Historical research guide · 0433 · 2008
Enhancement of deuteron-fusion reactions in metals and experimental implications
A. Huke · K. Czerski · P. Heide · G. Ruprecht · N. Targosz · W. Żebrowski
In one minute
Armin Huke, Konrad Czerski and colleagues in Berlin, Szczecin and at TRIUMF fired slow deuterons into metal targets to measure the quantity the whole lattice-fusion story rests on: how much easier a metal makes it for two deuterons to reach each other. Electrons in a metal crowd around a nucleus and partly cancel its charge, so a colliding pair behaves as though it had been handed a small energy bonus — the screening energy. In gas targets that bonus is about a tenth of what these metals give. Here they measure 322 electronvolts in tantalum, 313 in palladium, 297 in zirconium, 190 in aluminium, and none at all in pure carbon films. Much of the paper is about how easy it is to fool yourself: deuterium migrates inside a hot target and oxide layers grow on its surface, and both change the counting rate without changing any cross-section, so the team built an analysis that watches the deuteron density live and rejects the runs where it drifts. Their numbers are floors, not ceilings.
Connection
Chapter 12 turns on one measurable quantity — how much a metal lattice lowers the effective barrier between two deuterons — and this is the careful, published number for it, several hundred electronvolts, with the systematic traps that inflate or deflate it named and controlled. It is also chapter 1’s evidence ladder in action: the authors show which runs count and why.
From the source
Electron screening energies for the deuteron-deuteron reaction inside metals, measured by the discontinuities in the reduced yield rather than by absolute yields, come out at 322 plus or minus 15 electronvolts in tantalum, 313 plus or minus 2 in palladium, 297 plus or minus 8 in zirconium and 190 plus or minus 15 in aluminium, while carbon films show no screening enhancement at all.Section IV A, Table I and Figure 7
Because unavoidable contamination layers can only diminish an inferred screening energy, the values reported here — the range 190 to 320 electronvolts — are lower limits on the real effect; the differential analysis behind them is independent of the imprecise stopping-power coefficients and of the absolute deuteron number density, and it monitors the density online so that runs with shifting depth profiles are recognized and rejected.Section III, end; Section VI, Conclusion
The enhancement is carried by the conduction electrons: screening energies measured in insulating materials are much smaller, under about 50 electronvolts, while the contributions from polarization of bound host electrons and from cohesion should be similar in both cases — so what a metal adds is its free-electron gas.Section IV B, discussion accompanying Figures 8 and 9
Subtracting the calculated cohesion contribution and the bound-electron part leaves a free-electron polarization screening energy that follows a smooth law — the product of the two nuclear charges times 250 plus or minus 20 electronvolts, divided by the square root of the electron-gas parameter — which can be used to estimate the free-electron contribution for other reacting nuclei in a metallic environment.Section IV B, parameterization of the free-electron polarization
The measurements select the degenerate-electron-gas picture over the classical plasma one: the Debye-Hückel description applies only above the Fermi temperature, typically around a hundred thousand kelvin and far above the evaporation temperature of a metal, so no temperature dependence of the screening energy should appear in this regime — and the follow-up radioactive-decay measurements the authors survey agree with that expectation.Section V; Section VI, Conclusion
The size of the effect is still open: the experimental screening energies exceed the self-consistent dielectric-function calculation by a factor of about two, which the authors state plainly as an unidentified contribution still to be found, and they name what would settle it — precise determination of the screening energies in an ultra-high vacuum system where the contamination-layer problem is removed.Section IV B, comparison with theory; Section VI, Conclusion
The way in
https://doi.org/10.1103/physrevc.78.015803How to cite it
A. Huke, K. Czerski, P. Heide, G. Ruprecht, N. Targosz, W. Żebrowski (2008) Enhancement of deuteron-fusion reactions in metals and experimental implications doi:10.1103/physrevc.78.015803