Magic numbers and low energy nuclear transmutation by protons in host metals

The observed nuclear transmutations by protons or deuterons in host metals at low reaction energies are evaluated. Reaction probabilities N(Z) depending on the atomic number Z show maxima close to the magic numbers with the exception of Z = 20. The exponential decay of the maxima on Z have an increment Z' = 10. Exactly this empirically derived relation fits a sequence of the magic numbers of 3n , where the basis value 3 reminds of the threefold scheme of the quarks. (author)