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%     ``SOLID-STATE'' EFFECTS CANNOT ENHANCE THE COLD FUSION RATE ENOUGH
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%              J. Leggett and G. Baym (Urbana, Illinois)
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\c{\bf{``SOLID-STATE'' EFFECTS CANNOT ENHANCE THE COLD FUSION RATE ENOUGH}}
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\c{A. J. Leggett and G. Baym}
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\c{\it{Department of Physics, University of Illinois at Urbana-Champaign}}
\c{\it 1110 W. Green St., Urbana, Illinois 61801}
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    Most proposed mechanisms to explain the claimed cold fusion rates in
deuterium-soaked palladium and titanium must assume the probability of
overlap of two deuterons at the origin to be of order $10^{-7}$/cm$^3$.  We
derive an exact quantum-mechanical inequality for tunneling probabilities in
many-body systems in equilibrium which shows that for any reasonable deuteron
pair correlation function the {\bf upper limit on this probability is 7
orders of magnitude lower.}

    The argument proceeds in two steps:  first, writing the tunneling rate
from radius $r_0$ as usual as $e^{-B}$, we demonstrate, by judicious choice
of variational wavefunctions for the exact many-body ground state, the
inequality:  $$B(\mu,r_0)\ge{1\over2}B_0(2\mu,r_0),$$ where $\mu$ is
the reduced mass of the tunneling nuclei, and $B_0$ is the rate that would be
calculated in the lowest Born-Oppenheimer approximation for tunneling from any
radius $r_0$ in the classically inaccessible region of that approximation.
Second we combine this result with the inequality derived for $B_0$ in our
earlier paper,$^1$ based on information provided by the behavior of He in
solids, to show that for two isolated deuterons in Pd or Ti an upper limit on
the probability density at the origin at zero temperature is $\sim
10^{-14}$/cm$^3$.

    To attain the necessary $\sim 10^{7}$ enhancement at room temperature
would require unprecedented long range thermal effects of distant particles on
the tunneling process.  Similarly to attain the necessary enhancement by means
of collective processes among the deuterons, would require a totally
unphysical value of the deuteron pair correlation, $\sim 10^{7}$, at atomic
separations.

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1. A. J. Leggett and G. Baym, Nature (in press).
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