Show that the following processes are dynamically impossible

Show that the following processes are dynamically impossible because of violation of energy-momentum conservation laws. (a) A single photon strikes a stationary electron and gives up all its energy to the electron. (b) A fast positron (e^+ with m_e+ = m_e-) and a stationary electron (e^-) annihilate producing only one photon.

Solution

(a) photon + electron (at rest) ----> electron (moving)

This equation is okay as far as energy conservation is conserned but is not allowed from angular momentum conservation constraint.

(b) positron + electron ----> photon

Again energy conservation is ok here but the problem comes from the fact that in order for annhilation to take place the two particles have to be able to come at same point i.e. their spin must be opposite to each other. => initial ang. momentum = 0 and final ang. momentum = 1 NOT POSSIBLE

hence generally two photons are created.