

### Bob_for_short

You have to proceed from the fact that the electron is a wave and that proton/neutron size is finite, R_n, for example. In order to "see" such a small size, the electron wave-length should be shorter than R_n (to be close to the case of "geometrical optics"). Then simple QM and SR formulae are sufficient to resolve this problem.

Bob.

3. May 22, 2009

### wyse

hi bob, thanks for the reply.
so the proton size is $1x10^{-15}$, and so this helps me with (ii).

sorry i haven't done any relativity so i don't have a clue what it is on about (i'm a maths student doing a physics course). which formulae?

thanks