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electron-electron vs electron-positron

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In QED, I've always been a little muddled on how to tell the difference 
between electron-electron and electron-positron scattering. There's an 
s-channel 1st-order diagram that's present for the latter that's not 
there for the former. But if were going to ask what's the scattering 
cross section at a particular angle with respect to incident angle, I've 
been under the impression that the two cases are essentially identical, 
even though the bending of the incident particle is due to repulsion in 
the first case, and due to attraction in the second case.

But then looking over a classical mechanics book, I was reminded of 
something rather astonishing. For central forces (like the 
electromagnetic interaction), you can treat the problem as though it has 
an "effective potential" (see eq. 335 in 
http://www2.ph.ed.ac.uk/~egardi/MfP3-Dynamics/Dynamics_lecture_20.pdf) 
that goes like this:

U(r) = L^2 / 2mr^2 + K/r

where K = ke^2 for electron-electron scattering and K=-ke^2 for 
electron-positron scattering.

The minus sign here makes a big difference. For a particle of energy 
E>0, where the trajectory is hyperbolic, the distance of closest 
approach is defined by the "turning point" in the effective potential 
U(r). And that turning point is different if K>0 or K<0, where the 
distance of closest approach is quite a bit *smaller* for the latter case.

I would think that, because of this, we should certainly be able to tell 
the difference via QED between K>0 and K<0. At the very least, we should 
see less QED vacuum polarization if we penetrate deeper to the 
scattering center?

Anybody online that can shed some light on this for me?


-- 
Odd Bodkin --- maker of fine toys, tools, tables

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electron-electron vs electron-positron Odd Bodkin <bodkinodd@gmail.com> - 2015-10-19 10:50 -0500
  Re: electron-electron vs electron-positron "reber g=emc^2" <herbertglazier0@gmail.com> - 2015-10-19 09:51 -0700
  Re: electron-electron vs electron-positron dsr@mail.lns.cornell.edu (Daniel S. Riley) - 2015-10-20 17:12 -0400
    Re: electron-electron vs electron-positron Odd Bodkin <bodkinodd@gmail.com> - 2015-10-20 17:25 -0500
  Re: electron-electron vs electron-positron Fabian Russell <root@localhost.localdomain> - 2015-10-21 01:14 +0000
    Re: electron-electron vs electron-positron Poutnik <poutnik4nntp@gmail.com> - 2015-10-21 07:28 +0200
      Re: electron-electron vs electron-positron Fabian Russell <root@localhost.localdomain> - 2015-10-21 05:48 +0000
        Re: electron-electron vs electron-positron Poutnik <Poutnik4NNTP@gmail.com> - 2015-10-21 12:27 +0200
    Re: electron-electron vs electron-positron "Y.Porat" <y.y.porat@gmail.com> - 2015-10-20 22:32 -0700
      Re: electron-electron vs electron-positron "Raymond Luxury Yacht" <invalid@example.com> - 2015-10-21 22:23 -0700
        Re: electron-electron vs electron-positron "Y.Porat" <y.y.porat@gmail.com> - 2015-10-22 02:39 -0700
      Re: electron-electron vs electron-positron "Y.Porat" <y.y.porat@gmail.com> - 2015-10-22 02:57 -0700
        Re: electron-electron vs electron-positron "Y.Porat" <y.y.porat@gmail.com> - 2015-10-22 23:04 -0700
    Re: electron-electron vs electron-positron Odd Bodkin <bodkinodd@gmail.com> - 2015-10-21 07:31 -0500
      Re: electron-electron vs electron-positron Fabian Russell <root@localhost.localdomain> - 2015-10-21 16:15 +0000
        Re: electron-electron vs electron-positron Poutnik <Poutnik4NNTP@gmail.com> - 2015-10-21 20:04 +0200
          Re: electron-electron vs electron-positron Fabian Russell <root@localhost.localdomain> - 2015-10-21 19:50 +0000
            Re: electron-electron vs electron-positron Poutnik <poutnik4nntp@gmail.com> - 2015-10-21 22:02 +0200
            Re: electron-electron vs electron-positron Poutnik <poutnik4nntp@gmail.com> - 2015-10-22 08:01 +0200
              Re: electron-electron vs electron-positron Fabian Russell <root@localhost.localdomain> - 2015-10-22 14:30 +0000
                Re: electron-electron vs electron-positron Poutnik <Poutnik4NNTP@gmail.com> - 2015-10-22 16:49 +0200
        Re: electron-electron vs electron-positron Odd Bodkin <bodkinodd@gmail.com> - 2015-10-21 15:59 -0500

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