Study of the fusion reactions between hydrogen isotopes in muonic molecules is the first example of the accurate accounting of the nucleus charge screening by a muon in the fusion process. At LUNA installation the measurements of astrophysical reaction cross sections were extended down to collision energies of a few keV. The screening by atomic electrons of the target became substantial. The possibility to look over screening from unbound electrons is given by metal-hydrides used as targets in dd reaction measurements. The classical Debye screening in plasma, applied to quasi-free electrons in metal, provides an explanation of unexpectedly large screening potentials found for some metals in the research through the Periodic table of elements. 1 Electron and muon screening of fusion reactions Fusion reaction cross sections decrease exponentially with decreasing of collision energy. It is convenient to isolate this dependency and characterize the reaction with the astrophysical function S(E) rather than with the reaction cross section σ(E): S(E) = Eσ(E)exp(2πη), (1
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