Questions re Compton scattering

[outandbeyond2004]

I am not sure this is the right topic for these questions. They are for the people who are familiar with Compton scattering. Let

\Theta

be the angle that the trajectory of the scattered photon makes with the trajectory of the incident photon.

Suppose
\Theta
is zero. Does that mean that the incident photon misses the electron (or some target charged particle) altogether or it hits the electron but does not interact with the electron at all? I can imagine the incident photon usually misses the electron, but surely there should be some hits now and then. Therefore, Compton forward transmission (CFT - not really scattering) as I shall term it should happen. The formula predicts in this case that there shall be no redshift. I find this hard to believe. It's though the cue ball goes right through the 8 ball into the pool pocket without changing the position of the 8 ball at all.

Has anyone done any detailed QFT analysis of CFT? If so, what were the results? As for experiments, I suppose it would be very hard to measure any redshift in CFT.

[mathman]

The angle of scatter for Compton scattering can assume any value between 0 and 180o. The probability of it being exactly 0 (or any other angle specified in advance)is 0. In other words, the probability density has no Dirac delta function component.

[outandbeyond2004]

Yes, a theoretical reason CFT is all but impossible to check cleanly. Let me see if I understand: As the angular spread around zero theta is made smaller, the redshift results become less reliable for verification purposes. I suppose one of you can put that in more technical language.

What I think I can say: Redshift does happen, though we cannot ever know for sure whether that is from CFT or from theta very close to zero.

[mathman]

I am not sure what your question means, but essentially, if there is no energy change we can't tell if is was scattered straight forward or missed - there really is no difference. If there is any energy loss, there was scatter.

[outandbeyond2004]

If there is any energy loss, there was scatter.

My understanding is that we cannot measure radiation coming from theta = zero only. Rather we have to measure radiation integrated over a range of angles, zero <= |theta| < constant. Actually, a cone centered on the initial direction of the incident photon. The constant may be small but cannot be zero. Hence, we cannot know which photon in that range is a "straightforward" photon, and cannot thus verify the prediction of zero energy loss for theta = zero.

Not only would an experimentalist say that, but a quantum mechanics theorist would.

Am I correct?

[mathman]

The wavelength (or energy) can be measured quite accurately. Threfore if there was a change, there had to be a scatter.

[outandbeyond2004]

So, if you measured close to theta = zero and found a change in wavelength = scatter, you would conclude that the Compton formula value for theta = zero is wrong?