Quantum Tunneling and Deuterium Fusion

[Somerschool]

How close do two room temperature deuterium nuclei need to be to each other to have a one-in-a-quintillion chance of "tunneling" into each other so that the nuclear forces bind them together despite the repulsive effect of the positively-charged protons?

 

[Drakkith]

I don't believe 2 deuterons at that energy level could get close enough to fuse. The temperature is a measure of how much energy each nucleus has, and if you get very close to overcoming the columb barrier, but not quite close enough, then Quantum Tunneling can take you the rest of the way. From what I understand, at room temperature, the chances of Quantum Tunneling causing them to fuze is so low that you could simply say that it is impossible.

 

[Somerschool]

I'm assuming there's a way to push these room-temperature nuclei together. The question I'm asking is, "How close do I have to push them?"

Some quick googling tells me that quantum-tunneling diodes are on a 1-3 nanometer scale. Deuterium weighs about 3600 times one electron, so deuterium nuclei aren't t going to "tunnel" one whole nanometer with any appreciable frequency. But there should be a wave-function calculation that computes the probabilistic "spread" of room-temperature deuterium.

 

[Drakkith]

I don't know too much about quantum tunneling, but I know that for any appreciable amount of fusion, you need a LOT of kinetic energy behind the nuclei. On the order of a million degrees worth of energy or more. There isn't any way to "push" them together with enough force currently other than that.

For a 1 in one quintillion chance, it MIGHT be possible, I cannot say, but i don't see any practical reason for a fusion yield that low. Whats your interest in this?

 

[Somerschool]

Palladium hydride can store up to 900 times its own volume of hydrogen. (See: http://en.wikipedia.org/wiki/Palladium_hydride.) I want to know what would happen if two deuterium nuclei were "caged" inside an icosahedral palladium crystal (which is about 3.8 nanometers on a side) and then a strong positive charge removed electrons from the metal. This would create a positive charge that would "squeeze" the deuterium nuclei together.

From my rough research, the deuterium nuclei would be within a nanometer of each other at room temperature. Quantum tunneling routinely occurs with electrons on that scale. What's the probabilistic "spread" of something that weighs 3600 times one electron?

 

[Drakkith]

I don't believe that putting a positive charge on the crystal would cause them to be compressed into each other. Similar to how a hollow sphere that is charged to a potential has a net charge of 0 inside of it. It would probably strip the electrons off, but that's it.

 

[Somerschool]

I'm assuming the deuterium nuclei have already had their electrons stripped--chemically, deuterium in such a state is just a hydrogen ion, which is always present in any acid solution.

Are you saying that a positively charged ion inside a positively charged hollow sphere isn't "crowded" towards the center of the sphere? That seems VERY odd! I'm not saying you're wrong, but I've never heard about this phenomenon before. Is it documented somewhere?

I had been assuming that each of the vertices of the crystal would repel the deuterium ions, pushing them towards the center of the lattice. Suppose you could strip enough electrons from the crystal to leave each palladium atom with a net charge of +3. The deuterium ions have a charge of +1. Wouldn't the deuterium ions be "pushed" together?

 

[Drakkith]

Do a quick google on a charge in a hollow sphere.

 

[Somerschool]

Fascinating. So... does a cube with positively charged vertices behave the same as a metal sphere?

 

[Drakkith]

Fascinating. So... does a cube with positively charged vertices behave the same as a metal sphere?

I think so.

 

[alxm]

I'm assuming the deuterium nuclei have already had their electrons stripped--chemically, deuterium in such a state is just a hydrogen ion, which is always present in any acid solution.

Which doesn't mean that you can keep one stable in the vicinity of a bunch of metal atoms with considerably lower ionization energy.

Suppose you could strip enough electrons from the crystal to leave each palladium atom with a net charge of +3. The deuterium ions have a charge of +1. Wouldn't the deuterium ions be "pushed" together?

If each palladium atom had a net charge of +3, the crystal would have flown apart long ago.

 

[x_engineer]

I think it is simplest to think of there being no such thing as repulsion. When two positive charges are close together the fields conspire to attract them to negative charges at infinity, which looks like repulsion. The only way to get two positive charges to approach each other is to get a negative charge in between them. Individual electrons don't work because they are so light they flit in and out of the space between closely spaced positively charged deuterons too fast. But a lot of them, (like those spread out in a crystal) might together contribute enough apparent charge to hold things together when the positive charges are the right distance apart. Negative muons work better.

I saw a site that claimed a moving D2 would trigger enough free electrons to spend enough time in the space between them that they would be drawn further together. The site is no longer up, so can't refer you to it.

As for your question about wavelength, you could try using the De Broglie wavelength of a moving particle. Just make sure you never assume a particle is standing still, it always has its zero point energy!

 

[Drakkith]

I think it is simplest to think of there being no such thing as repulsion. When two positive charges are close together the fields conspire to attract them to negative charges at infinity, which looks like repulsion.

I don't think this is a good way to look at it. Positive charges would not be attracted to negative charges that are an infinite distance away because... well because they are an infinite distance away.

The only way to get two positive charges to approach each other is to get a negative charge in between them.

If you are talking purely about electromagnetic effects, then sure. But that's why we make them smash into each other at high speed.

I saw a site that claimed a moving D2 would trigger enough free electrons to spend enough time in the space between them that they would be drawn further together. The site is no longer up, so can't refer you to it.

What do you mean by "trigger enough free electrons"? What exactly is the D2 doing?

As for your question about wavelength, you could try using the De Broglie wavelength of a moving particle. Just make sure you never assume a particle is standing still, it always has its zero point energy!

I'm not sure that zero point energy applies here. One can easily do calculations from the frame of a moving electron, which in it's own frame is stationary.

 

[Q-reeus]

Somerschool is being clever about presenting his questions, but basically the idea is to justify 'cold fusion'. Isn't there a PF no-no on speculating on that?

 

[Drakkith]

Somerschool is being clever about presenting his questions, but basically the idea is to justify 'cold fusion'. Isn't there a PF no-no on speculating on that?

Perhaps, but he hasn't come out and mentioned it blatantly, so I'm fine in discussing the details. And it appears that he learned why it wouldn't work. Either way it doesn't really matter, as this thread hadn't been responded to in over a year until recently.

 

[Q-reeus]

Perhaps, but he hasn't come out and mentioned it blatantly, so I'm fine in discussing the details. And it appears that he learned why it wouldn't work. Either way it doesn't really matter, as this thread hadn't been responded to in over a year until recently.

Ah right - hadn't checked the OP's time stamp. Still it was obviously about CF and wonder why it wasn't canned back then. But I get used to such anomalies re rule enforcement.

 

[Drakkith]

Ah right - hadn't checked the OP's time stamp. Still it was obviously about CF and wonder why it wasn't canned back then. But I get used to such anomalies re rule enforcement.

I don't see it as "obvious" cold fusion personally, given that he was asking about a 1 in a quintillion chance of fusing. The discussion stayed on the physics pretty well, and didn't drift off into speculation. But yes, I can see how it's a bit of a gray area.

 

[Q-reeus]

I don't see it as "obvious" cold fusion personally, given that he was asking about a 1 in a quintillion chance of fusing. The discussion stayed on the physics pretty well, and didn't drift off into speculation. But yes, I can see how it's a bit of a gray area.

Well from recollection those Palladium electrodes tend to be a shade of grey, so yep, a grey area!

 

[questionpost]

Cold fusion is normal fusion, which can't happen at room temperature, unless perhaps super-power photons zapped the atoms which might take more energy than you would get out of it. The sun already works via quantum tunneling of hydrogen nuclei because the pressure of the sun forces them close together and the energy expands their orbital enough for their boundaries to overlap each others with the pressure.

 

[cmb]

How close do two room temperature deuterium nuclei need to be to each other to have a one-in-a-quintillion chance of "tunneling" into each other so that the nuclear forces bind them together despite the repulsive effect of the positively-charged protons?

As x_engineer mentioned, muons can provide a means by which fusible nucleii may fuse at room temperature. It is not so much 'how close' they need to be (or at least 'not only' that), but how long they need to be there.

If you were to get two deuterons both orbiting around a muon then, as far as I have read on muon-induced fusion, it is pretty much an inevitability after that that they will fuse. I believe the period of time for which you are 2 sigma likely to get a fusion between a triton and a deuteron in a muonic molecule is a fraction of a picosecond. So, so as long as it holds together for that long, you're most likely to get a fusion.

A collision between a deuteron and triton in an accelerator may well bring them closer together than in a muonic molecule, but they are at that distance for such a short infinitesimal time that the physics of the probability is very different.