Study on Polytopes and Nuclear Structure

Abstract

While the parameters   Z and   A indicate a general structural pattern for the atomic nuclei, the exact nuclear masses in their fine differences appear to vary somewhat randomly, seem not to exhibit the orderly kind of logical system that nature must exhibit. It is shown that separation energy [the mass of the nucleus before decay less the mass of a decay’s products], not mass defect [the sum of the nuclear protons and neutrons masses less the nuclear mass], is the “touchstone” of nuclear stability. When not part of an atomic nucleus the neutron decays into a proton and an electron indicating that it can be deemed a combination of those two.  Considering that, the nucleus can be analyzed as an assembly of A protons and N = A - Z electrons, where N of the protons form neutrons with the N electrons. Resulting analysis discloses a comprehensive orderly structure among the actual nuclear masses of all the nuclear types and isotopes.  The analysis examines in detail the conditions for nuclear stability / instability.  An interesting secondary component of that analysis and the resulting logical order is the family of geometric forms called polytopes, in particular the regular polyhedrons.