Nuclear magic numbers based on a quarklike model is compared with the Boltzmann distribution model from nuclear abundance in the universe and low energy nuclear reactions.

A new threefold symmetry is presented for derivation of the magic numbers of nuclei and compared with the model based on the Boltzmann distribution from the standard abundance distribution of nuclei in the universe in the endothermic branch. This results in a 3n relation leading to the motivation to explore the quark state in nuclei. But, this is in contrast (duality) to the fact that the confinement of nuclei by a generalized Debye layer can be based only on a nucleon and not on a quark structure. This Debye model result led to a change of the Fermi energy of the nucleons into the relativistic range at higher than nuclear density resulting in a mass-independent state at higher than nuclear densities for the quark state in neutron stars. This result and the 3n-relation motivated consideration of the quark state in nuclei. Success is reported here by quarklike statistics for nuclei reproducing the magic numbers up to 126 identical with the Boltzmann model. But. for the next higher number, the Boltzmann model definitely arrives at 180 while the new quarklike model leads to the number 184. The paradox may be solved by the very accurate measurements of a local Maruhn-Greiner maximum from low energy nuclear reactions. [ABSTRACT FROM AUTHOR]