Creating isotopes by shooting neutrons into an unstable nucleus [closed]

Question

I've been doing a lot of amateur research lately (youtube videos) on particle physics and find it all really interesting. I'm also a crazy alien conspiracy theorist who believes in the whole "Bob lazar story" which I won't elaborate on in this thread.

Anyways, from my understanding, new elements can be created by shooting a proton into a nucleus and having it get close enough to the nucleus that the strong force overpowers the repulsive coulomb forces between the protons (this is what happens in stars with fusion). This is difficult because the proton needs enough energy to be able to pierce the electromagnetic repulsion of the nucleus. On the other hand, if you want to create an isotope of an element, this is easier because neutrons are electrically neutral and are unaffected by the electromagnetic force. So all one needs to do to create an isotope is have the neutron come within a close enough range of the nucleus for it to react and be absorbed.

So lets say we have some unstable nucleus that will typically decay after 50us. If I were to shoot a neutron into this nucleus and it reacts successfully, from my understanding it would become a new isotope with a new rate of radioactive decay. This is a bad example because I am making up numbers, but lets say the new isotope becomes even more unstable and decays after 40us. If the neutron was initially shot into nucleus 1 25us after the creation of nucleus 1, would nucleus 2 "be at 25/40% the way through completing its radioactive decay? Or would the "atomic decay clock" reset so to speak?

I know that this is a gross simplification of nuclear decay, and that in reality it is more probabilistic than determinate. The reason I'm asking this is because I want to understand why we couldn't just keep shooting neutrons into a super heavy element until we find a stable isotope. Even if it were to decay near instantly, it shouldn't be impossible for us to create a high enough flux of neutrons for it to continuously plug neutrons into an element if this were the case.

Answer 1

The nuclei will decay independently. The fact that the parent is an unstable nucleus does not affect decay rate of the daughter. You keep using the word new when talking about some of these nuclei. Maybe parent and daughter would be better. A nucleus created most likely is not new in terms of the chart of nuclei. We think we have discovered all nuclei below the proton number (82) of lead.

There is a certain value that a nucleus must live in order to be classified as a daughter nucleus. So you can't just keep bombarding some nuclei with neutrons to get a different nucleus. As pointed out in the comments, you seem to think there is some super heavy stable nucleus. We don't know this to be true.

Answer 2

If you irradiate an unstable nucleus with neutrons, then it will generally evolve in time as a superposition of both its normal state (described by a certain decay rate) and the state where it has absorbed a neutron (described by a different decay rate), where the quantum mechanical probability of the latter state being occupied would in general be a function of the neutron capture cross section $^1$ and incident neutron flux. A paradox related to what you seem to be talking about though is the quantum zeno effect, where successive measurements of a quantum system really does halt unitary time-evolution (quantum clock). However, because of various impeding features of neutron/particle capture which I mention in my last paragraph, this is almost never talked about in the context of nucleosynthesis.

Also, as pointed out by @probably_someone, you're effectively describing the $r$-process of nucleosynthesis which is now known to primarily occur in neutron star compact binary mergers. In fact, the exact process of building up heavier elements via neutron irradiation until you reach a more stable $^2$ heavy element is a general characteristic of stellar nucleosynthesis (both $s$ and $r$ processes), and manifests as peaks in measured elemental abundance curves.

As for why we can't "search for stable heavy elements like this", there are two issues.

1. We don't really need to look for stable heavy elements because we already have cosmic abundances of them. The universe has already produced an abundance of heavy elements through natural processes ($s$ and $r$ processes).

2. Even if we were motivated to build up measurable amounts of heavy elements by neutron irradiation on our own - e.g. for scientific, political, or engineering purposes - it really is impossible for us to create a high enough flux of neutrons to do so. From my general knowledge on the subject, neutron capture cross sections are stupendously low, and thus the only way to produce measurable product quantities is to have cosmically large reactant densities and incident neutron fluxes, which as we now know is only really achieved in neutron star-neutron star and neutron star-black hole mergers.

I am not an expert in any of these areas though, so take my response with many grains of salt.

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$^1$ If you're unfamiliar with the word "cross-section", it is basically the more established measure of scattering/capturing process probabilities as they pertain to actual experiments.

$^2$ The keyword here is "more", as no nucleus with more than 208 neutrons is stable, as you can see in this nuclide chart.