Enhancement of deuteron-fusion reactions in metals and experimental implications

Recent measurements of the reaction ${}^2\mathrm{H}$$(d,p)$${}^3\mathrm{H}$ in metallic environments at very low energies performed by different experimental groups point to an enhanced electron screening effect. However, the resulting screening energies differ strongly for diverse host metals and different experiments. Here, we present new experimental results and investigations of interfering processes in the irradiated targets. These measurements inside metals set special challenges and pitfalls that make them and the data analysis particularly error prone. There are multiparameter collateral effects that are crucial for the correct interpretation of the observed experimental yields. They mainly originate from target surface contaminations owing to residual gases in the vacuum as well as from inhomogeneities and instabilities in the deuteron density distribution in the targets. To address these problems an improved differential analysis method beyond the standard procedures has been implemented. Profound scrutiny of the other experiments demonstrates that the observed unusual changes in the reaction yields are mainly due to deuteron density dynamics simulating the alleged screening energy values. The experimental results are compared with different theoretical models of the electron screening in metals. The Debye-Hückel model that has been previously proposed to explain the influence of the electron screening on both nuclear reactions and radioactive decays can be clearly excluded.

Figure 1

Experimental setup.

Figure 2

Analysis procedure at the example of zirconium at $10\hspace{0.5em}\mathrm{keV}.$

Figure 3

Exemplary results for the enhancement factor $F_{\mathrm{norm}}$ showing screening enhancement for Zr theoretically described by the curve with the single parameter $U_e$.

Figure 4

Scanning electron microscopic pictures of target surfaces. Left: Symptoms of embrittlement for Al. Right: Beginning layer formation for Ta in island growth mode.

Figure 5

Effects of different surface compositions on the inferred screening energy for Ta. Ta-A has a small C excess, Ta-E has slight C traces, Ta-C has a thick C layer, and Ta-D has a thick MO${}_x$ layer.

Figure 6

Development of deuteron densities depicting counter examples to the screening enhancement as in Fig. 2. (a) A medium thick layer obliterates the screening enhancement discontinuities at high densities, here at the example of an oxide layer on Ta. The full line shows the progression from a refinement of the statistics by recalculation with an increased step size. For targets featuring low hydrogen binding ability (hence allowing only for low and unstable densities with quick profile shifts), shown are (b) a density plot of a thick metal oxide layer overtopping the ion range on a metallic Na disk and (c) an example of how heating vanquishes the hydrogen metal bond for a beam heating a 7-$\mu \mathrm{m}$ Ta foil.

Figure 7

Measured values of $F_{\mathrm{norm}}$ for Pd and carbon in two different compositions

Figure 8

Comparison between experimental and theoretical screening energies.

Figure 9

Experimental and theoretical polarization screening energies vs the electron gas parameter $r_S$. For comparison the Thomas-Fermi screening of the electron gas is presented.

Figure 10

Screening energy dependence on the projectile energy. The Debye screening is applicable only for deuteron energies larger than the Fermi energy ($56\hspace{0.5em}\mathrm{keV}$ for Ta) or equivalently for plasma temperature larger than the Fermi temperature ($1.8\times {10}^5\hspace{0.5em}\mathrm{K}$ for Ta).

Figure 11

Overview of screening experiment results. Top: Deuterium to metal ratio $x$. The values for $x$ of Ref. 10 were estimated from Fig. 2 therein. The values of Ref. 14 are the data base; data points from Refs. [12, 13] are included only if they differ. Bottom: Screening energies $U_e$. Legend: Garching 1990 [43]; Tohoku 1998 [9], 2002 [10]; Bochum 2002 [12], 2003 [13], 2004 [14].

Figure 12

Scatter plots of (top) $U_e\leftrightarrow n_{\mathrm{eff}}$ with $n_{\mathrm{eff}}$ from the Hall coefficient $C_{\mathrm{Hall}}$ and (bottom) $U_e\leftrightarrow x$ with $x$ being the deuterium contents in the compound MD${}_x$. The star denotes temperature-dependent points for Ti.