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To the segment of nuclear physicists that predict that there is indeed an “Island of Stability” in super-heavy transuranic elements, where these atoms shouldn’t suffer the effects of radioactive decay, shouldn’t the fact that no astronomical or cosmological observation of the spectra of such element weaken the theory, considering we have used this method to discover Helium or even highly unstable Technetium in outer space?

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The lack of astronomical observations of such elements indicates some combination of: (a) they cannot be produced; (b) they are very rare; or (c) they are relatively short-lived. However, constraints from the lack of such elements on Earth are probably stronger at the moment.

In terms of (a), there are certainly production sites in the universe. These would likely be supernovae and kilonovae (merging neutron stars). These are expected to be the primary production sites for all elements beyond lead. Kilonovae might seem very promising since neutron star crusts already contain exotic, neutron-rich, heavy nuclei, that are stabilised against decay by the presence of ultra-relativistically degenerate electrons. When they merge and an explosion ensues, much of this material is cast into space where it decays into the more familiar heavy elements.

Thus I think there is a production route, but that doesn't mean that they aren't rare. Ultra-heavy but relatively stable elements like thorium and uranium are rare and very difficult to detect in the astronomical spectra of stars. If a long-lived element was being produced, but in trace quantities, that is not where it would be found - it would be found on Earth, in rocks!

Which leaves (c). The reason we find uranium on Earth is it has a half-life that isn't much shorter than the age of the Earth. My (limited) understanding is that elements in the island of stability could still have much shorter lifetimes than this. In which case, the only hope is to spot the element in an astronomical context shortly after it is produced, like the example of technetium you mentioned.

The difference here is that we cannot even identify the presence of individual rare known heavy elements in the spectra of supernovae and kilonovae, because these explosive events mean individual absorption and emission lines are smeared together by high speeds and the Doppler effect. It would be very difficult to spot the presence of traces of new ultra-heavy elements with current techniques. In contrast, short-lived technetium was identified because it is produced in an entirely different way (the slow, s-process neutron capture) in the interiors of relatively common low-mass giant stars. It is then mixed to the surface and can be hugely overabundant, making it easy to spot in the relatively unturbulent, quiet atmospheres of nearby examples.

In summary I would say that there are potential production sites for these elements, but the lack of their presence on Earth probably constitutes stronger constraints on a combination of their cosmic abundance and half-life than astronomical observations.

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In cosmological times, Neutral hydrogen forms after 380.000 years from the Big Bang. It is after the formation of stars from the mainly Hydrogen and helium matter that higher mass nuclei appear :

After about 20 minutes, the universe had expanded and cooled to a point at which these high-energy collisions among nucleons ended, so only the fastest and simplest reactions occurred, leaving our universe containing about 75% hydrogen and 24% helium by mass. The rest is traces of other elements such as lithium and the hydrogen isotope deuterium. Nucleosynthesis in stars and their explosions later produced the variety of elements and isotopes that we have today, in a process called cosmic chemical evolution. The amounts of total mass in elements heavier than hydrogen and helium (called 'metals' by astrophysicists) remains small (few percent), so that the universe still has approximately the same composition.

The heavier nuclei appear in two ways, up to iron while the star is forming. The heavier ones happen in the explosions of supernovas.

Supernova nucleosynthesis within exploding stars is largely responsible for the elements between oxygen and rubidium: from the ejection of elements produced during stellar nucleosynthesis; through explosive nucleosynthesis during the supernova explosion; and from the r-process (absorption of multiple neutrons) during the explosion.

You ask:

super heavy transuranic elements, where these atoms were to suffer the effects of radioactive decay, shouldn’t the fact that no astronomical or cosmological observation of the spectra of such element weaken the theory,

The hypothesis of the island of stability needs laboratory confirmation, as astronomical ones cannot be controlled at the level one needs to measure lifetimes etc.

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