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My question is rather simple but puzzles me altogether. I'm just studying electron stopping power and I see in few graphs (particularly fig. 30.11 in PDG booklet) that Moller and Bhabha scattering are plotted together with ionization and bremsstrahlung.

So my question is: what is the formal difference between Bhabha scattering and ionization, since I see both of them as the effect of an electron being scattered by another electron?

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  • $\begingroup$ Bhabha is electron positron scattering en.wikipedia.org/wiki/Bhabha_scattering . It is not an electron scattered by another electron, charges are different, there is no annihilation channel for e-e-.Ionization is the electron-atom scattering, removing an electron from the atom $\endgroup$ – anna v Aug 31 '16 at 10:41
  • $\begingroup$ Dear Anna, thank you for your answer. Yes, I know that Bhabha involves positrons, but ionization curves are drawn for positron too. So just to get your point, Bhabha and Moller are only intended for free target electrons? So why they can be seen as ionization when the energy lost in a single collision is less than 0.255 MeV as stated in PDG? Thank you so much! $\endgroup$ – Matteo Lorenzini Aug 31 '16 at 15:23
  • $\begingroup$ can you give me a link for the pdg plots. It might be the ionization curves of charged tracks . I have to see the plots $\endgroup$ – anna v Aug 31 '16 at 15:51
  • $\begingroup$ For instance, the plot under figure 27.11 in the following document: PDG $\endgroup$ – Matteo Lorenzini Aug 31 '16 at 16:05
  • $\begingroup$ It is not comparing of the basic interactions per se. It is quantifying what happens when particles pass through matter. All these interactions can happen and that is why they are in one plot, to judge the importance as a function of the energy of the particles, in how they lose energy. Ionisation are the tiny scatters giving enough energy to ionize an atom and give it a small kinetic energy in consequence. It is what one sees in bubble chamber pictures as tracks of various thickness depending on the ionisation. $\endgroup$ – anna v Aug 31 '16 at 17:42
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I am writing this answer to try and learn something about the various scattering processes for myself, so hopefully another more detailed and more sophisticated answer will also be posted, that both I (and the OP, of course!) can learn from.

Bhabha scattering is the electron-positron scattering interaction involving an electron and a positron :

${ e^{+}e^{-}\rightarrow e^{+}e^{-}}$

The two-order Feynman diagrams describing this interaction are an annihilation process and a scattering process.

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The Bhabha scattering rate is used as a luminosity monitor in electron-positron collider experiments. In scattering theory and accelerator physics, luminosity (L) is the ratio of the number of events detected (N) in a certain time (t) to the interaction cross-section (σ):

${ L={\frac {1}{\sigma }}{\frac {dN}{dt}}}$

Luminosity values are useful in determine the performance and efficency of a particle accelerator, as the greater the integrated luminosity, the more data emerges from the (often expensive) experiment.

Ionization, (as I'm sure you already know, apologies)  is the mechanism by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons to form ions.  Ionization can result from the loss of an electron after collisions with subatomic particles, collisions with other atoms, molecules and ions, or through the interaction with light.

enter image description here

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In contrast to Bhabha scattering , ${ e^{+}e^{-}\rightarrow e^{+}e^{-}}$, Møller scattering ${\ e^{-}e^{-}\longrightarrow e^{-}e^{-}}$ denotes  electron-electron scattering. The electron interaction that is idealized in Møller scattering forms the theoretical basis of many familiar phenomena such as the repulsion of electrons in the helium atom.

Again, as I am sure you are aware, we need to include the both diagrams to complete the calculation of Møller scattering amplitudes. These illustrations give an indication of some of the terms included in the scattering amplitude, but to calculate a measurable quantity, we need to pick a reference frame, usually the COM frame, and assign helicities to the particles or average/sum over all possible spin states.

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