Resolution in scattering experiments

[evilcman]

Here are two exercises:

1. ) The proton radius is 0.8fm. What energy electron beam do you need for this resolution, if the target is liquid H2?

2.) A pion radius is 0,65fm. What energy pion beam do you need for this resolution by scattering on the electrons of a stationary target(pi-e scattering)? Why is the beam energy so different than in the previous exercise?

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Now, i guess the main point in both cases is that the dr Broglie wavelength of the bombarding particle is the best resolution one can achieve. But, if I just go with de Broglie wavelength = spatial resolution , then I get approx. 1,5GeV and 1,9GeV respectively, which is not that different, so I don't understand the necessity of the last question. Also, I don't think the target material is important. Can someone clarify this?

 

[Bob S]

The common relation in electron scattering experiments is 197 MeV fermi =1, where MeV relates to the incident electron energy, and fermi is the spatial resolution.. (The proper units perhaps should be Mev/c fermi, i.e., Δp Δx = 197 MeV/c fermi). See equation 1.11 et seq. in

http://faculty.ksu.edu.sa/mahgoub/My%20library/Advanced%20Quantum%20Field%20Theory.pdf

Bob S

 

[evilcman]

That just mean that hbar c = 197 MeV fm, I know that, and it does not answer my question.

 

[Bob S]

That just mean that hbar c = 197 MeV fm, I know that, and it does not answer my question.

For pions, (pc)² = E² - (mc²)²

You probably need to transform to the center-of-mass (CM) reference frame. See Section 38.2 in

http://pdg.lbl.gov/2009/reviews/rpp2009-rev-kinematics.pdf

Bob S

 

[evilcman]

For pions, (pc)² = E² - (mc²)²

You probably need to transform to the center-of-mass (CM) reference frame. See Section 38.2 in

http://pdg.lbl.gov/2009/reviews/rpp2009-rev-kinematics.pdf

Bob S

Yes I know, but since for the pion bombarding I get pc = 1,9 GeV and m=140MeV
=> pc approx E

Now, if I have to transform to the C.M. frame (which is approximately the pion rest frame in this case) that may make a difference, but why should I do that?

 

[Bob S]

Now, if I have to transform to the C.M. frame (which is approximately the pion rest frame in this case) that may make a difference, but why should I do that?

The real physics is usually in the CM reference frame.

Bob S