Abstract. -To study the electron screening of nuclear reactions in metallic environments, angular distributions and thick target yields of the fusion reactions 2 H(d,p) 3 H and 2 H(d,n) 3 He have been measured on deuterons implanted in three different metal targets (Al, Zr and Ta) for beam energies ranging from 5 to 60 keV. The experimentally determined values of the screening energy are about one order of magnitude larger than the value achieved in a gas target experiment and significantly larger than the theoretical predictions. A clear target material dependence of the screening energy has been established.Introduction. -At sufficiently low projectile energies an enhancement of the cross-section for charged-particle-induced nuclear reactions can be observed. This is due to the shielding of the charges of reacting nuclei by surrounding electrons which leads to an increase of the Coulomb barrier penetrability and enhances the measured cross-section in comparison to the bare nuclei case. This effect, known as electron screening, was originally discussed for the dense plasma in the interior of stars [1], where, due to screening, the nuclear-reaction rates can be increased by many orders of magnitude. For laboratory thermonuclear reactions, the screening effect was predicted [2] and experimentally verified for several light nuclear systems [3].In the simplest picture, the enhancement of the cross-section results from the gain of electronic binding energy (called screening energy U e ) which can be transferred to the relative motion of the colliding nuclei. In an adiabatic limit, i.e. with velocities v nuclear v electron , this energy shift can be treated as constant. Consequently, the enhancement factor f defined as the ratio between the cross-sections for screened and bare nuclei can be calculated as follows [2]:

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The study of the 2 H(d, p) 3 H reaction at very low energies in deuterized metallic targets provides a unique possibility to test models of the electron screening developed for dense astrophysical plasmas. Here, we compare the experimental screening energies obtained by our group as well as by other authors for different target materials with theoretical predictions based on an improved dielectric function theory. The calculations are performed within the self-consistent regime and include polarization of both quasifree and bound electrons. Additionally, the cohesion screening, arising from different binding energies of deuterons and α-particles in crystal lattices, is taken into account. The proposed theory predicts only a weak material dependence of the screening energy in agreement with our experimental results but fails in the absolute strength of the effect by a factor of 2. The projectile-velocity dependence of the screening energy corresponding to the transition from the weak-screening regime to the strong-screening limit is discussed.

Abstract. -Based on our experimental studies of the electron screening effect in the 2 H(d, p) 3 H reaction for five deuteron-implanted solid targets (C, Al, Zr, Pd, Ta), theoretical calculations have been performed within an improved dielectric function theory. The theory describes correctly the observed target material dependence of the screening energies, underestimating, however, the absolute values by about a factor of 2. Applying an effective screening energy approach, the theoretical cross-sections, thick-target yields as well as nuclear reaction rates have been calculated down to the energies corresponding to the conditions of so-called cold-fusion experiments. This allows for a comparison of the experimental results at higher energies with those achieved in the heavy-water electrolysis experiments.Introduction. -Nuclear reaction rates at very low projectile energies, far below the Coulomb barrier, are sensitive to the electronic properties of target materials. The electrons surrounding the reacting nuclei can increase the tunneling probability through the Coulomb barrier leading to an enhancement of nuclear reaction rates at low projectile energies. The electron screening effect was originally discussed due to its importance for dense astrophysical plasmas, where nuclear reaction rates can be increased by many orders of magnitudes [1]. Experimentally, the screening effect could be verified only fifteen years ago in gas target experiments [2] by an observation of an exponential-like increase of the measured cross-section for decreasing projectile energies compared to the cross-section expected for bare nuclei. Theoretically, this effect was described [3] by applying a conception of the electron screening energy resulting from the gain in the electron binding energy between the initially separated atoms and the finally united atom. In the experiments, the screening energy could be treated as an energy shift of the kinetic energy of the reacting nuclei causing an increase of the penetration probability through the Coulomb barrier.

Observation of the enhanced electron screening in metallic environments is of fundamental importance for the understanding of strongly coupled astrophysical plasmas. Experimental screening energies determined by different groups for many metals are much larger than the theoretical predictions. However, a comparison between experimental and theoretical data is rather ambiguous because of the contributions of systematic errors in the experiments. One of the most important problems is the uncertainty resulting from the oxidation of the target surface during the measurements. Here, we present results of the first ultra-high vacuum (UHV) experiments studying d+d nuclear reactions in a deuterized Zr target for which the experimental discrepancies are especially large. The total cross sections and angular distributions of the 2 H(d,p) 3 H and 2 H(d,n) 3 He reactions have been measured using a deuteron beam of energies between 8 and 30 keV provided by an electron cyclotron resonance ion source with excellent long-term stability. The cleanness of the target surface has been assured by combining Ar sputtering of the target and Auger spectroscopy. In an on-line analysis method, the homogeneity of the implanted deuteron densities could be monitored also. The resulting screening energy for Zr confirms the large value obtained in a previous experiment under poorer vacuum conditions.