Newsgroups: sci.physics.fusion
Subject: <None>
From: jonesse@physc1.byu.edu
Date: 21 Jan 93 15:30:46 -0700
Distribution: world
Organization: Brigham Young University



Dieter Britz and Jim Carr have recently asked for clarifications on my
comments regarding distinctions between "cold" and "hot" fusion (see
"Quick Replies" by me and "Re:  Quick Replies" by Dieter and Jim).
I think I have time this p.m. to hammer out a response with apologies for
the delay.

It will be helpful to juxtapose potential energy curves vs. separation for
the deuteron (d) plasma (hot fusion) case and the muonic molecular d-d-mu
(cold fusion) case.  What is now called "cold fusion" MAY be similar to
one of these, but I really don't know if recent experimental results fit
into either category.  But plasma fusion and muon-catalyzed fusion are real
and the distinctions are instructive to scrutinize.  Warning:  the plots
are not to scale.

         POTENTIAL ENERGY:  PLASMA D-D FUSION
|
|  =
|  =+
|  = +
|  =  +
|  =   +
|  =    +
|  =     +
|  =      +
|  =  T1<-- +    E= 4 keV
|  =          +
|  =             +
|  =                    +       _     _
|+0---------------------------------      d-d separation (r)
|  =
|  =
|  =
|  =
|  =
|  =
|  =
|  =
|  =
|  =
|  =
  \ Strong nuclear reactions take over at few fermi separation-->fusion 

                  POTENTIAL ENERGY VS R FOR MUONIC DD MOLECULE (BOUND)
|  =
|  =+
|  = +
|  =
|  =  +
|  =
|  =   +
|  =
|  =    +
|  =
|  =     +
+0------------------------------------------_------------ d-d separation (r)
|  =      +               +      +
|  =  T2 <-- +         + <-- binding energy of ground d-d-mu state = 325 eV
|  =             +      <-- depth of Born-Oppenheimer potential = 557 eV
|  =
|  =
|  =
|  =
|  =
|  =
|  =
|  =
  \Fusion at r = few fermi

My picture may be semi-classical, but I assert that we can learn
much about cold vs hot fusion from the plots.  Tunnelling through the Coulomb
potential barrier is important for both bound and plasma cases:  note that
even for hot fusion, very few collisions are of sufficiently high energy to
surmount the barrier, for plasmas at say 10E7 kelvin.

The binding of the nuclei by muons clearly changes the WIDTH of the potential
well, as well as permitting frequent collisions of the deuterons so bound.
Excuse, Jim, the "classical" picture, but the fact is that the vibrational
frequency of a molecule is a relevant and observable quantity.  I do not
understand the vigorousness of your objection.  We can calculate the tunnelling
integral and multiply by the vibrational frequency of the molecule to determine
the d-d fusion rate, in a semi-classical approach.  Or, we can follow the
"pure" quantum-mechanical route of calculating the complex wavefunction over
ALL space, then calculate the probability of fusion.  I spoke
to Jim Cohen of Los Alamos this morning who has gone through the latter
approach (the more difficult method), and he said that the difference in
calculated rates is only about 20%.  He and I both defend the semi-classical
approach as useful calculationally as well as pedagogically.  Jim Carr is
correct that Clint Van Siclen and I used a semi-classical approach in 1985
in our paper on "Piezonuclear fusion in isotopic hydrogen molecules" (J.
Physics G12:213-220 pub'd 1986) as did David Jackson in his classic 1957 paper,
and Steve Koonin in his follow-up to the Van Siclen/Jones paper.

Cohen went further:  he contrasts the fusion rates in D2+ (bound by electrons,
a la Van Siclen and Jones 1986 paper) with that of (d-d-mu)+.  The
rate for the muonic molecule is faster for two reasons:
1-Shorter internuclear distance (see plot above:  binding decreases the
   d-d separation by the electron/muon mass ratio = 207, from about 1 angstrom
   to about 4X10-3 angstroms)
2-Increased vibrational frequency in the muonic molecular ion  - this 
    increases the fusion rate by a factor of about 3000, Cohen calculates.
    Clearly, the vibrational frequency in the BOUND molecule is important.

Note that in the plot for plasma fusion above, the nuclei are unbound.  This
is an important distinction WRT the bound or "cold" fusion case.  In the 
D2 molecule (neutral), the equilibrium separation distance R is about 0.74
angstroms.  When a d-d-mu molecular ion forms (we tire of saying this always
and often just say muonic molecule), the internuclear distance shrinks to
about 4X10E-3 angstroms.  In the ground state of d-d-mu, the zero-point energy
is (557-325) = 232 eV.  Screening of the coulombic repulsion by the negative
muon causes the WIDTH of the barrier to decrease.  This is important since
the tunnelling probability varies roughly as 
      EXP[- barrier height X (width)E2].
This holds for a square barrier; for the Coulombic barrier, we see that
decreasing the width increases the tunnelling rate more than would decreasing
the barrier height.    
   
Without the effects of screening, that is for bare, unbound nuclei, a 
center-of-mass energy of about 4000 eV would be required to allow the nuclei
to approach to 4X10-3 angstroms.  This energy is reached in plasmas of approx.
4 X 10E7 kelvin, which is achieved in "hot" fusion devices like TFTR.  Thus,
binding of the nuclei allows "cold" fusion to proceed rapidly without the
need for high temperatures.  BOTH proceed primarily by tunnelling through the
Coulomb barrier.  Thus, on the plots above I show T1 for tunnelling in the
hot fusion case occuring at an energy of 5 keV, while tunnelling T2 in the
cold fusion case occurs at a much lower energy.

  Therefore, I object to statements such as this which appear
commonly in physics texts:  
"To obtain energy from fusion, the particles must be heated to a temperature
great enough for the fusion reaction to occur as the result of random thermal
collisions."  (Tipler, p. 1353, "Physics for scientists and engineers", 1991.)

Note the distinction between random thermal collisions and collisions of
nuclei bound in a molecule.

I have endeavored to clarify the distinction between "hot" and "cold" fusion.
Other short discussions of the same subject are found in:
1. L. Ponomarev, "Muon cataysed fusion," Contemporary Physics, 1990, 31:219-245;
2. J. S. Cohen and J. D. Davies, "The cold fusion family," Nature 338:705-707,
     27 April 1989 (same issue as the original BYU experimental paper, in which
     we say:
  "When a current is passed through palladium or titanium
electrodes immersed in an electrolyte of deuterated water and various metal
salts, a small but significant flux of neutrons is detected.  Fusion of 
deuterons within the metal lattice MAY BE THE EXPLANATION."  (Emphasis added.)

The principal idea behind the 1986 paper (replying to Dieter) was that for
fusion in bound electronic molecules, the fusion rate might be increased by
distortion  of the molecular potential by subjecting the molecules to extreme
pressures.  I had the idea of considering the possible of piezonuclear fusion
inside Jupiter (which we then included in the Van Siclen/Jones paper pub'd 
1986).  BYU Prof. Paul Palmer extended the idea to possible fusion
inside the earth when I discussed the piezonuclear (or electron-catalyzed)
fusion idea at BYU colloquium on March 12, 1986.  Our lab experiments began
at BYU based on these ideas in May 1986, and have continued to this date.
We began with electrolysis in D2O in May 1986 and added D2 gas pressure loading
in June 1986.  We have experimented with diamond-anvil cells holding deuterided
metals Pd and Ti as well as LiH and LiD, but only at approx. 150 kbar.  The
diamond-anvil cell holding LiH and LiD reached 1.8 mbar but then the diamonds
cracked.  We have not yet studied metallic hydrogen isotopes, but I am anxious
to try this difficult experimental program.  Note that these concepts,
including the use of diamond-anvil cells and metallic hydrogen and fusion in
the planets, are all outlined in the original Van Siclen/Jones paper which we
wrote by June 1985, long before any of us heard of Pons/Fleischmann.  Our work
with electrolysis began in May 1986 (with nominal funding from DOE in fact).
Our research, therefore, should not be confused with P/F -- PLEASE.

Thanks, Dieter, for finally including the Van Siclen / Jones paper in your
list of early works related to cold fusion.  But let's not associate this
with Pons and Fleischmann.  Can't we all see the difference?  We
understand the difference between hot and cold fusion, now, hopefully.  And
the distinction between muon- and electron- catalyzed fusion seems transparent.
No one sees enough neutrons OR helium OR gammas OR tritium (I could go on to
include any products of nuclear reactions) to justifiably associate claimed
xs heat with nuclear reactions.  So why throw the BYU work in with P/F claims?
   PLEASE HELP STOP THIS NONSENSE.
The distinction is clear in Huizenga's book and Frank Close's, but uncritically
muddled in Mallove's (which I profoundly resent).  It seems that believers in
the unfounded notion that xs heat as claimed by P/F is nuclear  USE the
low-level nuclear findings of the BYU group and others to support their claims.
To me, this is grossly unfair and fallacious.  I will continue to fight such
nonsense.

Respectfully,
Steven E. Jones