Free/Bound Electrons and Photon absorption

[pallidin]

I've heard that atomically bound electrons can potentially "absorb" an incoming photon, whereas a "free" electron has no such potential.
Why is this?
Also, can rapidly alternating un-bound electrons emit photons?

[Farsight]

Electrons don't actually absorb photons. Atoms do.

How can I describe it? It's kinda like a billiard ball on a tetherpole. Put a gun to the billard ball fair and square, pull the trigger, and blam, the billiard ball goes whizzing round and round. The system that is the pole, tether, and billiard ball, has absorbed like all the energy of the bullet, which you find lying on the floor with a flat nose.

Now detach the billiard ball and throw it up in the air to emulate a free electron. Now try and shoot it. You'll probably miss. But if you do hit it, you'll most likely get a richochet. Your bullet whines off, going slower than it was, and the billiard ball kicks off in some direction or other. This is called Compton Scattering.

http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/comptint.html

Sorry, I don't understand your latter question.

[Meir Achuz]

I've heard that atomically bound electrons can potentially "absorb" an incoming photon, whereas a "free" electron has no such potential.
Why is this?
Also, can rapidly alternating un-bound electrons emit photons?
A free electron cannot absorb a photon and conserve energy and momentum. For a bound electron, the atom absorbs some of the energy and momentum..

An accelerating electron will emit photons even though it need not be bound.