A nonrelativistic particle of charge ze, mass m, and kinetic energy E makes a head-on collision with a fixed central force field of finite range. The interaction is repulsive and described by a potential V(r), which becomes greater than E at close distances.

(a) Show that the total energy radiated is given by

where r_min is the closest distance of approach in the collision.

(b) If the interaction is a Coulomb potential V(r) = zZe²/r, show that the total energy radiated is

where v₀ is the velocity of the charge at infinity.

Transcribed Image Text:

4 ze? 3 m'c y 2 dr dV VV(rmim) - V(r) dr dr min 21