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If we look at the atomic positions in a single crystal sample with a diamond like lattice, there exist directions along which there are long hexagonal "tubes" (I'm not sure if these have a proper term).

hexagonal tubes in diamond like lattice

This happens in silicon for example. Now if a hydrogen atom was inserted in the material, it would be too large and just get trapped in the 'matrix' of the silicon and present a defect in the material.

If instead I took a proton and muon in a bound "muonic hydrogen" state, the bohr radius which goes like 1/m would be ~ 200x's smaller. Due to being neutral, small, and tightly bound (a binding energy > 2.5 keV), I am tempted to view it almost like a large neutron.

My question is:
Due to its much smaller size, could such a 'large neutron' pass freely through a crystal along one of these tubes?
Could one eliminate trapped hydrogen in a crystal by making it "mobile" in this fashion by putting the sample in a muon beam of low enough energy that it won't damage the crystal structure but still create 'muonic hydrogen'?

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3 Answers

On the specific "muonic hydrogen" part of the question: yes it will be much more compact than hydrogen and would probably fit but I see difficulties in generating such a beam that will last long enough at the necessary low energy and be incorporated in the crystal.

A muon decays in about 10**-6 seconds. So a beam of muonic hydrogen could tunnel through a crystal along the axis and not scatter destructively, but I find it improbable it will be captured within. Anyway the muon will decay and the proton will be an imperfection in the lattice.

Beams of particles have been tunneled through crystals. The problem will be in targetting interstitial hydrogen because nothing guarantees it will be along the crystal axis.

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The decay time is not that big a constraint--- a microsecond is a long time, at thermal velocity its almost 10cm. –  Ron Maimon Sep 24 '11 at 8:29
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Mu-hydrogen has a large electric dipole response to external electric fields, will likely wind up getting close to a heavy nucleus, and transferring the muon to the nucleus and shedding the proton. The empty tubes are filled with electronic density anyway, and I don't see any reason that the scattering of mu-hydrogen should be small, considering that it has charged constituents far apart as compared to a neutron.

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This is a case of particle channelling. A particle can pass through planes or “tubes” in crystals of this nature.

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John asks about diffusion of that "muon-hydrogen" in silicon lattice. That is rather different from channeling of subatomic particles! –  Georg Apr 11 '11 at 11:19
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