John Carlos Baez on Nostr: When you have 3 helium atoms, they can stick together and form 'trihelium'. But even ...

When you have 3 helium atoms, they can stick together and form 'trihelium'. But even more impressively, the different energy states of trihelium are predicted to form an infinite sequence of molecules, each 22.6948 times larger than the previous one!

A while ago I talked about dihelium. This consists of 2 helium atoms held together, not by a chemical bond, but by the weak left-over remnants of the electrical forces holding each atom together. Trihelium works the same way, but it's more stable than dihelium. Indeed if you took one of the larger forms of trihelium and removed any one of the 3 atoms, the other two would fly apart.

This bizarre phenomenon was predicted by the Russian physicist Vitaly N. Efimov in the 1970s. He showed it should happen whenever you have 3 identical bosons attracting each other by a short-range force. As they come closer and closer to having enough energy to no longer be bound together, they form an infinite sequence of bound states, where the radius of the nth state is proportional to the nth power of some number λ. This number λ is close to 22.6948, but Efimov showed that it's actually

exp(π/s)

where s is the unique positive solution of

s cosh(π s/2) = 8 sinh(π s/6)/√3

Alas, I don't understand his calculation.

For a long time Efimov's work was just a theoretical prediction. In 2014 a team observed the first two 'Efimov states' in an ultracold gas of cesium. But trihelium is harder to work with, and it's only with great trouble that people have made it at all. So we have not verified that it has Efimov states... but the math and physics is solid.

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