Subj:   cold fusion constraints

Here is a LATEX file of a brief note discussing the rates of palladium coulomb
excitation gamma rays expected from fusion processes producing fast charged
particles. The observation (or lack thereof) can be used to constrain proposed
cold fusion mechanisms. There is also a brief discussion of the well known radon
daughter gamma ray at 2.204~MeV which is consistent with the line Pons and
Fleischmann observe.
   Feel free to circulate this. Does anybody have any coherent written
reports on any of the reported confirmations? We are now using our MARK IV
version cell and haven't seen anything.
                                     David Bailey
                              (Physics Dept., University of Toronto)
 
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\begin{document}
 
\title{Gammas from Cold Nuclear Fusion}
 
\author{David C. Bailey\thanks{BITNET address: DBAILEY@UTORPHYS} \\
        Department of Physics \\
        University of Toronto \\
        Toronto, Ontario, M5S 1A7 Canada}
 
\date{April 20, 1989 \\
       University of Toronto Physics UTPT-89-15 \\
       Submitted to Phys. Rev. C}
 
\maketitle
 
\begin{abstract}
The absence of both neutrons and gamma rays can be used to constrain possible
cold fusion processes in deuterium-metal systems. In particular, milliwatt cold
fusion processes producing fast protons, tritium, helium-3 or helium-4 nuclei
would also usually produce easily observable numbers of Coulomb excitation
palladium gamma rays.
\end{abstract}
 
\vskip 0.6cm
 
Two groups have recently reported evidence of cold nuclear fusion of deuterons
electrolytically infused into metals \cite{PONS}, \cite{JONES}. One group
\cite{PONS} reports large amounts of fusion heat from a palladium-deuterium
cell but with only small amounts of associated radiation.
 
Any search for radiation from cold fusion should cover a wide range of gamma
energies. In addition to gammas from capture of neutrons from $d + d \rightarrow
n + He^3 + 3.27~MeV$ or $d + t \rightarrow n + He^4 + 17.6~MeV$ reactions, there
are possible direct gammas from $d + d \rightarrow He^4 + \gamma + 23.8~MeV$ or
$p + d \rightarrow He^3 +\gamma + 5.49~MeV$. Some exotic processes such as $p+d
\rightarrow He^3+e^+e^-+4.5~MeV$\cite{HOROWITZ} would produce an intense broad
spectrum of bremsstrahlung radiation and a sharp positron annihilation line at
0.511~MeV. Other processes involving only heavy charged particles would also
produce indirect gamma rays and neutrons.
 
For example, the reaction $d + d \rightarrow p + t + 4.03~MeV$ produces a proton
with an energy of 3.0~MeV. Some of these protons will produce gamma radiation
via interactions with palladium nuclei. Measurements of 2.9~MeV protons being
absorbed in thick palladium targets show that gamma ray yields from Coulomb
excitations of palladium nuclei and from proton bremsstrahlung are about
$10^{-7}$ gammas per proton \cite{COULOMB}. In particular, gamma rays are
expected at 0.3738, 0.4339, 0.5119 \footnote{This line is unfortunately very
close to the 0.511~MeV positron line normally observed in background
measurements.} and 0.5558~MeV \cite{ISOTAB} with yields of $1.32\times10^5$,
$2.29\times10^5$, $1.14\times10^5$ and $0.255\times10^5$ gamma rays per
microcoulomb of protons\cite{COULOMB}. These gamma lines are, respectively, the
lowest $2^+ \rightarrow 0^+$ transitions in $Pd^{110}$, $Pd^{108}$, $Pd^{106}$
and $Pd^{104}$. In terms of gamma rays per proton, the yields are
$2.1\times10^{-8}$, $3.7\times10^{-8}$, $1.8\times10^{-8}$ and
$0.41\times10^{-8}$ gamma rays per 2.9~MeV proton being absorbed in palladium.
The gamma yields increase with the proton energy\cite{COULREV}, so the yield
would be slightly higher for the 3.0~Mev protons from $d+d \rightarrow t+p$
fusion - the extrapolated yields are $2.5\times10^{-8}$, $4.5\times10^{-8}$,
$2.3\times10^{-8}$ and $0.52\times10^{-8}$ gamma rays per 3.0~MeV proton
absorbed in palladium. These yields are extrapolated from the data in
Ref.\cite{COULOMB} using the formulas of sections II~C.1, II~C.2 and III~B.2 of
Ref.\cite{COULREV}. (The accuracy of the measured 2.9~MeV proton gamma yields is
10 to 20\%.)
 
One watt of power from $d+d \rightarrow t+p$ fusion corresponds to
$1.55\times10^{12}$ fusions per second. The expected gamma yields from this
process for each of the above four Coulomb excitation lines are thus
$3.9\times10^4$, $6.9\times10^4$, $3.5\times10^4$ and $0.8\times10^4$ gammas per
second per watt of fusion power (i.e. gammas/joule). Hence typical gamma
detectors are easily sensitive to milliwatts of fusion power. Coulomb excitation
gammas due to protons produced by unexpected reactions such as $d+He^3
\rightarrow He^4+p+18.3~MeV$ would also be easily observed - the expected yields
would be $1.6\times10^6$, $3.2\times10^6$, $2.5\times10^6$ and $0.6\times10^6$
gammas/joule.
 
Another possible process of interest is $d + Li^6 \rightarrow He^4 + He^4 +
22.4~MeV$. This reaction does not produce any direct gammas or neutrons, but
indirect neutrons are expected from $He^4 + Pd$ interactions. The yield of
neutrons from interactions of 11~MeV $He^4$ nuclei being absorbed in palladium
is $4\times10^{-8}$ neutrons per incident $He^{++}$ \cite{ALPHAN}. Such a flux
is consistent with that reported by Fleischmann and Pons\cite{PONS}. If such
processes were occurring, however, the yield of palladium Coulomb excitation
gamma rays (from $He^4 + Pd$ collisions\footnote{Note that there are two $He^4$
per fusion.}) would be even larger than in the case for $d+d \rightarrow t+p$
fusion discussed above and very easily detected; the expected yields of the
0.3738, 0.4339, 0.5119 and 0.5558 palladium Coulomb excitation lines would be
$3.9\times10^5$, $8.3\times10^5$, $5.6\times10^5$ and $1.5\times10^5$
gammas/joule of fusion energy. The accuracy of the extrapolation of yields from
3~MeV protons to $\sim$10~MeV alpha particles was confirmed to $\sim$15\% using
$Cd^{114}$, $Te^{126}$, $Te^{128}$ and $Te^{130}$ data\cite{EXTEST}.
 
A third, more hypothetical, fusion process could be $d + d + Pd  \rightarrow
He^4 + Pd + 23.8~MeV$, where the palladium nucleus balances momentum for the
process. The $He^4$ nucleus would have an energy of 22.9~MeV if it recoils
against a single Pd nucleus, or 23.8~MeV if it is recoiling against the entire
palladium metal lattice. In either case, very large rates of Coulomb excitation
gamma rays should be observed. For 23.8~MeV $He^4$ production, the four Coulomb
excitation line yields would be $1.8\times10^6$, $4.3\times10^6$,
$3.2\times10^6$ and $0.9\times10^6$ gammas/joule.
 
One useful indirect fusion gamma line is produced by neutron capture on protons
producing a 2.224~MeV gamma ray. Observation of a gamma line at 2.2~MeV has been
used \cite{PONS} as evidence for neutron production by cold fusion. This method
is, however, subject to a well known strong background from the 2.204~MeV gamma
ray produced by $Bi^{214} \rightarrow Po^{214}$ decay. $Bi^{214}$ is a radon
daughter produced via $Rn^{222} \rightarrow Po^{218} \rightarrow Pb^{214}
\rightarrow Bi^{214}$. The 2.204~MeV gamma is produced in 5\% of all $Bi^{214}$
decays. Radon levels vary by large amounts depending on location and local
ventilation \cite{NERO}. The typical resolution of NaI(Tl) counters is such that
careful calibration is necessary to distinguish a $np$ capture line at 2.224~MeV
from a $Bi^{214}$ background line at 2.204~MeV. Using a single crystal coaxial
germanium detector the two lines can be readily distinguished. A 5.4\% germanium
detector at the University of Toronto typically detects the $Bi^{214}$ line at a
rate of $0.003s^{-1}$. This corresponds roughly to an expected count rate for a
typical 3 by 3~inch NaI(Tl) detector of about $0.06s^{-1}$, comparable to the
$0.1s^{-1}$ reported\cite{PONS} for a 2.2~MeV neutron capture line. Such a line
cannot be identified as a neutron capture line without very careful
consideration of the background from the ubiquitous 2.204~MeV line.\footnote{The
reported line is actually observed to peak at 2.204~MeV, not 2.224~MeV,
according the energy scale of Fig. 1A in Ref.\cite{PONS}.} A good test is to
monitor the other gamma lines produced by $Bi^{214}$ decays\cite{ISOTAB}; for
example, a line at 1.764~MeV should be observed with about 3 times the intensity
of the 2.204~MeV line.
 
It is very difficult not to produce detectable radiation for any known fusion
process, even those with only charged particles in the final state. If fusion
can occur without such radiations being detected, the energy is not being
transferred by the normally expected processes of scattering and absorption of
nuclear particles - the energy must be directly coupled to low energy
excitations of the metal-deuteride system in some unknown manner.
 
\vskip 0.2in
 
I would like to thank Steve Errede for many useful comments and for pointing out
that the reported\cite{PONS} 2.2~MeV gamma ray actually peaks at 2.204~MeV. I
would like to thank Richard Bailey, Dale Pitman and Jim Prentice for helpful
discussions. This work is supported in part by the Natural Sciences and
Engineering Research Council of Canada.
 
\vfill\eject
 
\begin{thebibliography}{99}
\bibitem{PONS} M. Fleischmann, S. Pons, and M. Hawkins, J. Electroanal. Chem.
261 (1989) 301, plus errata.
\bibitem{JONES} S.E. Jones, {$ et \> al.,$} submitted to Nature.
\bibitem{HOROWITZ} Charles J. Horowitz, submitted to Phys. Rev. C.
\bibitem{COULOMB} P.H. Stelson and F.K. McGowan Phys. Rev. 99 (1955) 112.
\bibitem{ISOTAB} Table of the Isotopes, 7th Edition, eds: C.M. Lederer
and V.S. Shirley, John Wiley (1978).
\bibitem{COULREV} K. Alder et al., Rev. Mod. Phys. 28 (1956) 432.
\bibitem{ALPHAN} P.H. Stelson and F.K. McGowan Phys. Rev. 133 (1964) B911.
\bibitem{EXTEST} P.H. Stelson and F.K. McGowan Phys. Rev. 110 (1958) 489.
\bibitem{NERO} Anthony Nero, Physics Today 42, No. 4 (April 1989) 32, and refere
   nces
therein.
\end{thebibliography}
\end{document}

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