# Antiproton inside fullerene

1. Dec 26, 2012

### vemvare

I'm sorry, this question must've been asked before, I'm just not finding it in my searches.

Has anyone calculated if it is theoretically possible to put an antiproton inside a fullerene?

2. Dec 27, 2012

### VantagePoint72

I'm assuming you mean "put inside a fullerene in such a way that it would stay there" (i.e. trap it). This isn't possible, which can be argued without even doing a quantum calculation: Earnshaw's theorem (https://en.wikipedia.org/wiki/Earnshaw's_theorem) says that it is impossible for a charged particle to be held in a stable equilibrium by any configuration of charges—there is always a "leak" somewhere. The electric field of a neutral atom is naturally very weak (effectively zero over distances larger than the typical scale of molecular bonds), so for a best case scenario, imagine you replaced each carbon in the fullerene with a negatively charged particle. In this case, negative charges will be able to leak out through the center of each icosahedron face. So, if the antiproton were slightly displaced from the center (as its own thermal movements would do) it would be carried out by the electric field. Griffiths has a similar exercise for a charge inside a cube of point charges (ex. 3.2) which might be instructive for seeing how this works. So if you can't trap a classical negative charge with an icosahedral distribution of negative charges, you certainly won't be able to do it with neutral atoms whose electric field is much weaker—and if you can't do it for a classical negative charge, you certainly can't do it for a particle obeying quantum mechanics, where quantum tunneling allows even classically trapped particles to escape under the right circumstances.

3. Dec 27, 2012

### Staff: Mentor

Even worse: The antiproton would not have to leave the cage - once it sees the electric field of a nucleus (at a radius comparable to the electron wave functions), it gets attracted by it and the antiproton can annihilate with a nucleon there.

There are some ways to avoid Earnshaw's theorem, but I think you need neutral antihydrogen for those.

4. Dec 29, 2012

### vemvare

I had actually heard of Earnshaw's theorem, but I can't say understand it very well. I thought that since the fullerene is an aromatic molecule it'd be more like a solid charge-shell, if of course the molecule has a negative charge.

What would happen if one instead tried to keep a charged particle between two charged plates, or in a torus?

Perhaps I should bat my head a bit more against it, though.

How? Are there any other theoretical concepts for storing antimatter? The Brillouin limit is brutalizing my sci-fi fantasies.

5. Dec 29, 2012

### Staff: Mentor

The important result of Earnshaw: Geometry does not matter. You cannot store a charged particle with electric fields. You can store diamagnetic materials and moving (spinning) ferromagnets, but an antiproton is neither.

Neutral antihydrogen is attracted my minima of the magnetic field strength, and those are possible. This is done at the ALPHA experiment at CERN.