Small Angle Scattering: Electrons & Angles

[asdf1]

Why are electrons elastically scattered at very small angles but not large angles?

 

[OlderDan]

Why are electrons elastically scattered at very small angles but not large angles?

Does "elastic" in this context mean the electron retains its energy during the scattering event, but loses significant energy at large angles? This could be nothing more than an issue of momentum transfer. In a glancing collision with a stationary object the electron retains most of its initial momentum. In a more head on collision, the electron transfers a lot more momentum to the target, so the target acquires more momentum and thus more energy.

 

[asdf1]

That makes sense. Then why is it okay in general physics to assume that a head on collision doesn't lose energy?

 

[OlderDan]

That makes sense. Then why is it okay in general physics to assume that a head on collision doesn't lose energy?

It depends on what energy you are talking about. In a head on collision of two billiard balls (neglecting rotation and friction effects) the cue ball stops and the target ball moves off with the velocity the cue ball had before impact. We call this an elastic collision because the total kinetic energy of the system is conserved. But the cue ball loses all its energy. If two things collide and stick together, we call that an inelastic collision because a lot of the initial kinetic energy is converted into some other form of energy. This does not mean that energy was lost in the process. It just means that some kinetic energy has been converted into some other form of energy.

If a small (less massive) object collides with a large object and bounces (e.g. ball bounding on the floor), we tend to talk about the kinetic energy in terms of the relative speed of the two objects, and we say the small object has all the speed and kinetic energy because we assume the large object is at rest and stays at rest. If the relative speed does not change we say the collision was elastic, and if it does change we say it was inelastic. If a ball makes glancing contact with the floor, even if the collision process is inealstic the ball retains nearly all of its kinetic energy because the horizontal component of its velocity is responsible for most of its kinetic energy, and this component is unaltered by the collision. A glancing collision is always nearly elastic because at most only a small fraction of the kinetic energy can be lost.

On a microscopic level, what is the electron target in a scattering experiment? It's usually a complicated assembly of interacting particles that have a combined mass that is enormous compared to the mass of an electron. When scattered electron energy is measured, we are not really looking at the whole picture. If the target acquires any form of energy from the electron, the electron loses kinetic energy in the frame of reference of our laboratory. The kind of energy the target acquires depends on the very complicated details of the interaction. Even if the total kinetic energy of the system is conserved, we have no good way of measurinng the recoil of the target. As in the case of the bouncing ball, if the force the target exerts on the electron is nearly perpendicular to its direction of motion, very little of its kinetic energy is lost in the process, so we say the process is elastic (or very nearly so). If the electron leaves the target with lower speed we say the collision was inelastic even though from a purely mechanical standpoint the total kinetic energy of the system might have been conserved. We know the electron gave up some energy. The question is, what kind of energy did the target acquire? In this context, inelastic or elastic just means the electron did or did not lose some of its kinetic energy.

 

[asdf1]

Thank you so very much for again explaining my questions in so much detail! ^_^