# Can electron beam accelerate electron capture beta decay?

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## Main Question or Discussion Point

Some nuclides undergo decay of electron capture or beta plus.
Can electron beam with appropriate energy accelerate electron capture beta decay?
Same scenario: If I am looking for something, and my friend kindly hands it over to me, then I say thanks, because my seeking time is shorten.

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Electron capture is teh capturing of K electron by nucleus. That electron may be replaced by the slowed down electron of beta ray. In that sense it may accelerate. But if you think the beta ray electron getting directly taken by nucleus for that the electron must have very huge KE of the order of MeV then electron will be travelling almost with speed of light. Use Heisenberg principle and think about it.

Electron capture is teh capturing of K electron by nucleus. That electron may be replaced by the slowed down electron of beta ray. In that sense it may accelerate. But if you think the beta ray electron getting directly taken by nucleus for that the electron must have very huge KE of the order of MeV then electron will be travelling almost with speed of light. Use Heisenberg principle and think about it.
The inner diameter of electron shell is still too large with comparison to nucleus size, but artificial electron beam can penetrate the "vast" space anywhere between the inner K shell and nucleus, so I guess more chance for electron capture.
The kinetic energy does not have to be too high, maybe only (2~100) * (K shell electron binding energy), that may be far less than 500keV

mfb
Mentor
The reaction $e^- + X \to Y+\nu_e$ is certainly possible, but I doubt you would get notable reaction rates with realistic setups. Typical electron capture lifetimes are of the order of days to millions of years, with a significant fraction of the wavefunction of the innermost electrons in the nucleus. Compare this to the probability that an electron in your beam goes through a nucleus, and the timescale of this passage.

The reaction $e^- + X \to Y+\nu_e$ is certainly possible, but I doubt you would get notable reaction rates with realistic setups. Typical electron capture lifetimes are of the order of days to millions of years, with a significant fraction of the wavefunction of the innermost electrons in the nucleus. Compare this to the probability that an electron in your beam goes through a nucleus, and the timescale of this passage.
I wish find some literature to address my speculation, but Google gets nothing pertinent. So why not setup a project to deeply investigate on it?
The K shell electron wavefunction must have very small distribution around nucleus, because the distance is in pico-meter level, and nucleus size in fermi-meter level.
Even low energy incident electron (less than the binding energy) may shove the K electron more closer to nucleus.
If I mentor a PhD student and have good equipment, I will assign this theme for his or her thesis.

mfb
Mentor
The K shell electron wavefunction must have very small distribution around nucleus, because the distance is in pico-meter level, and nucleus size in fermi-meter level.
Below a picometer for heavy elements. Sure, the fraction is not large, but the fraction of your electron beam hitting a nucleus is even smaller.
If I mentor a PhD student and have good equipment, I will assign this theme for his or her thesis.
Poor PhD student. On the other hand, if a PhD candidate does not spend the 5 minutes to see that this project doesn't work before working on it for years, he should not get a PhD anyway.

Below a picometer for heavy elements. Sure, the fraction is not large, but the fraction of your electron beam hitting a nucleus is even smaller.Poor PhD student. On the other hand, if a PhD candidate does not spend the 5 minutes to see that this project doesn't work before working on it for years, he should not get a PhD anyway.
Imagining the electron flying by a nucleus, though not exactly hit, the attraction between nucleus and electron does force them meet or divert, or at least temporarily bind it in a fractional quantum orbit, e.g. 1/2, 1/3, etc. just like unverified hydrino, then probably catch it because of higher wavefunction overlap.
So it is hard to say lesser probability then normal K electron, all we need is the experimental data to prove it.

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a fractional quantum orbit, e.g. 1/2, 1/3, etc. just like unverified hydrino
Sorry. No such things.

Sorry. No such things.
I also think no such things, but there should exist very short lifetime transition, because the centrifugal must be equal to attraction force, though angular momentum only ℏ/2, ℏ/3, ... ℏ/n. The fractional angular momentum is never stable, unless metastable, because such small angular momentum is vulnerable to perturbation.
After the transition, to be or not to be captured are both possible, just like Vanadium 50 can both β+/β-/EC decay.
Fractional quantum number does exist in Hall effect, maybe the quasiparticle or low temperature is immune to perturbation.

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K electron has total negative energy and is quite different from the incident electron which has only KE. So in order that this electron has sufficient amplitude inside the nucleus its energy need to be very high and can be estimated using Heisenberg principle. We already have lot of difficulties in understanding classical physics and quantum physics. Do not try to invent impossible things by the flight of your imagination. And finally kindly avoid the term centrifugal from this will confuse and other readers. One can understand all possible things without using that avoidable term!

mfb
Mentor
I also think no such things, but there should exist very short lifetime transition, because the centrifugal must be equal to attraction force, though angular momentum only ℏ/2, ℏ/3, ... ℏ/n. The fractional angular momentum is never stable, unless metastable, because such small angular momentum is vulnerable to perturbation.
After the transition, to be or not to be captured are both possible, just like Vanadium 50 can both β+/β-/EC decay.
Fractional quantum number does exist in Hall effect, maybe the quasiparticle or low temperature is immune to perturbation.
This is just nonsense. We don't discuss nonsense here.