Nuclear and Atomic Physics


Polytopes and Nuclear Structure

Authors: Roger Ellman

While the parameters, Z and A, of atomic nuclei indicate a general structural pattern for the nuclei, the exact nuclear masses in their fine differences seem not to exhibit the orderly kind of logical system that nature must exhibit. At first consideration atomic nuclei are considered as an assembly of Z protons and N = A - Z neutrons. That description is not to say that such an assembling action actually occurs as such. Rather, the assembly point of view is a procedure for determining what the characteristics of the resulting nucleus must be: it must have a mass defect relative to the sum of the masses of those components in an amount equal to that which is required by the theoretical scenario of so assembling the nucleus. Unlike the case of the neutron as a combination of a single proton and electron [see "A New Look at the Neutron and the Lamb Shift"2], the components of an atomic nucleus cannot come together to form the nucleus naturally and unaided because of the mutual electrostatic repulsion of the protons and the electric neutrality of the neutrons. That is, to assemble the particles as in a nucleus and make them stay so assembled requires removing from them the potential energy that they would have when assembled were it not somehow removed. Analysis discloses a comprehensive orderly structure among the nuclear masses of all the nuclear types and isotopes. A component of that analysis and logical order is the family of geometric forms called polytopes, in particular the regular polyhedrons.

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Submission history

[v1] 25 Feb 2007

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