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

[tex]\Theta[/tex]

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

Suppose
[tex]\Theta[/tex]
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 180^o. 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?