In many books I read that bremsstrahlung effect (for e+) only occur when the electron goes near the atomic nuclei. Why is not possible when cross near an atomic electron?
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The simple answer is that you are misinterpreting the text. Bremsstrhlung occurs when electrons are accelerated. Due to their much larger mass and charge, nuclei generally produce much greater acceleration of electrons than do electrons, and consequently greater radiation. For teaching purposes, this dominant cause is the one talked about.
However, if you Google "electron electron brehsstrahlung" you will find any number of papers discussing just this phenomenon. For instance, this one states,
Although both electron-ion and electron-electron bremsstrahlung contribute to the hard x-ray emissions from solar flares, the latter is normally ignored. Such an emission is not justified at electron (and photon) energies above ~300 keV...
A charged particle will always interact with an electric field, so an electron will interact with the fields of the atom, electrons and nucleus, depending on the energy of the electron.
Bremsstrahlung Radiation is in high frequencies, X-rays
"Bremsstrahlung" means "braking radiation" and is retained from the original German to describe the radiation which is emitted when electrons are decelerated or "braked" when they are fired at a metal target. Accelerated charges give off electromagnetic radiation, and when the energy of the bombarding electrons is high enough, that radiation is in the x-ray region of the electromagnetic spectrum.
The kiloelectron volt energies are much higher than the binding energies of the electrons around the nucleus, so the effect comes from the combined electric fields , and the first order Feynman diagrams are
One has corresponding ones for e- fields and e- incoming.