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 probabilitiesN(Z) depending on the atomic numberZ show maxima close to the magic numbers with the exception ofZ=20. The exponential decay of the maxima onZ have an incrementZ′=10. Exactly this empirically derived relation fits a sequence of the magic numbers of 3 ⁿ , where the basis value 3 reminds of the threefold scheme of the quarks. Dedicated to Prof. Dr. D. Sc. Drs. h.c. Arthur Sharmann to his 70th birthday, 26 January 1998.