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I know beta ray refers to a flow of electrons with high velocity created in the nucleus. So, if I increase the kinetic energy or velocity of an electron, at some point its velocity can be close to that of beta rays. Then will there be any difference between the beta ray and the electron with high velocity created artificially? If so, what will the difference be?

I know that we can also have positrons coming out of the nucleus, but for now, let's keep that aside. And about the neutrino or, anti-neutrino, can't we just ignore them because they don't interact that much?

A simple explanation would be greatly appreciated.

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Electrons are identical particles, and an electron from any source will interact with the rest of the universe in exactly the same way.

However, there is a transient difference between a beam of "beta rays" being emitted from a radioisotope and a beam of electrons with the same energy distribution produced via some other method. That difference arises because beta decays are mediated by the weak interaction, which is not symmetric under mirror symmetry. The net effect is that electrons emitted during a beta-decay tend to be slightly polarized, with their north poles slightly more likely than their south poles to point back towards their originating nucleus. (We call such a polarization "left-handed"; the charged-current part of the weak interaction likes left-handed particles and right-handed antiparticles, but not vice-versa.) The polarization is stronger in electrons with more energy, so it's a minor effect in most radioisotope sources; however the weak interaction's preference for left-handed electrons is the reason that the meson decay $\pi^\pm\to e^\pm\nu_e$ is (much!) rarer than the much less energetic $\pi\to\mu\nu_\mu$.

This polarization of beta radiation was first observed in 1927 by Cox and collaborators, who were doing a very early electron-electron scattering experiment and were confused when their control configuration seemed to indicate that their beam of beta particles was polarized. Cox et al. solved the problem by switching to a thermal electron source, which produces unpolarized electrons, and their result was forgotten until the discovery of parity nonconservation thirty years later. The story is told in Allan Franklin's book "Are There Really Neutrinos."

For a possible real-world, large-scale effect of this temporary polarization difference between beta radiation and fast electrons from other sources, see this question.

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