Tau catalyzed super heavy elements

[andrew848]

TL;DR

Tau catalyzed super heavy elements

Today I was reading about super heavy elements and was wondering if a tau lepton could be used to synthesize SHE's? As a side note, as relativity is applied to hypothetical SHE's Would you not end in a black hole as a limit to possible elements? and maybe a way to calculate and predict quantum gravity?

 

[mathman]

tau lepton could be used to synthesize SHE's?

from what?

 

[andrew848]

I assume any two isotopes you want, Sorry I meant to say tau catalyzed fusion reactions. I figured the larger particle would act like a large muon and aid in larger nuclei reactions.

 

[lpetrich]

Muon-catalyzed nuclear fusion works on D-D, D-T, and D-He3 fusion by the muon orbiting much closer than an electron, enabling the nuclei to get much close to each other than they normally would. Tau-catalyzed fusion also works like that, but would be even better.

One has to replace every electron in an atom by a muon to make this work, and it is much easier on a hydrogen isotope than on any other element's isotopes. For that reason, muons are not any help in making superheavy elements -- too much charge to cancel out.

For a hydrogen atom, the effective radius is the Bohr radius, about 5.29*10^(-11) m. Doing these calculations for an infinitely massive nucleus, a muon is about 200 times more massive, making its effective orbit radius about 2.56*10^(-13) m. A tau lepton is about 4000 times more massive, making its effective orbit radius about 1.52*10^(-14) m. A tau lepton is about as massive as a deuterium nucleus, making the combination's reduced mass twice as large, giving an effective orbit radius of about 3.11*10^(-14) m.

Tau leptons have a big deal breaker, however, their lifetime. A muon has a mean life of 2.197*10^(-6) seconds, and a tau a mean life of 2.903*10^(-13) s. Multiplying both lifetimes by c gives 659 m for the muon and 87.0 micrometers for the tau. So a tau will not last long enough to do much catalysis.

 

[snorkack]

Effectively, D-μ works like a dineutron. But its lifetime is 2.197*10^(-6) s, while the lifetime of a mononeutron is 6*10^2 s.

 

[mfb]

If you produce the taus in high energy collisions they don't even live long enough to slow down to be captured by atoms. To produce superheavy elements you would need as many taus as protons in a single atom. Forget it. Even two muons around the same atom is beyond current capabilities, and muons are much easier to produce and live much longer.
But even if you could do this then you still would not get fusion because the reactions need additional energy (unlike fusion of many light elements). So you need the accelerator anyway, and if you have that you can just give it enough energy for fusion that way.

Would you not end in a black hole as a limit to possible elements?

No, the limit comes from the other interactions much earlier.

and maybe a way to calculate and predict quantum gravity?

This has nothing to do with quantum gravity.