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The similarity of the abundance of heavy nuclei in the Universe with that of the nuclei produced in the fully reproducible reactions of protons in host metals like palladium, nickel or others is evident and can be described by the same exponential function of the distribution probability N(Z) depending on the proton number Z of the nuclides. This agrees with the earlier derived consequence of a 3n relation for magic numbers and an alternative foundation of the nuclear shell model. Compared to femtometer-attosecond reactions in the big bang, the low energy nuclear reactions in the host metals have picometer distances and megasecond duration. For this picometer distance, a combination of the swimming electron layer and Debye screening model with a metal-plasma dielectric model is presented.