3. Are there any indications that there are elements beyond the 118 we have current...

Are there any indications that there are elements beyond the 118 we have currently discovered or synthesized? If so, is there any indication that there is a finite number of elements, other than their increasingly short halflives?

So without going into a very long and detailed explanation I don't have the time to give just now, I will say that the biggest issue is that the most stable forms (predicted) of the heaviest elements are much more neutron rich then we can currently generate. This is primarily because the best neutron rich low nucleon number element we use is Calcium-48 ( a very rare isotope with 20p/28n).

This nets us +8 (n-p) overall.

Even then to use the heaviest neutron rich isotope target (say berkelium-249, which has an EXTREMELY short half-life and thus is very time sensitive), we only gain an additional +152 or so (n-p).

This is significantly less neutron rich than the most stable predicted elements of 117/118 ought to be (idea of the island of stability), by as much as 10-20 neutrons. The best isotopes of these elements could have half-lifes in excess of a few years, but right now creating them is next to impossible due to neutron deficiency.

This problem is further expounded when you get to higher and higher elements so they might not be reachable for a long time (if ever.)

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