[ExI] [ACT] cold fusion

Tue May 8 03:20:50 UTC 2007

----- Forwarded message from "Perry E. Metzger" <perry at piermont.com> -----

From: "Perry E. Metzger" <perry at piermont.com>
Date: Mon, 07 May 2007 15:45:24 -0400
To: act at crackmuppet.org
Subject: [ACT] cold fusion

[People should feel free to forward this if they like.]

Some people got a brand new "cold fusion in Palladium" paper published
in the last couple of weeks, and it has made several news sources,
including the Kurzweil blog.

See, for example:
  http://www.dailytech.com/article.aspx?newsid=7168

A friend asked me what I thought, so I did a quick Fermi estimate.

The answer is, I have a lot of trouble believing it. See below for
detailed calculations.

The general hypothesis given is that, if the phenomenon is real, what
is happening in such cases is that the deuterons are close enough
together to tunnel over the coulomb barrier into each other -- it
would have to be that because the number of deuterons with enough
thermal energy to fuse with another is essentially zero.

So, what sort of tunneling probabilities are we talking about?

I don't now enough to do the calculation "right", but, as I said, lets
do a "Fermi estimate". Lets consider the coulombic repulsion of two
protons held 5fm apart. A helium nucleus is order 1fm.

An elementary charge is 1.6E-19 coulombs. The potential energy between
two particles of that charge is

U = \frac{e^2}{4\pi\epsilon_0 r}

So we're talking (1.6E-19 ^ 2) / (4 * 3.14159 * 8.854E-12 * 5E-15)

Plug that in to calc and I get about 4.60E-14 Joules.

That doesn't seem like a lot, but an electron-volt is just 1.60E-19
Joules -- so that's a barrier of 287,500 eV, which is pretty high for
wee particles like this, and we're still probably several times too far
away.

Unfortunately, at this point I have a bit of a problem because the
textbook solutions for tunneling through a potential well assume that
we're talking about a square well (a step function) and the potential
function here is not really like that. However, I've gone this far
with the back-of-the-envelope, so lets go all the way. I doubt I'm
*that* far off.

The distance between nucleii in typical bonds is not less than about
an angstrom, 1E-10m. I presume the way that Pd solvation would
catalyze fusion would be by getting the deuterons closer together. So,
lets do the calculation for .1 angstroms -- impossibly close given the
energies that would require.

We also need to estimate the thermal energy of the deuterons. Normally
we'd say at room temperature (where these things are being run) that
it would be about 3kT/2 with T=300K and k=1.38E-23J/K  or so, but
we'll double it just to be kind and say 3kT for a value of about
1.25E-20J. Given the height of the barrier this isn't going to make
much of a difference anyway, even if I multiplied it by ten.

The mass is about 3.32e-27kg. I'll assume that the potential energy
barrier is pretty "smooth" and pick a value for the square well
barrier of 2.3E-14J -- an "average" of zero and something order of
magnitude of the maximum.

I'll follow the formula in one of my texts that says that the
probability of getting through is very roughly:

  prob = e^[-(2a/hbar)*sqrt(2m(U-E))]

where "a" is the distance, U is the potential of the barrier and E is
the kinetic energy of the particle attempting to tunnel.

At .1 angstrom, the probability of tunneling across the square
potential is somewhere in the range of 1 in 7.8E1021 events. Already
we can see this isn't pretty.

Now, how many "events" can we expect? Lets say we have a mole of
deuterons (6.023E23) and that we have (probably far more than we can
realistically expect, based on usual vibrational spectra, but it won't
matter even if we're off by thousands) somewhere around around 1E10
collisions a second. Lets consider the events over 1 hour.

6.023E23*1E10*3600 is about 2.2E37. Divide.

That means we can expect to wait something like 3.5E986 hours between
seeing fusion events -- something like 3.9E970 times the life of the
universe.

I might be off by ten or twenty orders of magnitude. Who cares, though?
This mechanism doesn't look like a realistic possibility.

Perry
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